Control Systems Engineering Masterclass | Tahir Yaqub | Skillshare

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Control Systems Engineering Masterclass

teacher avatar Tahir Yaqub, I Teach Online

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Taught by industry leaders & working professionals
Topics include illustration, design, photography, and more

Watch this class and thousands more

Get unlimited access to every class
Taught by industry leaders & working professionals
Topics include illustration, design, photography, and more

Lessons in This Class

10 Lessons (2h 29m)
    • 1. Introduction to the Course

    • 2. Open Loop and Close Loop Control System Examples

    • 3. What are Linear Systems

    • 4. Finding Transfer Function of a Mass, Spring, Damper System

    • 5. Converting Differential Equations into State Space Equations

    • 6. Time Constants of RL Circuit and RC Circuit For Skillshare Class

    • 7. Nyquist Stability Criterion Without Mathematics

    • 8. How to find Transfer Function of a DC Servo Motor

    • 9. Heaviside Method and Cover up Method

    • 10. Forced and Natural Response of a System for Step Input

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About This Class

This is a growing masterclass of control systems engineering. My intention is to cover all the topics of control systems engineering. I will be adding lectures as soon as I get time to prepare them. Although I have mentioned the topics in the first video of this course which I will cover at the minimum. However, my plan is to make this a masterclass of advanced control systems. Some of the lecture topics are listed below:

