Designing a PID Controller Using the Root Locus Method

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In this video we discuss how to use the root locus method to design a PID controller. In addition to discussing the theory, we look at Matlab tools to enable this workflow. In addition, we demonstrate the effectiveness of the resulting controller on a real system. Finally, we discuss how this approach is generalizable to designing any linear controller.
Please ensure you have watched the following videos before this lecture:
-Introduction to Proportional, Integral, Derivative (PID) Control (TBD)
-Practical Implementation Issues with a PID Controller ( • Practical Implementati... )
-Understanding and Sketching the Root Locus ( • Understanding and Sket... )
-Using the Control System Designer in Matlab ( • Using the Control Syst... )
-Designing a PID Controller Using the Ziegler-Nichols Method ( • Designing a PID Contro... )
Topics and time stamps:
0:00 - Introduction.
3:27 - Designing a PI controller.
12:34 - Proportional only controller on a real DC motor.
15:04 - Using the Control System Designer to design a PI controller.
28:51 - PI controller on a real DC motor.
31:31 - Designing a PID controller.
37:52 - Designing a P, I, Pseudo-D controller.
49:50 - Using the Control System Designer to design a P, I, Pseudo-D controller.
58:35 - P, I, Pseudo-D controller on a real DC motor.
1:00:24 - Generalization to general linear controller design.
Download the ExtractPIDGainsFromSecondOrderTransferFunction.m function at
faculty.washington.edu/lum/Edu...
Additional videos in this series:
-Using the Control System Designer in Matlab ( • Using the Control Syst... )
-Understanding and Sketching the Root Locus ( • Understanding and Sket... )
-The Routh-Hurwitz Stability Criterion ( • The Routh-Hurwitz Stab... )
- Modeling a DC Motor with Ordinary Differential Equations (TBD)
-Introduction to Proportional, Integral, Derivative (PID) Control (TBD)
-Practical Implementation Issues with a PID Controller ( • Practical Implementati... )
-Designing a PID Controller Using the Ziegler-Nichols Method ( • Designing a PID Contro... )
-Designing a PID Controller Using the Root Locus Method ( • Designing a PID Contro... )
Overview of engineering videos and curriculum located at faculty.washington.edu/lum/Edu...
Errata:
40:58 - I should have written a real pole, not real zero
You can support this channel via Patreon at / christopherwlum . Thank you for your help!

Опубликовано:

22 июл 2024

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Комментарии : 126

@selamhendrix5252 5 лет назад

It's great to see all the connections between the topics we've been covering. The DC motor example really solidifies the theory you're discussing.

@darylfishback-duran3580 5 лет назад

very straight-forward and intuitive! glad for functions. The real-life example vs. theory is great.

@wes1588 5 лет назад

Awesome lecture, really cool to see how the adding the integrator then the derivative made improvements in the real system.

@krystoflis7157 5 лет назад

The example of a simulated proportional controller versus the real plant was a great lesson!

@metalslug97 4 года назад

Professor Lum, I am truly blessed to have found your channel because you are an absolute godsend. You are by far the best controls resource on youtube because you explain everything so clearly and effectively. Thank you so much!

@ChristopherLum 4 года назад

Thank you for the kind words, I'm glad the videos are helpful. It sounds like you are interested mostly in control theory but I also have videos on Matlab/Simulink and other engineering topics on the channel, many of which augment your understanding of control theory. Please feel free to check them out and let me know what you think in the comments. I hope to hear from you on another video in the future. Thanks for watching!

@beerman081 3 года назад

@@ChristopherLum it ould be really helpful if you could go through HOW to obtain the mathematical model of a system.

@nathanlipshutz3140 Год назад

AE511: I like how you used the PID example as a case study of a more general linear controller. Pretty powerful toolset that we're learning here!

@SMV1972 7 месяцев назад

Спасибо. Отличная подача материала. Вы классный специалист и преподаватель!!

@arshivramsahai6307 4 года назад

I wish I knew about these videos last year, when i actually had the control systems course xD. Great videos!

@milesokeefe2308 4 года назад

You are 10^10 times better than my controls instructor. Keep up the awesome work.