1. Open Loop and Close Loop Control Systems

2. Transfer Function Modelling

3. Block Diagram Reduction

4. Time Response of First Order Control Systems

5. Time Response of Second order Control Systems

6. Root locus method of Stability and Transient Response Analysis

7. Routh Hurwitz Criteria

8. Frequency Domain Analysis

9. Bode Plot

10. State Space Modelling

Meet Your Teacher

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Tahir Yaqub

I Teach Online


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1. Introduction to the Course: Hello and welcome for someone who don't know me. I'm not. I have PTSD in robotics for amnesty of new software is Australia. This is a collection of my lectures on control systems Engineering. I have recorded these lectures with a video course in mind. These are not in a colossal settings. I use various former toe record these lectures. Some are talking heads. Some are just skin captures control system engineering has many applications in mechatronics engineering, electrical and mechanical engineering, in robotics and in other fields of science. The topics which I have covered in the scores they fall under various subject names such as linear control systems, feedback control systems, classical control system are simple control systems engineering. In this introductory video, I would like to answer the most important questions about this course. The first is whether the scores covers all the important topics in control systems engineering. And the answer is probably not. I know you tried to cover all the important topics in this course, but there could be a topic which is very important for you and missing in this course. So why don't you watch that as this course get season and students and rule in this course , I might get some feedback and we'll include some more videos in this course. I wish many subjects, but the subject, which I love the most, is controlled systems engineering. Because I did my PhD in this subject will and I'm very passionate about this. So I would like to engage with my students, get your feedback and improve my course. So I would encourage you to look at the titles of the lectures and see whether the topic which your industry din has been included in the course are not before and rolling in the course. The second important question I would like to answer in this video is that are there any prerequisites for this course? And the answer is yes, there are. These are the six subject areas which you should know about before and rolling. In this course, you must have some knowledge of these areas. These include differential equations left last transform, partial fractions, your course laws, high school algebra and mattresses. So we're developing this course. I realized that three of these topics are not very common in many subjects. So therefore I decided to add a 30 minute video about left last transform. That will be a refresh course for you and also a 15 to 20 minutes we do about partial fractions. And I'm also thinking toe act another. We do about differential equations. But if you don't know anything about high school algebra, armor theses are simple laws of physics. Then I am afraid that I will not be able to cover all those topics in the score. So you might get some course on those topics and then you enrolled in this course. So these were the two important points about this course and no, I would encourage you. So look at two important things before enrolling in this course. Number one is look at the titles of the lectures. So on all my villages, I have tried to put a very explain notary type of title so that you could see what is inside that video. And the second thing is there are some free preview reduced available in this course. Watch those videos and see if you are happy with my eating style before enrolling in this course, because your money and your time is also valuable. So it is important that you look at these two things before enrolling in this course. So I hope that this is a short video will enable you toe make a decision. Whether this course is suitable for you are not Thanks for your time and I will see you insert the course. 2. Open Loop and Close Loop Control System Examples: in this lesson, we will learn some very basic concepts of control systems, and we will see some simple examples. A control system has an input and an output, and there are few systems which are considered as open loop systems. And there are more systems which are closed loop control systems because open loop control system have some limitations. So there were most of the control systems that closed loop control system. So we will see what is an open loop control system and what is a closed loop control system . And then we'll see a few examples. So let's talk about system. So let us say that this is a black books. You don't know what is inside, but whenever you give our input to this black box, it gives you an output. So, for example, if you put any value is input X one, this give you a value? Why one as a doubt put. So if you give another 1,000,000 next to it gives you a different value, Why two and out? So it means we can say that I m whenever we put actually get why. So there is the relationship between input and output And if this relationship is linear, then we will say that this is a linear system. So it could be a function. So, for example, as Mr Y is a function effects means that whenever a report x we get why why is dependent on X axis Independent, variable and wiser Ah, dependent variable. So if we say that this a Linnean system so Linnean system, we will discuss a linear it in detail later. What are the conditions of lady? And we will look into this. But at the moment you can assume that linear system is the most simple system. So in visual input and output have a proportional relationship for a direct relationship. So for example, we can say that why it was X. So what it would mean is that whenever we give X as an input, we will get why as, ah, some multiple of X. So no open loop control systems. Open looking toe systems are the simplest mental systems in which we want toe control any variable and we give a command to the controller controller, try their best to manipulate the system to get their desire, dessert and these type of systems can it handle the disturbances? So, for example, toaster is an example in which our desired output is a certain bread color. So this we want a sort of bread color, and what we set it on controller is we set a timer. So this is a were commanded input that reset the timer and based on our experience that we expect that after this much time, the bread color will be whatever we want. But because of the different factors, For example, if the bread is changed or if the room temperature is took order heart so the bread color might not be 100% same as our desire color. So because the system is not measuring anything at output, we're not making the color of the bread. We're not taking into consideration. What is the output? Another example could be a microbe again. The same. You set a timer to get a certain hate level in your meal, but after their time, you might notice that sometimes the mill template it is not the desired want because there is no monument of the temperature of the mid actual temperature of the meat. So we're not making anything. It out. So this is the reason why these systems cannot handle any of the disturbances any of the unexpected things. For example, in turn example, which is a show over which was very common example, you try to get a certain water temperature which is comfortable, and this comfortable water temperatures also has a certain range. You cannot even detect the weather. It's exactly 37 degree are it's 40 degree or whatever. But even then, what you do is in order to get their temperature, you put the horn and court ball at a certain position and that position is based on your own experience that okay, if I pull this world in this position, I will get a temperature in this range. But after some time, do you do the disturbed mint? What is the disturbance? Disturbance could be the water level in your visa if the water level drops if something happens. So the water tried toe gift from towards the hotel quarter site. So this is what happens in this type of system because you are not measuring entity. So these type of systems are very poor in handling disturbances. But for some application, you don't need a very expensive feedback control system like these everyday applications and open loop control systems work perfectly. A is a neighbor, so these systems are the basic systems and no, we will discuss the closed loop control systems. Know the closed loop control systems control. Most of the control systems are closed Loop because these are robust systems and these are insensitive to disturbances. They can handle the disturbances very red. So in this type of systems, we give the command and we expect that the whole sister will follow the command so that our control output should be as the commanded input. So and this is guess what happens is that re actually measured output. So if, for example, we want toe setter temperature toe 30 C, so we actually, whatever the controller tried to manipulate the plant in the system and then we get an output and we actually many of this output and whatever is the output. For example, the output could be 28 degrees and ticket and then we feedback these output again in the input of the controller and here the others is dilated. And this enter the difference between these two the commanded input and output. We feel this error into the controller. So based on this error signal no controller, Try toe, manipulate the plant once again, so there to achieve the desired result. So this is an example Very simple example. So in this example, what is happening is there is ah ah ah heat exchanger This state exchanges and which steam is flowing him. This is a stink flowing in and getting out and water is coming in on the other side and going up. So this water, we need this water at a certain temperature. So this is a work controlled variable. So we want this water to be at a certain air temperature. Esteem is hitting this water and our controller is manipulating the steam or toe. Open it up. Are too close it up if the temperature is achieved and we're also measuring the temperature of this water. So this temperate is being fired into the controller because this is our output temperature of the water when the water just ready to leave the system for any processing for example, any food processing or anything. So at this estate, Just before leaving the bank, the heat exchanger. We 1,000,000 the temperature of this water and give it back the control. So based on this measurement and the best on the commanded in port, which we have already setting to destroy Controller, the controller opens the steam. Volver closes the steam. What? So this is a simple arrangement for a feedback control system and we will see some more examples of these type of systems. Okay, let's see another example and you will notice that how easy it is to make a feedback control system just with the help off a link it without any electronic component. So let me first draw simple feedback control system. So, in a simple feedback control system, we have ah blunt here and then we have a control. It they're still the controller has certain game kid and we are in poor signal. We have an input reference signal and then we made output. And if the output is different from the input, we send it back here. This is a one output signal. So this is the feedback system. So this is minus and this is the important signals. The difference of these two will be sent to the controller and that the controller will manipulate the system so that the system follow the imports of the output. Follow the input, the commanding position. So this is over out. So in this system, this is our simple to other tank. So in this trailer thing, when you press the button, this water flushes the toilet and the 10 gets them to eat. So this ball comes to this point. So this linkage has a challenger attached here. So when this goes down, the calendar becomes out of the way of this water. The top is the where and the water started. Feeling said the thing and no, if you compare these two, our imports signal. You can say that we want to keep this height of the tank at a certain level. We don't want to go beyond this level. So this is our commander Input Etch. So then when you press the button, the height becomes at this point roughly zero and know what happened. This s soon as blended goes out of the way of this water. The water quickly comes in, but as soon as this height started a starts to rise, for example, the height is at this point this is any height at one. So no. You compare the functionality of this system with the feedback control system. So as soon as this height you achieve some height. This planter goes up so it means it restricts the flow of the water and the floor Water decreases and this is what controller will do. So as soon as this letter signal, the imports signal the hybrid you want to maintain and the current height which is sense that output this output discover sensing the current height as soon as this difference starts to decrease, What controller should do Cantona Shoot for example controllers controlling a ball so control a short decrease the flow of water from this war. So this is what is happening here. As soon as the height is going up, this planet is going up and we are restricting the flow of water. So a very simple feedback control system with the help of a linkage for as you make this teacher is very small as compared to the length of the linkage. So now ho toe hard to design this bill under. In order to design this plunger, we have to find how much movement of the plunger we want, so that within that movement we want to fully open this opening and close this opening. So there is a little bit of movement here. So in that movement we want to fully open the wall and close it. So that movement is, for example, that movement is you. So you is the movement of the plunger. You Is this distance from here to here? Because this is the minimum position of the Clinton Rent of water is fully flowing. And this is that Brenda Planetary is closing the flow of the water so hard to find this. You just look at these two triangle because did I? Smart. So these are two tryingto summer triangle, right? Angled triangle. So the ratio of the perpendicular to base of the smart triangle you divided by L one is same as the ratio of the perpendicular off the large triangle, which is e do everybody l one plus l toe. So these two rations there Same So you can find you. You is. L want to worry by l one plus l two multiplied by the heat is the better. Signage are you can see the commander. So no, you can. You have tojust put on appropriate l one here so that you can get this you value. So for example, you decide that you want to put up a ninja at a certain distance from this corner. So this is your el one. So then you will see. Okay. With this l one, I will get this you and this you. This movement should be appropriate so that this splendor is fully opening. Are closing this the water flow? So this is all your design, this plunger. And with the help of a mechanical linkage, you can actually get a feedback control system. Our last example at this stage is a temperature control system off a car. So this example is taken from this book you can look into for the in this book if you want . And in this example ah, we commander in poetry, for example, any temperature comfortable temperature, 2% your compartment and our controller Try toe maintain to manipulate the hitech air conditioning system toe give us ah, compartment on Bridget. And then we also made it the pressure of the compartment and using a sensor and feed it back to the controller. And these are some of the disturbances. And we also measure the level of disturbances. For example, the ambient temperature. You may get it with a sensor and we give it to the control similarly, son, because son also contributes to the passenger compartment and do the radiations. So we also milieu the tradition of the sun with a heat sensor and then we also give it back to the control. And based on all these information three type of measurements the controller no continously tried to refine the control off this year conditioning system toe. Keep the passenger compartment at the desire to Bridget. So this is how this system should work, that it should take into consideration all the information coming to the control. The actual temperature there, through temperature of the compartment, left the temperature values off the disturbances, and the Israelis are going into the controller and controller continously try toe optimized . The system for the best performance are for the best temperature, so best temperature will be when the desired temperature and the passenger compartment temperature there at the same level. So this might never happen that there exactly at the same level because the disturbances are random. These disturbances are not at the same way with all the time. So therefore, this system will try to keep the difference between the commanded input and the actual outward to a minimum. So this is what the system will attract. What? You So this is how a closed loop system works? This will give you an idea that what factors can contribute toe lack of control and hope we can improve the control of the system. 3. What are Linear Systems: Hello. In this video we will see what are linear diamond Where it in systems So anytime unitary systems are important because most of the control system to is every cable only this type of systems. If the system is nonlinear, we try to leave, the system passed and then we apply the control system principles. So what are any time? You very insistence. I mean very easy gentle, Understand? So there's first double time you areas. If you give a certain import your system and we get the airport which is independent of the time So then the system is time in variant. So this is very easy to understand. So no doubt about the linearity of a system. So in order for a system to be linear, it has to certify satisfying the principle of superposition. So the principle of superposition has two parts the first parties negativity and the second parties or more genital. So if the system satisfies these two conditions, then the system is linear. So what are these two conditions? So let's say that we have a system s and give our input are won t and we get the output. Which is why won t And then we give another input to the system which is different than the 1st 1 And we get a different output. No, The negativity says that if instead of doing this individually, if we add these input first and then give it to the system the Opel which we get if that our food is the addition off these two or port the individual our course, then the system satisfies the objectivity condition. So it means that if being act these posting that's first Well, I won t our duty and then we give it to the system and the system gives us an output which is the some of these two individuals, our ports Then the system is said to be satisfying the activity condition. So let us talk about this faster than you were discussing opportunity. So this is the system in which we have in poor Pierre and our food is on the y axis. So these are important values. Whenever I give in poetry and get our one whenever you are in post six, I get our foot off to and so so let us say that whether this system satisfies this condition are No. So let us take these ready values between How do you draw So if the R one is three lesson for R one B, he was three. Give beget. Why won t one and let us take any other. When you six, for example, When our who is our cookie is six we get Why do why do y is a function of X So we get at six. We get white too. Why do it was to no instead of three and six? No, if I add these first So it means three plus six is nine. So if I give 90 the input This is all the same system This is the car draw a graph of the system. So if we give nine as I import, what will you get in front of 9 93? So it means my white tree. You can see why tree when are three is nine I get whitely as three. No, you can see that if I add these input values first and then we give that values the input I am getting the Opel which is the addition of these two individuals outputs so it means the system is satisfying the objectivity condition. So the first condition is satisfied. The system is linear. We have to check the home of unity. Know what is the opportunity? How much in this is there? If a system gives for any imported, the system gives output. Why do you for our key and no more deep later import with a constant value scale. Really any Boston and I might apply this kid. I give the system input and a multiple of the original import. And I get the same murky bunny the same where depart the case would be the same as output of the first case. Then the system satisfies the homogeneity condition. So again, on this graph, let us say that over our d waas three and knowing when to play. And I get whitey as one from this system girl. No. If I multiply this RTV tree there, say Jesus killer. So three time rt three day Marty means three times three is nine. So my normal Artie's night. So at in front of nine again, the system off has three, which is equal to three times the original output. So now you can see that the system also satisfies the homogeneity condition. If I give us system or for three in poetry, I get output one. And if I multiply this input with anywhere, you can take any value because I'm taking this three value because I have grown these red lines toe make it clear to you other ones you can take any other lawyer say our rt is four . Next they were rt was four So in front of or would be roughly the what is the value of white? It is roughly 1.3 So what? Why be before he is 1.3 So no, it has multiplied this with two case to plastic equal school So two times rt is it? So what is the open and it and it I was born with the system graph and then bought Why exes ? So as you can see that it is enough to 0.6 questo 0.6 So if I might have like gave it to my output is getting multiplied by to the same number. So it means that the system satisfies the or maternity condition as well. So the system is linear because it satisfies both of the activity and homogeneity conditions. So this is home. Check our systems linearity and some things. Temples are damper Spring Systems master for spring system linear systems in electrical circus of the repressive components resistors Conductor's Cap Pistols are inducted. The system is linear in little next if you talk about Tony's, most of them three fire suckers in most of the reindeer linear. But there could be a little bit of a lonely immunity. For example, let's say this graph after sometime would go like this. Then this is up known linearity. So this type offer systems are linear, and I hope that this video will need to understand what a linear systems and hope project any idea of a system. 4. Finding Transfer Function of a Mass, Spring, Damper System: hello When learning control system, the most important step is to find out the pastor function of any system because once you know the loss of function, you can apply a lot of principles and a lot of matters to understand the system. But to find out the loss of function, there are essentially only four critical steps. So in this video, we will let hope to find the loss of function of a simple mechanical system. But it doesn't mean that it is only alluded to a simple system. You can apply this print support, any system, whole complex it might be. So let's get started and see how to find the doctor function. So this is our system. In this system, he has a month. We have a mosque am, which is a Pashto, a spring and damper. We apply your four Steph in this mosque and the mosque moves or distance X. So this is the situation. No. One of whenever you want to find out the transfer function the first step, The first step is who will decide what ratio you want. What is your output and what is your input in between these two in between what two areas you want to find or the transfer function because doesn't function is essentially a racial off the or part of a system to the import. But what what permitted is our private test for us. So in this situation, as you can see there, our input is the force applied to the system and our open is the displacement of the mouse . So therefore we said that we want immigration off the displacement would applied force as our transfer function. But this initial have to have we have to find this Nissho in Estonia. So what after function of this system which we are interested in, which is represented by GFS, equals the ratio off the displacement as our put to the force as a input. So they should displace pretty nice to me. Forcing us to me is our plants affection. So once you have decided these two values, the next step is to apply the noodles laws and to find the original motion. So in this situation we are saying that we're applying a force 50. So all the rest of the forces are opposing the motion so they impede the motion of the force. So there are three forces a year, one in the spring Force one is the damper force and the next forces. I mean toe the masked acceleration. Soma's in preservations. All these three forces are opposing this force. So we invited a simple free body diagram here. So let's This is so The force on the right is force. He means in time domain. So about posing for the four due to spring is getting Blix extra p. The force due toa Denver is always have being Corbijn multiplied by velocity. So when a damping coefficient is that me and the ballistic and militant as DX by beauty? Because the velocity of the first really work displacement The third Forces do toe the mass of the system which is having A and M and is the davidoff the velocity of the secondary ready for displacement So and we can write acceleration as the school next by beauty square . So these three forces directing on the left hand side and applied forces on right so the fastest of wasp to decide our port. Any port, this is your own choice. The second important step is to write the equation of motion. So let's write down these equipment. So we say that all these forces impede the applied force. So therefore we can write on the left. Inside we have chaos, extra spring force plus f b. He explained it either temper force plus secondary directive. You school and expert duty Time The mosque equals that like force. So this is our equation of motion. So this is the second critical step to write that question. The target step is to go from time to men s to me because I will transfer function is always of issuing as dooming. So this is your time Critical step. So step number trees move from time domain quest to me. So in order to move from timeto estimate, there are three quantities in time domain the displacement that we lost in the acceleration . And we have to find out what are the last transforms off x x api, the expert beauty And what is the class transform off D square expert Duty square. So let me write down here the plasters for any function off time equals the function in the as doing so far is number. This is fourth, so you can write the plasters form off FTS f s And if it's x'd displacement of the last transform off X t will be simply access. So excesses the last. Transform off this and give the costume No What is the left? Us Transform off the first day already. So let clusters form of David in Is s what? This minus Because it's a four star rating. So there will be one initial condition. How many ships condition But for venous system we we ignore only all initial conditions. All the road conditions are ignored so we will consider this condition. So this is the plasters for my first day already the clusters form of second derivative off any function he could do s Disquiet s off ffs and minus. No, There were two initial conditions plus something else. But again we ignored me and initial conditions than we already take this. Will you similarly this value in this rail? You know we can put these were use here so we can have plus FB de expert duty. So this is X instead of f So we will simply light s x up is unless as things quiet x self Yes, my deployed by M and Equal Group. If all this So this is our in questioning as doing so, we have moved. This was the work. Tired of step to move from time to Mento. Assuming so, the first was to decide output inboard 2nd 1 to write the equation of motion Tireless move from time to rest. A moment on the fourth in the last step is to take this racial. So first we have to simplify. Remember, if you can see here that we can take excess as coma. So if you take excess as common so we get okay plus f b in guess plus Ambien do Is this quit? He was if well as so. No, the last step is to take the initial so we're protected issue of excess over there fest. So we have to bring this FSC and investing on the inside. So be right. Access B Y b by and press equals one. Do art invite all this and normally it's a good practice toe, right? The highest estern first, because this is the order of the Tractor City question. So be like Nemesis Square Less have B s less kid. So this is okay. This step, you can stop here. You can see this is the start of a function of the system. But a small vial for a common practice toe. Keep this the coefficient of the highest, um, has won. So we can be wired numerator and denominator with em, and that will be able to find a step. So x office, the wiring by f off this equals toe one to argue. But you and then we have s the square in the US f b. I am dying. Pissed, plus kill. Beware Didn't like him. So what are these? Equations are correct. So this is the transfer function of this system. And as you might expect, that all the critical perimeters are in this. But kids spring constant the damping coefficient. In the