@ChristopherLum 4 года назад

I'm glad it was helpful. There are other similar videos on the channel, please feel free to check them out and let me know what you think. Thanks for watching!

@karthickpn450 5 лет назад

Informative video as always, Chris. Thank you.

@ChristopherLum 5 лет назад

Karthick, thanks for watching, I hope it was helpful!

@sitifatimatuszahro3874 4 года назад

thank you for your informative video. I can understand to do my undergraduate thesis.

@kaisemuw7074 5 лет назад

AE 511. I liked how the lecture progressed from PI to PID controllers to demonstrate the physical difference with a DC motor example.

@kristenleenerman1351 5 лет назад

Useful video for designing a PID controller

@edwardsanchez2331 5 лет назад

ae511, good way to show how useful Matlab can be for designing a PID controller.

@alanlee4326 5 лет назад

AE511 - These videos are amazing! The use of the DC motor example wonderfully illustrate the concepts.

@ChristopherLum 5 лет назад

Alan, thanks, it was fun to get the DC motor up and running. Let me know if you see anything odd in this or other videos, thanks.

@nanoglez9248 4 года назад

Your videos are awesom, thanks from Mexico :D you just helped a future enginer (sorry for my english

@MinSangSeong 2 года назад

This is a great lecture. Easy to understand and practical. Thank you very much

@ChristopherLum 2 года назад

Hi Min-Sang, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris

@whynotchoi 2 года назад

감사합니다~

@minhajisminhaj 2 года назад

Awesome explanation 👏

@ChristopherLum 4 года назад

In case it is helpful, here are all my Control Theory videos in a single playlist ru-vid.com/group/PLxdnSsBqCrrF9KOQRB9ByfB0EUMwnLO9o. You can support this channel via Patreon at www.patreon.com/christopherwlum. Please let me know what you think in the comments. Thanks for watching!

@arshivramsahai6307 4 года назад

Hi, sorry to bother you, where are the introduction to PID control, the Practical implementation Issues with PID control and the DC motor Derivation videos? Thanks!

@aubreydebliquy8051 3 года назад

Did nobdy tell you it's not "bodee" plot, it is pronounced "boad" as in toad. Did your lecturer also pronounce it wrong? And his teacher. Is that another Americanism as in aluminium pronounced aluminum?

@davestaggers2981 2 года назад

Very informative

@kylemathenia8591 3 года назад

Christopher, great job. I am really looking forward to the release of the practical PID implementation video. I see it is still TBD. Thanks for all your great content!

@ChristopherLum 3 года назад

Kyle, you're in luck, I'm actually working on this right now. If you're subscribed, hopefully you'll be notified when it goes live (probably in the next few weeks). Thanks for watching and please let me know what you think of any other videos, thanks.

@kylemathenia8591 3 года назад

@@ChristopherLum Wow. Awesome! I think a really interesting series would be sort of a survey of advanced control methods. I find that conceptually many advanced methods are easy to understand. Although I think there is good content out there on individual methods, I think there is an opportunity for more content comparing methods with each other in terms of strengths, weaknesses, use cases etc. I think building orientation and subject breadth awareness is really valuable. Some specific areas I don’t find content on are passivity based control and energy/power shaping. Trajectory optimization.

@stsanat249 4 года назад

so excellent training of PID controller

@ChristopherLum 4 года назад

Thanks for watching. If you are interested, here is another video showing an alternative way to tune a PID controller ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-n829SwSUZ_c.html.

@amarmail8033 5 месяцев назад

Superb.

@preetham56 4 года назад

Amazing!

@ChristopherLum 4 года назад

I hope it was helpful!

@amarmail8033 5 месяцев назад

Just wonderful man. A large number of doubts of mine r gone. Thanks a lot. And I would request u to write a book like dspguide by Steven Smith.

@khengari77 2 года назад

Awesome series thank you for contributing this effort. I wanted to ask are we going to see the introduction to PID video any soon?

@zimdollar3229 3 года назад

A real MVP

@VanWarren 2 года назад

Thank you for a very well organized and clear presentation.