months, all of these values are here. So this is our transfer function for this simple mechanical system? No, we can do this. We can apply this principle to find or the function of more complex systems. And this week, we learned in our next videos 5. Converting Differential Equations into State Space Equations : Hello. What's up, guys? In this video, we will learn all we can work our differential equation in tow a stretch specification and hope to get an open question. So this is a standard form of the differential equation. We have done it every people. Why respect be then minus one. They would. You know why I respect Cody. And with accosted in minus one. So the first posture is one. Because what? That But there is any question we can't divided by the same number that we can get other constant. So we have written that question in this form. So this is the standard form. The issue is then put through the system and one who can work this into states basically, in so states basically desire in this form extorting waas e x plus bu This is God's status , physical region. And then there's are open degree in, which is why I was C X plus Leizhou. So this do you is normally far feed forward type of systems and make the system one stable . So alerts, as you know, this is you. So we will be left with extra because explosive issue. And why was C X So these are our state space equations. So hope we can work this differential equation into this stairs press equation. And then you will see that if you have any problem in any questions that you have become what different question in this form, it will be a matter of less than one minute. You can do this if you know this matter than you look carefully to the packed enough does the max is again. You will be able to solve questions very quickly. So we do this. So this is a vector X door x one nor extra dark off to extend goat. This is another American ex Matics A And then we have this rectal overstate very was x one x two a u x n So this is this part is this is it so a X and plus B, we will be a vector like this and any input proof. So this is a world Be so This is the standard form of the state in question in Matics food . So we want to get all these variables X one dog works and or from this and then what are these coasters and automate this so know that the selection off the state very was excellent. One to extend. This is we have to take There are few things. Number one. The state variable should be linearly independent of each other. So what does it mean? Is for example, let us say that we have three stayed where he was x one x two and x three. So linear independence means that no one can be a leader in the form of any other variables . So if, for example, I can write this extremely waas x one plus x two. So it means that extra is dependent on X one and x two. Because this is a linear equation and x one extra, he's dependent on these would be no extra natural. We can find X tree while instead very was We must select very was which are independent of each other linearly independent. But luckily we know that in for example, X one is a variable Then if x two is the very worried about this with respect to time, then we can take these x one and x two as variables. Because the generative is not dependent. No actual If I'm taking the very radio off X one, then extra is not dependent on excellent because that anybody was in order here and deliver it to our the successive derivatives. They are independent of each other. They are linearly independent. So therefore no weakens like variable state where iwas indiscretion. So then we will book here and we will get that stated Williams. So to do that who? So they're distinct? That X one is equal to what? So this is the solution of this equation because this in question is in the form off a differential question in white with respect to time. So the solution will be a value of why it's simple. So this is why and over for state very well x one. This one is white so no extra We big X tweet waas David, give off X one With respect to time, this can also return as x one thought esta will be with us one door similarly extreme will be Puerto extrude up and so on So x MPB where do eggs and minus one dork. So this is the way we select up variables. So no, we have selected all these variables. No, I want to put these values into this differential equation and solve it so that we can get the state equivalents. So how we do that is that we start from the right hand side so that it will be easier for Afghanistan. So you know, this will be like this being or you, you know. And why is that one x one less you want? And what do you want? My duty? This is Exxon Dog, the day everyone x one So I can write X one door unless similarly if you will be yet before this on in tow, extra dog. And similarly, we can reach here and we can say that it is a sup and minus one X and minus one door. But this and what is this? This is X end up extend or so No, this is the value off X and dog plus all these equals tow this thing. So we want to get the value off extend or this one So extent no will be We're going extent . Normally we would do I think, all these very on the other sense site and start from this so minus a lord x one minus 81 And what is X one daughter X one, Doctor's x two. So we can write extra because we have taken X one daughter as X to the next state variable this one. So this before this is extra. Also, I'm not know in the form of state variables instead of that at their derivatives. So minus Analects want minus table next to similarly minus eight Do except three and similarly up to this point is up and minus one. And as you can see that if it is able, then it will be the time state variable. So it means if it is it and when this one so it will be and that state very with X m. And plus this, of course, because this is plus on any on this side of the equation, so being or into you. So this is the value of X and dog. No, this is the only very evil extend. Norwich has such a long region because all others are very stupid. X one door. What is extra indoor? Excellent. DOrtiz basically extra you Similarly extra dark equals X tree and X and minus one door will be equal to as you can see, that if it is one here it's story. So X minus one means it will be extend because this is the Maybe you find all these variables so no, we have district er the complete information off this record so we can write in the vector form. And as you can see, that X one dot extra Lord the same for me to be everything before and X and dope This equation This one this is the extend our equation Big waas. And no, I'm writing the last rule because this will be more people like by this corner director, which is about the vector of state very was x one x two upto x And so these value this constant will be here minus day nor minus one minus it go up to this point minus. This is minus here minus He saw end minus one. So no, If you open this, you will see flesh be shoe off course B is a vector and used the input So no. If you open this, you will see that X end door. It was minus in order to extract so anymore depart with this call. So minus a Nordex. Once you get this minus K one extra, you get this and similarly goes up to this point. Then this plus and be you. So nobody, everything. This the best of the values are very simple. But you have to be careful about a patron of zero and one which will emerge here in this practice. So what is explored or explanatory? The Australia, which is you put two extra esto is here in the second row of this vector. So it means the first and live in zero. And the second will be one so that when you open up this we will get expert Nordic waas you know, Time X one, which is zero plus one time. Actually which is extra. This value and the rest of the values will be zeal very simple. Similarly, for XTO extrude articles extreme which is the tire value here. So the 1st 2 will be zero than one and the rest will be zero. So this is a pattern. This pattern is very important because when we will be solving problems, then this pattern will help us. Who can work for a differential equation into status basically, in less than a minute. Really simple. Very quick. So no. After writing this, u can write this for them. 0010001 and so on. And it will go from up to minus eight and minus one. Which is this one? No. Whatever. Be director be so we have to Could only be nor so because it is. This is in this equation, extent so we can put being on here, and the rest of them will be zero. So normal step spirits equation is complete. So this is the state specific region Extra because X plus bu No oh, clinic vision. So in the beginning, we have taken y equals x one. So this is from where we started. So no, this is our expect. Er so if I can write it here Beverage Excellent extras that this is over ST Victor. Excellent. Blix in. And why Waas? There must be a royal. Why? Because only a walmart declared by your column can give us only one value, which is this one and this is X one. So explain is the first a trip. So it means one will be here and the rest of them will be zero. So, no, we have Why was one deal zero and in tow, This straight record. And if you open this up, you will get Why was ex one and the rest of that? This will be zero. So So this is the way we could want a differential equation in tow State space equations. So if you look carefully, you will notice here that the last rule off this metrics here is the coefficient off this differential equation in the reverse order. I mean, the older son. So, you know, the last coefficient is in the beginning, but that it was signed minus a no. Similarly, anyone is minus a one and upto this point because this is the value of X and dog. So if you know this spectrum, and if you know that the coefficient of this differential equation come to the last room that gave us orders with the opposite sign, you can stayed awake and water differential equation in tow upstairs, basically. And this we were doing in the next review 6. Time Constants of RL Circuit and RC Circuit For Skillshare Class: Hello and welcome to my channel. In today's video, we will talk about our circuit and are accepted and their time constants from where these time constants come from. And what is the significance of this time? Constants. So this word that discussed in this video and in the next week ago we were derived the equation off currents for these two senators. So let's get started. So the first circuit is this circuit, which is card our circuit because we have a new assistant and conductor. So the value is a tool for resistor and Henry's foreign doctor, and he replied 10 words. So when we close this switch initially, there's no correct because in Dr stores that uses the current to store the energy. But slowly this current starts to build up and then it reaches a maximum value. So for this kind of set, the maximum value off the Koran, which can ever passed through this circuit, is the correct which is n do remember to this resistor. So this is five MP years, so this is the maximum value of current which this circle can ever pass on the pestis circuit RC circuit. It happens in the opposite way. So when we close the switch initially all the current passes through the pastor just like the short circuit. Then this capacitor starts to charge and the current starts to drop, and it reaches that value, which is very close to zero. So this is what happens here, and no, these are the graphs and these are the questions. Using this equation, you can find the value of current at any time. So on this graph time is on the X axis and currently is on the way except and this is the maximum value for capacitor circuit and the maximum value of the injector circuit. So this is the brief introduction off what is on this white board at the moment and not just talk about the time constant. So time constant off a decaying perimeter, Any perimeter, it could be current. It could be thwarted. Currently use incorrect. So time constant for a decreasing the perimeter is the time at which the time taken by the perimeter to reach 37% average maximum, will you? So we're looking for a 60% drop. So if this is the maximum value, you can say 100%. So this is the 63% drop off this value. So that is the time taken for this is card time constant. So if you maybe this time in seconds. So there will be time Constant, very lovely for a rising graph. The time constant is the time taken to achieve the 63% off its maximum value. So this is one sixties of 1 16 off the maximum value. So what? What is the time picking? So if you drop a perpendicular and who made you this time in second, flex it So this is one payoff measuring the time constant. If you have this graph so you can just actually physically take this on escape and then 63% of that scared drop or particular on this graph, then dropper particular on X axis and calculating the time on here. So this is a simple of it using the graph to find the time constant. But what is this time constant. And we know when you normally use the questions. After this type of questions, you use a time constant off and beware did by our This is for L'Arche type of suckers this type of suitcase to be used time constant. And this is denoted by normally tall. And for this type of circus visuals, time constants, which is equal to R C. R. Is the distance seized up? A pastor value the past tense value. So these are the formulas. So homey Hovey this on these four molars. Why you these formulas for time, Constant. So this is what we're talking about in this video. So no one step back. What is this? 0.37 point 37 is actually one divided by E and Wonder ordered by ease the base of the nature logarithms. So one divided by E which is 2.78 something. If you divided, you will get this 0.37 where you so this is one to everybody and similarly, this 163 is basically one minus one to everybody. Are there any other ways you can say one minus 10.37? So we just 63% at 1 60 So basically there is only one factor, which is one door by E because if you extra rising just subjected from one, it was because it would take this as a kid so whole begat this as a value off. Everybody buy art because this is very important if we know activated by are so we have Ellen are mentioned years so we can state over there the time constant of destructive. And this gives us a very important information, which I will describe later. But first, from here we get these values. So in order to understand this, we have toe have a look at these equations which we were driving, and we will actually see homey reach here. But in this we do. I just want to explain how we get this. Why this separate reach and this will you and why? I hope we can get these were used from these equations. So no, First we look at this equation. So if you look at this equation, this is the value of the maximum. And this is the factor which we're looking for. So this is the rising factor. We want this victor, this victor, he went to this thing one minus one. Do anybody? So if you look here and if you look