@ChristopherLum 2 года назад

Hi, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris

@MS757-p3l Год назад

@@ChristopherLum Sir, can you please make a video on fractional order PID (FOPID) controller

@ChristopherLum Год назад

@@MS757-p3l Hi, Thanks for reaching out. If you have questions or would like to request a video, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching! -Chris

@dhananjaywarthe2695 3 года назад

Thank you, Sir, for an informative talk about the design of the PID controller. I've seen all the video conference control theory playlists and sir, I quite enjoy your explanation. Sir, I had queries on designing a higher-order system (3rd order). I want to design the PI controller for the 3rd control system, which had a transfer function: 1- real Zero and 3 - poles (one at origin and the other two are complexes). I have more problems with the design of the third-order system. Please, sir, can you give more information about the design of the 3rd order system.

@bigiluma 4 года назад

Hi Professor Lum. I just wanted to say that this video has taught me things that I could not get into my head before. I have a question about a little project that I am working on. I have adapted your method for designing and tuning a PI controller using the Root Locus method. I have come up with a final transfer function which I chuck into a MATLAB script and run the controlSystemDesigner command. I was expecting a similar step response to the one you have showcased at @16:00, so that it would be easy to work with it and tune the appropriate zeros and poles to achieve the design requirements. However, I get a weird response and struggle to work with it. I understand the whole process of calculating values for P and I for the PI controller with the Root Locus method, but I cannot do this without a step response that I can work with. Any advice would be appreciated. Thank you and please keep the videos coming - you're helping a lot of people out here! :)

@vaibhavsinghgaharwar1397 3 года назад

thanku you for your all great videos... sir i have few questions... 1) how to decide requirements (overshoot, rise time peak time GM PM BW and others parameters) for complex control system like spacecraft , missile etc 2) how to create controller(PID etc.) on microcontroller after satisfactory simulation result from MATLAB

@charlesokoh3373 3 года назад

Great Video Sir💯 I learn a lot on this channel; One question, “when it comes to real world application as you’ve shown, is this controlling action and/or parameters programmed into a software or hardware component for it to interface with the real plant? “

@pedrin_humilde 3 года назад

You are an angel in my life sz

@wessamahmed9577 4 года назад

Great & Useful Lecture,,,, thanks a lot for your generous effort I have a question please,,, Is using (velocity feedback) equivalent to (the derivative) part in the PID controller ?? and thank you again

@mokhaladhasan6937 4 года назад

Thank you very much for your interesting videos , but I can't find (Introduction to Proportional, Integral, Derivative (PID) Control (TBD)) !!

@TasfiqueSarwar 3 года назад

sir, where can i find ""dc miotor position control using root locus "" this video?

@timproby7624 Год назад

[AE 511] 30:52 It's interesting to see to that the integral part of the controller can actually bring the system into compliance without have the explicit dynamics that is causing the error. It seems like with the right controller components and settings, you can actually use simpler linear dynamics for a non-linear problem and still have a controller that can successfully command the system to the desired input.

@SaumikKhan 2 месяца назад

you made me love this subject and hate my varsity teachers.

@ironman5034 25 дней назад

Hi, in which video do you calculate/find out the transfer function (plant model) of the motor setup?

@cynthiamoricordova5099 3 года назад

Where coul I find the video "Introduction to Proportional, Integral, Derivative (PID) Control (TBD)"?

@MattAero 5 лет назад

AE511: great comprehensive lecture. Just wondering....is there a rule of thumb for knowing at what point your plant becomes 2nd order dominated (maybe a rule like poles that are 2 orders of magnitude greater are no longer relevant)? Or better yet, is there a way to (formulated by hand or using built-in matlab functions) determine performance metrics(PO, rise time, settling time, etc.), exactly, for 3rd order or higher systems without the need for the 2nd order approximation (dominant poles requirement) and without needing to graph the input response? It would just be nice to graphically see more accurate restricted areas on the RL plot for 3rd order or higher systems.

@ChristopherLum 5 лет назад

Great question. I'm not aware of any formalized rules for 2nd order dominant system. I've seen people use a single order of magnitude real part comparison to consider faster poles irrelevant. Unfortunately I'm not aware of analytical results for 3rd or higher order systems.

@jimzhu6315 3 месяца назад

At 42:51, the PID controller provides 2 poles and 2 zero. The -a point should be a pole.

@gitarplayer13 5 лет назад

AE511. I think there is an error at around the 40:59 mark. You said and wrote there is real zero at -a, but later in the control system designer you used a real pole.

@ChristopherLum 5 лет назад

Great catch Brad! I indeed should have wrote/said a real pole, not real zero. I tried to add an annotation to the video to highlight my mistake. Please let me know if you catch other problems in the future, thanks!

@johnyang799 4 года назад

@@ChristopherLum I noticed that as well. But otherwise really really helpful video.

@thatWMDdude 5 лет назад

AE511: thoroughly enjoyed the puns. Seeing the difference between simulation response and the practical response is very helpful. Is there a way to simulate/approximate non-linear external factors (friction in this case) as a part of the controlSystemDesigner?

@ChristopherLum 5 лет назад

Brian, unfortunately I'm not aware of any ways to take non-linear factors into account with the Control System Designer. This is a linear tool by definition so exact non-linear effects can't be modeled. That being said, there are ways to approximate non-linear effects. For example, a time delay is a non-linear effect but it can be modeled using techniques such as Pade approximations.

@alexsteahr8458 3 года назад

AE 511: Love the pun!

@jrcleeman 3 года назад

Can you please explain how you got the transfer function?

@justinhendrick3743 5 лет назад

You mentioned that the performance requirement regions on the root locus plot only apply to second order systems. For higher order systems, how do we know which way to move the poles and zeros to alter the system behavior in a particular way? For example, does the real part of a pole location influence settling time in the same direction as for a second order system?

@ChristopherLum 5 лет назад

In general, you have to be careful. The safest way is to look at the simulated or analytical step response of the system. If you really wanted to, you could try to re-derive the expressions for settling time, percent overshoot, etc. for a higher order system but it gets very messy very quickly. The easy fomulas we developed earlier are only accurate for 2nd order system. The easiest way is to just simulate the step response.

@wat_herbivore1844 3 года назад

good video. Just in need of the DC motor parameters. Can you share please?

@siphojerry4220 4 года назад

Could you please provide the other Matlab code link to get the kp ki and kd values because I can't access the code from the link you sent

@dawitgebreslassiegebremesk1668 2 года назад

Dear Christopher, I can not find the video on "Introduction to Proportional, Integral, Derivative (PID) Control (TBD)"?

@amarmail8033 5 месяцев назад

Just superb. I have no words. I request you to write a book like dspguide by Steven Smith. I believe you can write such a book. Superb.

@ChristopherLum 5 месяцев назад

Hi, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. I can also answer any questions, provide code, notes, downloads, etc. on Patreon. Thanks for watching! -Chris

@shashankkulshrestha2346 6 месяцев назад

Can we automate the process using matlab script that we are doing using Control system designer tool

@zafaryabkhan3025 3 года назад

Take the case of PI, it added one dynamic zero & one pole at the origin. Now the transfer function of PI block (c(s)) would be multiplied with G(s) & thus it will add one more pole (which is at origin) in the list of open loop poles. As we know that in root locus by changing the gain (kp in this case ) we change the location of closed loop poles which starts from open loop poles and ends at open loop zeroes or zero at infinity. Now my question is on moving the other poles or changing the value of gain (kp) in the root locus of PI why not the position of pole (which is at origin) is changing?

@rahulsylvester4715 5 лет назад

Thanks for the amazing videos. How about making videos on Non-Linear Control? A kind request :)

@ChristopherLum 5 лет назад

Rahul, thanks for the kind words, I'm glad you enjoyed it. That is a great suggestion and is on my list of videos to make in the future.

@rahulsylvester4715 5 лет назад

@@ChristopherLum Thanks a lot. Eagerly waiting.

@akulaakuni4198 4 года назад

cant open ur extract PID gains the m file..cant u reupload it?