here, this is either to the power minus R divided by helping toe be So now imagine what Will you have? Tea if I put here? I get years to the power minus one only. Obviously the value off. He should be the reciprocal of this. Are you? Are you? But l which is already ready. But if I put this radio for P for time in this equation we will get one minus e. It is to the power minus one which is respected because it is the power minus one means 1 20 but e So therefore, this is the time constant off are in subject because if I put this for time, I will get I maximum multiplied by 0.63 This value will make this part this factor 163 So therefore, this is the time constant off. Any are inserted similarly for RC circuit. What were you off if I put here which will make this thing as one to anybody. So the value off he should be our see if I put RC 40 years. These two are single began Salau and either to the power minus one there which is one divided by e. So therefore RC is the time constant off R c type of circuit in which we have a resistor and a pistol. So these are the time Constant Know that the next thing is in most of the grabs. You will see that the state of time you will, you will see one toe to toe three go fordo and fight always dine constant. So sometimes these graphs instead of time they do You know this thing and why it is so because generally it is accepted that after five time constants wants the five time constants have been alleged, the system will lead its final value. Are the steady state, will you? We couldn't stay there. So after five time constants the Tempesta circuit related minimum current And after five time constants, the injector circuit will also reaches maximum where you want to. 345 time constants. So whatever is the value of the time Constant left state this example. The time constant of this circuit is rewarded by our which is tended by two, which is five seconds. So it means that after 25 seconds this circuit religious, maximum current value. This is very significant because just by looking at this circuit, you can state of a tell they ran the second with Regis maximum current by looking at this diagram only if you know that the time question is off the second Oliver's R. C. So by looking at RNC, you can state over there the next day if you've been to work too much. Declined by 36 six second in the time constants of five time constants means Turkey sickening. So after 30 seconds, this circuit religious when you So this is the importance of time constant once you know how it hope it is this. So in this video, I only explained the end and result the end of the equation from this equation. You can see that we can get the time constant values these will be normally do. These were used without thinking from where these Where is that coming from? So this is the explanation of this time constant. And in the next video, we will actually drive these two equations. So really see that Hovey reached here. So thanks for watching and see you in the next video. 7. Nyquist Stability Criterion Without Mathematics: if you can ignore this little bit off great six mathematics in next 10 minutes, I will try to explain Nyquist stability criterion without much mathematics. So let's get started. But because there could be some bigness watching this video, so I will take hostile manners just to explain a little bit off basics. And then we will start up. Nyquist Able decried it, so let's start with the open loop system. So this is open loop system. I could have written this G and H in one block, but I'm just writing that year so that I could compare it with a closed loop system. So does the function of this open loop system. Is GH two years up and the transfer function of this close No feedback control system is given by D F Sub Sea, which is GE rewarded by one plus G h. Whatever we do here is that simple fractions operations. You can see their TV's affection denoted by Newman iter of G by denominator of G. Similarly edges and ceviche the savage. And if you find one plus d eight, you got this equation. Similarly, if you find the Council can do to everybody one plus GSO, this is G you ordered by one idea so you might deploy it with their separate color one last year. This cancels out and look at this. So the reason I have written this here is to explain to you one very important concept. And so I like this thing that if you look at the numerator off one plus g edge and the denominator of the closed loop transfer function, they are exactly the same. So new miniter one plus g edge and the denominator of closed loop tosel function are exactly same. So what does it mean? How can we explain this in terms of the system stability? So no. When we talk about the stability of the control systems denominator off that close look, pastor function is very important. If you look at all these equations, they are basically function off a complex number s which has two components. So this is explain. So this is a real part. You can see a stigma. And this is Joe Mega. So this is card s plane. So these are the complex numbers, All these corrections there basically Polly Nahmias in S variable s. So for example, this one less GH if we like one plus g edge. So this would be a function of s something like you can say It's plus six b y by less makeup And yes, a square minus 30 s my understand. So this one plus g, it would be something like this several lovely. This transfer function will also be affection something like this. But when we're talking about Nyquist 70 authoritarian, we will be talking about one plus g edge instead of the transfer function off the closed loop system. And I will explain this wife were concerned about one plus g h. But the point here is that these are function off s and what I'm trying to explain is what are zeros and what are polls? This is only for bigness. First, let me put this in the factor form. So this is s plus six. And he replies, This will get s minus five. And as for us too, if I'm right, But anyway, you will get something like this. If I put it s equals minus six year, this whole direction will become zero. Less than minus six is here. So this minus 60 scarred, zero off distraction one plus g h. So the value off s for this? This for which discretion becomes zero, is zero off this fraction and the value off s. For example, if I put s equals five arrested was minus two. This war faction will become invite. So for s equals play. And Jessica was minus tool something here. So these are card oppose of the system. We normally be notably the cross and deals with gov the circle. So the values off s for which this friction become zero are zeros and zero to reside in the numerator and pulled reside in the denominator. No, I'm talking about this past for function off a closed system. If the bulls off this direction, whatever is the friction? This one If the polls that rules off this equation light in this region right half plane, right side of the indignity exit. The system is unstable. If pulls out here, the system is unstable. This is the way we used to define the stability. If the polls are for transfer, close Newcastle function are on the right hand side. The system is unstable. Why? We don't talk about the cause of the open loop system because if the bulls of the open loop system are on the right hand side, the open loop system is unstable. But because we want toe make it a closed loop system feedback control system, there's the purpose of to make it a closed loop system. So therefore, if even the open loop woes our unstable, there is no problem. So we are more concerned about the pose of the closed loop system. This is one way to define the stability that if the close loopholes are on the right, have playing. The system is unstable, so it means when we know that 01 plus GH same as the old bastard function. So no, we can define the stability in another way and the ways that if the use of one plus g h are on the right hand right half plane, then the system is unstable. So instead of saying that if the polls are the clothes, look, transfer, function on the right and say we're not saying that if the zeros off one plus g h are on the right off plane, the system is unstable because one plus D, it's has zeros with the numerator are same as the denominator of the prosper function. A fraction divine instability in this way is very important because of the next concept, which I'm going to introduce to you. And that is card the mapping off complex number and that will lead us toe one little concept in the complex number theory, which is card the cautious principle, and that will take us to the Nyquist stability criteria. So these are three or four steps in war. In this all these is conceptual. There's no mathematics and the little bit of mathematics which is in here I will explain in the next video. So now let's talk about the mapping off complex. Now, let us say this is one plus D H, which is a function off Harris, and we put a very off s here s equals. Let's say two minus three j. So what? We will get out another value off s this. That could be minus five plus for you because this is a function of s. So if you put some value off s, you get another value off s. So this is mapping very simple. You put a complex number into some complex function. You get another complex number. This is guard mapping. No, this is s plane. So let us say that this is Esplen. We are hoping some values from this plane into this function. And we're getting some values in another plane. Which name based on this mapping function, we call it there. This is, Let's say one plus GH Blame the name with another complex plane. We can name it. Any plane w plan that plan. Whatever. So there are a few things about mapping and those are If you make one point, you will get one point somewhere on this. If you are lying, you will get a life, any life. And if you met, undo a close tab. Do we get a close car? Oh, maybe any ship or anywhere. These are a few things about mapping. You should know that if you map a point, you get the point. If you map a line, a line a close, can you get a close? Come on. All You know what is mapping and whole week unmet? No, we're getting very close to the night, Christine. So we had noticed that if the zeros of one plus g h are in this region from this indignantly access up to infinity in this direction and then in a sampler of semi sector, you can say and then we board minus infinity and the ideas off the simple is also in one night eventually affinity. So this is a big info night, seven circle. So if zeroes off one plus d h and zero is in this region in this closed loop, our control, then the system the closed loop system will be unstable. If any zero of one plus g eight year, because that zero will be the pool of the closed loop starts a function. So this is what we're trying to find. The credible and zero lies here are not what will help us. Here is the mapping off complex functions and the Bush's principal off argument And what that says they're says that if there are that zeros in this control and there are people in this control and you start mapping this control upto onto another man, let's say this is one plus gs blame and we have mapping this So this plane, through a function complex, function one plus yet we are mapping this to this so as you know, that we will get a condor so that I can do is something like this. And when you are mapping George putting values so you can start from anywhere you can start for our region and both this way and then come like this. So it could be a clockwise direction. It could be anti clockwise direction. But you have to choose one because the action is important. And this I will explain in the next video. But for no, you just understand the direction you can take any direction. But better, whatever you take, you stick to their direction. So let us say that I did. The block was direction. I will start mapping all these points for this point into dysfunction and math wherever this point gifts and then go on and complete this control and I will get another control here. So if I map it globe wise before I do that, I want to highlight wanting which I forgot. Uglier is there that this semi circular this whole region, which we are looking for is card Nyquist control Nykvist control and when we pass it through this one plus G h uh, through D h. And I will explain this in a minute. When we pass it through dysfunction, this complex function and we get another control. So this is guard night. Missed block? No. So this is one thing which I forgot. Uglier. So this is nitrous contour. When we map it, we get night explored. No. The principle of our boomers stays their names. There are the number of zeros. We are the number off balls and we are mapping in a clockwise direction any contour, then the globe wise in sir government off origin visit the region. And that means number of times. This company, this encircles the region. So then the number clockwise encirclement of the origin. And so let's say and is the number of encirclement of the region in the cloak with direction and will be for you There might speak. So this is what principle of argument says This is very important because if you know, be the number off pulls off the open loop system, then if it won't be and we are looking for said whether any there is in this region are not and if not be the bloated night explored using, for example, a software Mac Labs I left. We get a necklace, bloat, reading become the number of encirclement. But just by observing the graph, how many times the graph in circles, the region. So we get in from this simple question we will get said, If there is any set here, then the system is unstable. If they know that the system is stable very simple. So this is Nyquist, a Nyquist stability criterion. You just floored the Nyquist float by using one plus G h RG edge. And this is the last thing I will explain and you get a blood. And in that block off one plus gs and circus zero, you just go on the number of encirclement, the value of get the really off and, you know, be this is important that this be the open loop. Control and bulls should be known so open. RuPaul's are known to you, and normally we know the open loop holes. And normally we don't have any unstable born in open loop. We want to start from a stable, open system. But even if there are unstable the fall in this region it doesn't matter because we're concerned about closed loop system only. So then it's very easy to find whether there is any that are not if there is any there in this region, the system is unstable. And if there's no that, the system is stable. Very simple. No, let's talk about one plus G h and G H whether we use one plan. Thr deal. So the good thing about my Chris plot is that if you plus one plus theater, you get this float when you plop using the GH function. When you put the rallies in G eight and brought it here, then this floor will be shifted. One unit towards left. You will get something like this. So this is one unit left G s will be one unit left, so it means the same to me. Applies Know will only see the settlements off. Not zero brother. Encirclement of minus one, because there's zero watts for one plus g h. So if we are floating, if you're using the it function for mapping, so we will see that whole many in circumvents off minus one are there and that will be the value off and If we're going clockwise, we will see how many clockwise and circle mints off minus when one are there. And then if we have some of you know the polls, you'll get the zero. So let us begin its simple example. Suppose we want if we had two bulls in the unstable region in the open loop system and then we counted here and we counted that there are two not blow boys even broke well, but we noticed that our on our Nick Wispelaere there are two anti clockwise and second men self minus one, the D A function. So if there are two and anti clockwise in settlement, that would be minus two, because only counter only, only clockwise and settlement will give us and positive in counterclockwise will give us and negative and be what waas too. So what is there that is and plus P so their request two plus minus two zeal. So it means there is no unstable poll in the closed loop system, so the system is stable. So this is how you find the values of zeros. If there is any zero on the right time side or not. Three, for example, we get toe clockwise is a sensor comments off minus one using Deitsch then and would be too . And there will be four pulls on the right and plain and the system will be unstable. So this is one example. No, The final thing is it seems that mapping off this whole plane in in tonight here in minus infinity and this are tends to infinity mapping this whole through GS onto a plane, which is no card GH blame because we have mapping using this function, We got it a d h. Blame. So on this function, it seems that there will be a lot of values we have deplored on this function and get some blood. But the fact is, in most systems gs this d a his new editor, you can't numerator gs and the nominated off just going back to the simple notation of numerator and denominator. Normally, this is a s in a polynomial in s like, for example, s minus last June and the denominator s x squared plus plus fight in this case, the order off this polynomial Next The end is the order of the numerical. We just won the maximum poverty ffs the order of this polynomial m The maximum power off s which is to so normally and is less than m. The order of the new military polynomial is less than the order of the denominator polynomial. You might have noticed this thing already. Normally, this is the case. If this is the kiss and this is again, I'm going to reward the mathematics. But if this is the case, all this semicircle, all this semicircle maps, toe origin, one single point. All this semicircle met to a single point. And if anyone wants to him next, An equal, slim and equals two lasted two. Unethical, stupid. And this then all this time. Circle, match, toe. Any number on the sexes. Any real number? It could be any number. This this, this business, any number. So all this same is that girl excluding this exes? I'm not talking about the Axis. I'm talking about anything on the right side of the active. This maps to a real number three days. In most cases, this whole thing matched only a single point. So no problem. So we have to map only this this excess. We have to put the values Oh, here as equal school. Jail made up. You're America is equal to minus infinity to infinity. Only this access. So we have reported only these values into this. And so this is left. No. What is this? What we're doing here? You might have saw some problems Are questions in your textbooks? Might have seen this, That we put some values off. Jill Megan, State office. What is this? This is basically the frequency bloat on the working Is that from this to this and from distribute, these two are mirrors of one another. So we in fact, we have to find only this part are this part, whichever is easier. So you find only this part. And this part is the mirror off. So you, for example, you plot one part like this started on the other Is the minute off? Very simple. So you can get them. Make this block only by floating this much off course in visitor situation, which is the most cases. And for the whole, you don't have to floor from zero doing tonight. You just float value infinity radio and then this point at this point, we're displaying crosses the access so you just floored for four points and in most gets you are done. So this is whole. It's very easy toe plot the Nyquist plot and to make the comment about the stability of the system just by counting. Then settlements off minus one. Get function. And there said no few words about this. What if you're don't go clockwise and you want to go? And the Globe boys, What will be the vision for the argument principle of argument. So if you're going Andy Grove boys, then the number off anti cloak was in Circle Mus and will be equal to B minus there. But these are the anti Claus words and circle marks, and so then counterclockwise will be equal to B minus there if to decide to go in this direction. So this is the difference. But neither the counterclockwise you will be counting going clockwise and circumvents up minus one. So if you're using the it function, so that is it. I hope that this video will make some concepts clear about Nyquist, a political 8. How to find Transfer Function of a DC Servo Motor: Hello and welcome to my channel. Into this video, we learn hope. Get the transfer function off our business. Our water will just I majored control, so I would go into these dictates. But before that, this is a room. Waters are very important component in control systems applications. So there is a difference between BC mortars and basis sophomore This immortals are very itchy. Why, This is some water there Very expensive because this is some waters are kind of a very small closed loop control system. So why we used this is our war mortars. We do disassemble waters in applications where we want toe, get a very precise position. We want toe rotate the motor upto a very precise, angular position. Then we use this is servo motors. And in order to do that, we have to put a some sensor there which is normally a chef and quarter, and then we use their sensory information as a feedback and try toe, minimize the other between the current position and the desired position. So this is a really sophisticated closed loop feedback control system, so you can do so many things in DC Motors you can use them for various genuine spirit applications. Changing torque application. You can put a gearbox and you can change the talk as well. And you can also change the direction of rotation by changing the polarity. But for position control when there is the precise bullshit condone required. For example, there's the robotic hand and you want to rotate the hand. Are the actuator any robot actuator toe A very precise position are, for example, you are machining the material on you want to feed them matter to a 1,000,000 machine, then you want toe that matter to be a very precise position where you want to make the cut . So in this type off, very precise application used. This is several more today when we derive the casa function of this, this is the water. We will get this transfer function in the form of a few constants, so there will be a few constants motor constants and we confined those costumes by using some matters, but that we will discuss in the next video because I don't want this with you very long so that you can usually digest the contents in this video. So therefore this video will only derive the transfer function of this. This is a room water so that you can know the procedure on in the next video, we'll look into the constants or to find those constant values which will appear in this class for function. No coming toe. This this is a walker. This is the separate Bagram. Off the dishes, several motor. So we have a fixed fee. You can get this fear by permanent magnets, electromagnets and then our major, the rotating component of the motor. Be a lie aboard Ege he a and then b Miss wasting Time domain. And then the mission term flows. And when we say I controlled, it means that we are changing the current in the army. So if it is feel control, then we're getting the current field. But if it is the armature control, we're changing the parent in the Army. Gin? No. What is the purpose of this mortar? What motor does mortar for? Why's the talk? And based on the tour, you can rotate the load and then you can position the load as well. The time genetic bottom openess piece of em, uh, position of the motor at any time is denoted by detests of em. So remember that we're talking about the rotational positions or additional position is the angle Just like a linear position are translational Position is denoted by X the distance But we are When we're talking more mortars, we have to donate the position, Tita. So when I said retirements position when I say omega admits velocity So this is the position and these are the Internet resistance and the inductive. It's normally this this component is very small. No, when we set for us for function. So transfer function is basically the ratio of the output so that in port off the component in esto me, you know that as I have mentioned already in my previous video, when we direct the transfer function offspring mass damper system that you can take anywhere you you can take any value as output and any value is input and find the relationship between those two values in S Domi. So therefore you want to know ho toe go from time momento s do me so there are only two or three formula which we will be using in this division and I will explain to you before we start. But this is what we have to do. We have to move from time domain to estimate So you know beforehand what we have to do before I start doing something. So then do. It will be easier for you that you know that What are the critical steps in the derivation of a transfer function? And there are only four. There are only four steps in driving this transfer function. And I will show you how easy it is to find their toe. Also function over DC servo motor. No What? We have to decide what do para meters. We want the castle function between So what? Our foot perimeter is far. It is very important for us. And what is the input parameter which is important for us. So as you can see here, the most important perimeter for which we are using this business several mortar is the position. So therefore tee time is very important for us. So therefore we will take time as that would put very able and the in port which is very important is that line mortgage a flight quarters to disassemble motor that is our import. So our transfer function would be. Do you have this, Ernesto? Being and ever open is the position. And there were input would be that applied wordage. So when we going s domain, you like deputy So I would tosser from your GS Would be were due to time s b Y u by e yes. So ds will be where do the output be white by the light awarded next domain. So this is transfer function. So this is what we have to find and know how to proceed. You should understand four critical steps, as I mentioned earlier. So what is the 1st 1? The 1st 1 is that when disorder is rotating, it cost off me. It interacts with this fixed field at a right angle and do that it generates awarded across this terminal. So this working this just guard B b. So this is back e m f. So this is the first thing you should understand. So this maybe be leave it be his report inner door. Well, mayor, gone the speed of the motor. So this is also time domain. So no. When deriving these distracts a function, you will be using a three formulas for our late last transformed. As you know, that our transfer function is a ratio in s domain. So we have to move from momento estimate. So there will be only three for which I'm going to right here. So the 1st 1 is that if FB there is a function of time and you want to I work this to estimate so it is simply the function off s if the first elevated for any function of time and you can work it too s domain, then there will be s and then f s and plus our initial conditions which we will ignore if it's a cell second day for tip off time, any function and we can work in tow as demand. So we get s Esquire plus two initial conditions which we are ignoring again. So these are the three former very simple, which we will be using here. So no, this backboard data back MF four ditch originated across the rotor is proportional to the beauty. So what is the beauty? It's a speed of the motor. So where you were interested in position instead of omega and be begin right? The Peter Empty by DT So beware duty up. Do you don and be so America is very, very far position Very simple. So no if you look here, this is the day video before there everything. So we will use this formula. This is simple function. We will use this formula So now we're going. But I'm time us do me going to do as a man by applying the late last transform So what we get BBT becomes maybe Yes Waas Gaby babe, I didn t using this formula This is just a dash of dash after time So am I best and oneness besides this. So this is the first formula. So there will be four critical steps as I mentioned So this is the 1st 1 so you can take security one So my boat is small so I have to believe this and then I will rewrite it from my north. But this is the foster step No What is the second step? What is the second important thing you have to apply here. So the second important thing is kick off mortgage in this loop. So this we have to apply So by lying there This is that light mortgage. So, e, I really do working because this which is that Got anything, major? Here's what I would make it in time. Domain. Audie? No. And it b i by beauty. This is also it. I'm done. Blessed this be a beauty, Really a feat. So this is a question of work it by using the Kickoffs law? No, From this as we can see that this is a function of time punch enough time, function of time, function of time. So we can easily move from time domain to estimate using this formula on our second step will be complete. So let's do it. Going from time has come in you'd be no be right capital and then s this formula I So this becomes a s No in tow are here last and it And what is this? This is the first day ready. We have people s e a then i e s on. Then what did this b. B. Vicky's again? It was formula. So no, we have Yes, I remember. This is part of over tassel function. This is the input of the Gaza function. So this is a good equation. So This is our step two. If you want to get I take a big bone. I He s going from this to them, so it will be here for us. So if I take you coma, then I have are here most times I love else of it. Less BVs instead of BBs. I can put this value instead of the mortar. Yes, and he does. And this And this is also very important. Because this is our output. This is one of the better. We didn't have a chance to function. So we have to find that the ratio between this and this No, in music vision only. We want something Peter M s woman from these two times so that we can take the issue off this toe, get the tasa fusion. But we don't care any If you die a mess here, so what we can do? So there is our measure. Correct. And nobody is going to step number three. So this was the step number two. There are only 32 more stuff with you want to remember when deriving out rather function and what is not tired of step? The 30 step is your knowledge off the fact there's the talk of the motor PM depends on the armature current there. See, this is the third important knowledge you should have that the talk of the water depends on the current of the images. So if you increase that much current, Thorpe will increase. So torque is proportional to the armature. Correct. So this is the third inning 30 port instead. And there is one more thing which is also about your the 4th 1 here we're seeing the thought is warning current and in the fourth and final step vivid writing the tortoise William instead of in terms off in Isha and the friction which is the damping here. So last two steps related to the torque off the motor so fastest there because I have to believe this. So therefore I am reinforcing this thing that they're only four days there. The first step is the back mortgage. The second step is get coughs Law on this circuit. The party step is knowing that the dark is proportional to the image of current. And the fourth step is knowing that this talk has two components. One is Dinitia. This has to overcome Dinitia on the second thing, it has to overcome the friction because this is the purpose of the torque Dog has to overcome Danish you, the Lord which we have to move on the border zone in Isha board directors and the door also has to overcome the friction over types of friction. So we will see how we drive in the fourth to step back first the tired The step for the talk of the water is proportional to the mission. Correct. So we can say that. Go on. For 40 years ago I mentioned that I So again I have to remove this for I report a Boston here. We didn't know your constant gaity, our aged around at time. T so I gave me a rectal go from to arrest a man. One cannot die. Well, simply get P. M s goes there and this becomes I e. So this is a boy for more on the door. So no, we can put this formula in the equation which regard in the second step. So this was a one equation which we derived at step number two, Our a plus s ailing toe the armature current Inez Dumaine Last game, B s M s. No, Vegard. The value off our magic current in s domain from years. If you put their value on this place, then this equation will change. Just just put this value off. Yes, which is equal to the door divided by Katie. So I have to put this value here. What? I get r plus s end of it? Yeah, over 80. So I can just hear the woman. No, you be you go. And this. No, no. Again. Same approach. We want to get a racial between Peter M s. And yes, this is constant. This is constant. This is gone. Stand The only thing, the only thing which we don't want it is this. Do you know I m s talk of the motor? We don't want this. We want something which contains tea time s so that you can take teacher Miss Common and then simply take the ratio of these two and we get the transfer function. Very simple. So this one of the 30 step this is the position after the hardest. And you can say this is the 30 step. But when you put the values this is the petition after that Tired of step. So the fourth and the most important step is you can visualize here that we want the value off PMS The thought we want the value off door in terms off. If you could get the value of talk in terms of Thida and put it here, this store will be gone. Do you? I will come here and we can dented common time s and then take the issue of time has been this and get over transfer function Very simple for the last question is hopeful. Get this PMS in terms off premise the position, position of the water. And in order to get this, we have to understand the loading of the motor. So it's a little bit different production half off this part We will understand in the next video, baby, when we will find the constants The door constant And the baby the bag gm of Constant barked For this video I will explain a little bit off about whole. We lured the motor and what happens? I never said this is the sheriff of the water and B if you're for and it will go to opposition. No, this thought has two jobs. One is to overcome down in a Shia. And then the next year is Jim Marty Light by the Read of Julia Omega. So this is the first part the stork has to do to overcome the inertia. This is just like you can. It's not a dictum, president, but you can say they're just like and moss in the Libya portion and acceleration in the linear motion. So this is first part. So this talk has overcome number one business and number two. Then there should be an associative damping with this and that is card Viscous damping are the friction because whenever there is a velocity did that this card, the friction that we lost his card damping are the viscous damping. And soon, as in the linear motion, we have the formula damping coefficient into Ed's door. So this is the formula which we already used in when they were driving the mosque Spring damper system. We won this war damping coefficient in Judah velocity, linear velocity. So, similarly in rotational velocity, we also have this friction present there, which is God viscous damping the similar time off, and that is instead of see, we are using here be damping motor and indoor instead of extort, we lose off course Umeda in our case. So this dark this dog has to overcome these two things the initial and the friction. So this is in a Shia on. This is friction. So actually this motor must be attacked with Lord some Lord. So the rear diagram which we will discuss in the next video This motor more. There has some here you can see And then there is a lord attach. So this is Lord and then we have a damping here. Basically, it is something like this. This law is contributing. So the total industry averages or come by the store. So this lord will also be contributing and the ultimate contribution comes to the measure winding. So this lord effect is also included in here on this law, in fact, is also included in this jam. So therefore but this river disgusting next video. But here you can say that this talk has overcome two things the nation and the friction. The portal for initiating this in the formula for the friction is just like we had in Union motion, the damping coefficient prepared by velocity, the damping coefficient of the viscous damping coefficient multiplied by the angular velocity. So, no, this is the formula off PM. And if you look here, you can replace this man. Peter, you can replace this with Peter. So this is what we have to do next. So door in time for me Because Jim, nor day and another by DT view by duty. And if you replace my job, do you buy beauty out? He'd I am. No, we have B is quiet. Do I did my duty. Square last b m The damping into omega, which is B a t m by DT. This is will get caught. It was here. Be square. He died. I am the Squire. Plus beer beauty. My duty. So you know, we have store in terms of Peter. So as you can say no regard the talk in terms of Peter, this is what we were looking for. The value off dog done of freedom. So the only thing left is we have the photo as domain, using again the same formula. This is square formal of this one. So when we go to ask Oh, man, You get dog. He was? Yeah. And this is Esquire. You don't Last year, as in group you don't. But this is the final step. This is the final step, Novia. Yeah, The value off talk in terms off T damage. So in fight for this indoor here and then pignoli? Sure, if you damage, do argue, But this I get the transfer function so very simple. So this is how you get there? Transfer function of RBC said Well, water. The rest is only you have support this where you here floor. I will put this valuing and then you can simplify. But what you have to do is he s watch it last s l E market. Like by Instead of this you can write this whole Where did you Yeah s the square last year ? Do you? Dammit? Divided by TNT I'm writing yet that they have just show you one thing lost. Mr. Can you be? Yes, you got No What you have written this then? Every mentioned in that pence complements our DC Motor is very small as compared to the resistance component. So therefore be ignored This we take this to zero So this is the only thing you have to will be. It equals zero. So this is you have support. So if you go there, what will happen next? Yes. No. This time it becomes you. So you have toe only multiply our into anybody. 80. But Mr So I know you have all three times. Yes. So first I might reply only this Arctic with this two times So I get Yeah, it's Squire. Damn it! That's b m as damn it Unless maybe And I you diamond I should be baby Because when I take this thing comma, we will be in give it plus this factor or deployed by dear And what s left here and here. Only GM is there, so no, we have to take the initial t dia messed with the applied warded years. And when we do there, so I everything the last two step here again. There's no we can just think this you know this e s the white boy You don't Emmett, He was yes. And we for this estimates for us. So it is Guia already. You are but be does you can take this. Gave you next on then you can take this Are guests of the so Know what we want to do? You want to make this first left in the reciprocal of this So that you can take this into the denominator Because over tasa function is teatime. You are but years Just be skeptical of both sides. So you get diameter equals 100 boy asked market night buddy, as in g m r you start be so no skeevy so no one toe get rid of this coefficient of s here So what? We can do it because my people I don't separate all of this So it would want to brag by all these three times So you might be plying this with DT Case of day divided by a year also it so we have to do this in the new military as the numerator. So here's our y did my gear. So because of this coefficient has to be one No, we are almost there. So on the Newman, you're dead. We get Mr Yes. Yeah, on the denominator went to market like this With this you get only s as to you Been nothing gave the market but this is Gaby, Do you see you wanted by G m R? Yeah. It. And when you're just system, this ardor will cancel. Oh, it will also cancel out. So you will be left being be wired by GM. All right, We can take Coleman again. Want to argue with GM So you can take from these two terms So this I will do next. This is ever faster function on the left hand side. It is the issue of the well. You should have motor to anybody at like quarter. So this is our cost function. I just want one more step to simplify this. So then we can take this one Worry about G coma Otherwise we can keep it appears perfectly fine. So our past functioning because we have to be smash am awesome this month I want to argue body gm is woman from this inside here baby, he's wired Boy, are No. Yeah, well, this is no money. You like it like this. Look in any book you will see something like this. Oh no. This tosser function is in the form off some constants. And this we would find in a what next video so I hope that know you understand that there are only four critical steps. If you want to find the transfer function off a DC servo motor, I hope you find this really useful. If so, please like this and subscribe to my channel If you're invested in control systems video and thanks for watching. 9. Heaviside Method and Cover up Method : in this video, we learn to matters off doing partial fractions and the lamenting in doing partial freshen is finding the constants. And I assume that you know, what are the basics of partial fractions and Hovey select these constants. So, for example, in this example s minus one is a reputed defector, and it is repeating twice. So we have to select a constant first with the maximum power and then with about all other powers. So in our case, there are only two powers. So this is how we select Constance for a repeated, effective And if there are known depleting factors, so we simply select one constant for each and every factor. So I assume that you know all this basic self Hovey, select these constants, and then these matters will save you a lot off time. Because what happens is that when we're finding these constants, doing partial fractions were solving simultaneously near equations. And although these airways simple equations but you do silly mistakes and therefore these matters will not involve any simultaneous solution of linear equation. These are very simple matters and we in control systems engineering. We have to find partial fractions when we want to find output response off a system in time domain. So what we do, for example, the CS is the output off the system. So we make the partial fractions. So we make some simple fractions, and then we use the left loss transform tables go back from as to time domain. So this is how we find the time response off the system. So the first method is guarded, coverup mattered Israel. And both of these methods are also card heavy side matters, as you can see at the bottom of the screen. So discover of method works like this. So this is our main fraction, and we have to find a one in there, too. But everyone we take the denominator off. This direction equals 20 So ask minus one equals zero, and this will give us one value off s s equals one. And then we put this value off s into the main faction. We will ignore this time and we will get a one so everyone will be equal. Cool one minus seven. And we ignore the first er. Some say for toughing it here, Just ignore it and then s plus two we What s plus two? So we will get minus 60. Y did by T is minus two. So state of where you go to the constant. Similarly, for a two we take their denominator off a two equals zero. So as plus two equals zero, it will give us as equals minus two. We take people this here and we ignore the second time. So it will be equal to minus two minus seven. And we ignore this term which it Xs plus two. We only take the first time, which is minus two minus one. So it will be equal to minus nine, divided by minus three, which will be three. So these are your two constants. Very simple. No coming toe. The second matter. So this mattered only works when the factors are distinct, very easy method, but only works if the factors are distinct. If the factors are repeated, then you use this matter because this is a comprehensive matter. This works for all type of situations. So we will use this formula for all those factors which occur only once used this formula for the maximum power of the reputed factor. We used this part of the formula. So this will be used to find a to and for all other powers off the reputed factor in our case, there is only one, but there could be more powers for all other powers. We use this formula so therefore it's good practice. Toe right. First, all the distinct roofs factors first. For example, if there are two distinct assigned constants Trudeau a one divided by first distinct plus there to the word of a second and so on. And then once all their distinct ah Constance affected are finished. Then you take the maximum power first because this formalize only used once for the maximum power and then you write all other powers in decreasing are increasing order whatever you like, and you use the third formula for all the remaining powers. So in our case, there are only two here. So let's start using this formula and you will understand It's so simple. So for a one, a one equals limit s tense were Arky Arky is the same as we have already found here they're to report their denominator of everyone equal to zero. And whatever the value off s you get is your arcade. So for anyone, we will get s equals minus two. So s tends toward minus two and s minus minus two. So it will be plus two. Then the mainframe affection, which is three years plus one. The wire did Boy s minus one Holy square and s plus two. No, make sure that at this stage, this term must be cancer. Here. If this time is not cancelling, it means you're doing something wrong. For example, by mistake, you are changing some sign of something like there. So this time must be cancel. Otherwise, if you we will be putting minus two in the next step, so minus toe will make these times zero. So therefore, these times must be cancer here. So nobody put minus two in the remaining terms, a three in minus two is minus six. Bless one and rewarded by minus two minus. One is minus three. So minus three Holy square. So this will be minus Phi rewarded by night. So this is your everyone state of it? No. Here too. Again, we used similar kind of formula. This is used to find the constant for with the maximum power workers or limit s tense toward for this case as well B plus one. Because if you equate this to zero, you will get a sequence plus one. So s stance toward one, then s minus one. Raised to the power EMS M is the maximum power of the repeated factor, which is to maximum power is too. So, um, is to, in our case, so to then to the spls one you ordered by s minus one whole disquieting us plus two. As you can see here that this term will again cancer. And no, you apply one. Put one in tow. These two terms so three into one is three plus one is 41 plus to his three. So this is your toe? No, for a three. Again, as our case one. So limit s tends toward one and know what is this case? Here is a counter which starts from two. So this game is for Constance. So a one a two a three. But this game this formula starts from two. So and it goes to the order. Whatever is the maximum power of the repeated defector. So in our case, it will start from two and there is only two because M is also to If if the maximum power waas four then we would have found the maximum power using this formula than the rest of the three constants. We will start from 23 and four. In our case, we have only one which is a tree. So we will use this one divided by two minus one factorial. And then the two minus one means the foster reverted. So the first day they were Do off. Beware the yes. Hit again. Blue minus one is one product off s minus our kids which is s minus one Raised to the power M Bitches too. And, uh, me infraction, which is three s plus one s minus one holy square and s plus two. So now again, this will cancel out here and we are left with three years plus one and X plus two. So let me find their derivative off. Three years plus one t s less one de wired it by s plus two. So this is ah fraction. So the formula for derivative of this kind of friction is we take the squared off their day nominative as plus two holy square, then denominated time derivative of the numerator deliver two of the numerator is only three minus new mediator time, Derivative of the denominator. So three s plus one the numerator and deliver to arrest plus two is one. This derivative comes out to be est into 33 years plus six three s plus six minus three s into one into minus minus three years minus one and s plus two esquire. So this Trieste and three s are cancer. Six minus one is fight so five. So instead of this, we have to put five awarded boy. So we just write down again. One step s tends toward these and this is one off course just to write one. And instead of this, we can write no for you be warded boy as plus two Holy square And no, If you port this limit one here you will get for you Be worded by one plus toe three Holy squared is nine. So this is your it to be so very simple. Instead of solving three simultaneous linear equations, you have found all three constant state of it. So I hope you find this useful and you will use this heavy side method a partial fractions in your control system Problem 10. Forced and Natural Response of a System for Step Input: Hello and welcome to my channel. In this video we will find the step response off a control system. So we have a control system. With this transfer function, we apply your step input and we have to find the daughter response of the system. The total response consist of two parts the force response and the nature response. And we have to find both of them. Then we will also see hope we can obtain the form off control system response. Just we're looking at the transfer function, so let's get started. So let us see that we have a system denoted by DFS and we apply in books which is denoted by artifice. And the output of the system is denoted by CEO. And let us say that this input is a stepping so which is represented by one to argue, but yes, So this is over stepping. So let's start with a tosser function. So the system has a transfer function equal to s plus two. The wind it by s plus fight. So this is a simple first order system which is a polar minus five and zero minus two. So if you blocked this on see, my deal may go. One tool, it is a zero. Yet this is minus. Flyers made a point here. So know when we applied this step imports, as you know, that our port is the product of the input and the transfer function. So our foot off the system she is. So this is called also Carter, dispose off the system are the old response of the system. So when we say this phone so it means what is CFS are the output of the system. So you can also find this indeed element which will do what you will do next. But if you start from the as dormant because the transfer function is always in, as do me. So this is the chance of function. So let me a place they've been put, the whole court will be ask plus two s plus why you market black bite. I want to argue. What s the step? Input. So this is the old part of the system? No, here. This is the Parthenon infraction and in order toe. Go from estimate to determine what we do. We use partial fractions and we decompose this in tow. Tow some other directions. So let's say a word about this less Beauport way as plus fight. So this is what we have to find these Constance in orderto as you will see, that at the end of this video, we don't have to find this constant without refining the constants. You can write down the four off the output response and this is what we will do. Just by inspection of this transfer function, we will be able to write that it's most of the system both in s two men are into domain. So this is what we're going to learn here. But we will start from the mathematics just to let you know that whole we find these constants and there is a video about heavy side matter which we are using here to find this constant, which is also called a cover of matter. So there is a video you can find in the list of the reduced, so there will be everything available. So what we're doing there beside method is if we have to find it, what is the denominated off a s? So we put s equal to zero. You find the verdict value and put that into this and we ignore Mr Denominator of a similarly in order to find be people that's plus five equals +20 which will give us s equals minus five s minus five into this hole. And we know that in a minute B s plus fight. So we put a finger here is also called a cover of matter. We just covered this with your finger. So this is what we're going to do so is equal to unite here has blessed to it's plus points testicle zero and we're ignoring this thing. So which will give us if I put a zero in his in this to get a would worry about fight really be well, I don't ignore this thing for dividing by s that s it was minus pipe. So what we get to you? You were toe minus y plus two is minus three. Do Hardaway minus point. It will make it. You know anybody? So this is all we get End. You know, these other two constants. So no. Here. I want to show you something that if you look at the variation of these constants, you will see that zero and the poor botel Ian Ward in finding these constants. So no, I didn't go forward now to come back to this point. So no, the airport dispose of the system equals guarded by fight less. Do you do everybody fight And this is in the esto Me know If you use the left plus transformed table from going toe to toe men, you will find that pistol fired. Worried by s is basically in time Domain. No, we're going from s domain group time with me. So the are put in time domain will be or do This is simply to fight. And plus this is simply three word by fight. It is to be forward minus fight. Be so this is the inversely plus transformer. This s domain output of the system. So no began this, But this is that sort of response off the system. And this has two components. The first, which is due by fire. If you look at EST Omen, this is s. This is wonder anyway, as which was in port. So the first part of this total response is beautiful. The input function, the step function and the second part is due to the transfer function or the whole of the system. So this is all of the system. So there is the part of the response which is due to the input function. Is God the forced response? Because we are trying toe get a response. You're trying to import something and that part of the response that is dependent on then that in port is basically a forced because we're forcing it. So this is called the fourth Response and this is Garda Natural Response. Because Paul is a characteristic of the system so that its most due to the pole are pulls off the system. If there are more than one poll, there will be more times here. So that is Skarda natural response. And that is small, which is due to the import. Is Skarda forced response. Let's say in the beginning we have this and they want to find the response of the starter function. So as you can see that this poor, the zero only affects the Boston because when we were finding the constant, we're putting this in the simulator. So the hero of the system only contribute to the constant. Only the balls contribute to the response of the system. The output of the system as you. So we can We can say that. But you can get that there will be some Boston. That's it, you say? Do you want now the estimate So there will be some constant here. One you argued by the then potus Step, step blessed. Some constant people. They do. And you are Good bye s plus fight. So this is all we can By looking at the parts of function, we can write down this equation. And from this equation, we can also write down in time domain because only this will be in time domain. So seeing time domain would be care one plus two. It is the power minus whatever is the ball, which is five. So this is whole. We can write the response straight of a s dominar impute moment in both ways, we can easily find. So it has to be have to write the input function in time domain we have. You don't get that constant. So let us do one of two exercises so you can quickly see that Hogan. We quickly find the response of a system just by looking at the transfer from one of the system. So you should be able to write down this equation by looking at the transfer function of the system. Let's just do some examples. So this is the example. So we have DFS and again our office was stepping and the CIA finished. We have to find out the transfer function of the system. There were three or four point so first likeness right down as domain. So you say now of the system s domain would be Gordo, some constant K one more deployed by the input. So the one my leg buddy, I want to do anyway. Yes. Or it is simply you want to weigh us, plus second Ballston and the 1st 4 you do, everybody. This one plus three you are by s plus for must give for do our bodies as a last fight. So this is the response of the system in excrement. But normally, when we say the output response of the system way, we're talking about in time domain, not in estimate, because in time domain it is easier for us to visualize. Tell you this right down this in your domain. So see you. He will be only here. One here. Last table days depowered minus three years. Last gate three. He is to be powered minus four over. And your four. It is to be forward minus. So this is the response of the system. No. If you have to find these constants, then you can use the heavy side matter which I described earlier. And you can find these. Constance, watch that heavy side matter video and you will be able to find the constant if they find the costume. Otherwise, this is just under warm form of a response. But this is the total response. Only this part is due to the input. So this is the fourth response and all these terms, they are the natural response of the system because these times are do toe the characteristic of the system due to the pools of the system. So therefore, this is natural and this is forced so very simple. So know what if there are more than one zeros, they will be step. But the cost function has more than 10 That's plus west plus three plus four. So even in that situation, because they put his steps, So you will get one s here. I have not read the 1,000,000,000 here because she s will be. Or do you want to argue by s into the transfer function? So if for example, there are 40 still you have only the step Input is coming here, so it will only get one constant and all the effect of other zeros will be in calculation of these questions. So that will be the effect of those zeros. Otherwise, the form of the output this is in the form of the output will be just like this one. Poster do toe zeros and all other constants. Beautiful pools. So the form of the system response would still be the same, even if there are more zeros. So I hope that after this you should be able to write down before off the response of the system and both components the force in the nature just by looking at their transfer function of the system. So I hope you find this video useful. If so, please subscribe to my channel on Hit the Bell icon so you can get the notification whenever I post. Videos on control systems are only take on other subjects. We checked each thanks for watching by for no