@israelalmaraz7889 8 месяцев назад

hi, I am simulating a continuous pure PID (unfiltered) controller with parameters kp= 11.4 , kd = 3.16 and ki = 1.2, these parameters give me a desired overshoot, rise time and settling time, the idea is to discretize the PID to control a continuous system, I discretized the PID, but when I run the simulation, it's like I had two different controllers, the transient response of the system is very different, why would that be? , thanks

@abslon4772 2 года назад

Thank you! But what happend to "Introduction to Proportional, Integral, Derivative (PID) Control (TBD)"? I can not find it

@ChristopherLum Год назад

Hi, Thanks for reaching out. If you have questions or would like to request a video, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video. I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching! -Chris

@Qaidi_804 Год назад

Hello Prof, with due respect, Can you provide me the circuit diagram of DC motor with the PI/PID controller so that i check my PI controller is working well or not, or is it possible that i could contact with you i am facing many issues in designing the PI controller for AFM.

@reginaldbreyton5265 3 дня назад

How would you design a PID controller using the root locus, when the open loop transfer function has complex poles

@12turo 3 года назад

I can`t download the ExtractPIDGainsFromSecondOrderTransferFunction.m because it says this is not the page you are looking for

@johnviljoen271 4 года назад

Is it possible to do this without the control systems designer

@burakyurtoglu6113 4 года назад

did we get pole at -a or zero at -a after using pseudo D controller? And thanks for the great lesson.

@poopface011 3 года назад

think it was supposed to be a pole? The whole point was to have equal number poles and zeroes and he ended up with 3 zeroes and 1 pole...

@kobieabaidoo7472 Месяц назад

Can you present a tutorials on observers such as extended state observer, ESO, slide mode observer, SMO etc

@ChristopherLum Месяц назад

@rajsekhar38 4 года назад

Excellent videos... Can you please help me in finding Introduction to PID controller and Practical implementation issues with a PID controller

@ChristopherLum 4 года назад

I'm glad it was helpful. I'm currently working on getting that video finished and posted. Hopefully it will be up in a few weeks. Thanks for watching!

@rajsekhar38 4 года назад

@@ChristopherLum Thank you very much for your response and eagerly waiting for the videos

@naderelgohary9514 4 года назад

Please doctor upload the missing vedios very soon

@mahmoudel_dabah7946 5 лет назад

introduction to gain and phase margin video is not existed in your uploaded video, may you upload it

@ChristopherLum 5 лет назад

Hi, that is a very good observation. I'm working on this video right now and I hope to have it up in a week or so. Thanks for watching!

@mahmoudel_dabah7946 5 лет назад

@@ChristopherLum Thanks for your kind reply....really I appreciate your work

@RavindraSingh-jz8ji 4 года назад

good video, but not everyone is not following your whole playlist, someone wants to just know how to design PID controller only. Please keep that in mind.

@spiroskarpouzis4808 10 месяцев назад

Hello sir, real zero at a or real pole at a? I think there is a mistake

@sterlingg2454 4 года назад

The Matlab code link to get the kp ki and kd values isn't working, could you possible provide us with another?

@sterlingg2454 4 года назад

Actually, I can solve it by using your equations for each ki kp and kd, no worries.

@akulaakuni4198 4 года назад

@@sterlingg2454 can u share the equations?

@sterlingg2454 4 года назад

I’ll look back to my notes to see if I have it

@akulaakuni4198 4 года назад

Wow thanks..huhu got assignment to design pi and pid controller to control speed of bldcmotor using root locus method..stuck at pid haha..hope i can finish by this week..

@shaikhsumitnoor9759 4 года назад

@@sterlingg2454 Hi! Yeah, the github repo isn't available. Could you share the code for getting the tuning parameters? Thanks a bunch!

@SMV1972 9 месяцев назад

Спасибо! А если нет matlab? Как просчитать вручную?) Вот это было бы круто

@sethwhittington28 Год назад

AE511: This technique seems a lot more graceful than the Ziegler Nichols method.

@ChristopherLum Год назад

Yep, if you have a model you should use it as it lets you bring tools like this to bear.

@100MillionThoughts 4 года назад

⚡️ Tuning a PID Controller Using the Ziegler-Nichols Method | MATLAB code available ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-8MMcPLTwo_s.html

@sumitbarua8241 4 года назад

who else thought it was a large motor until he starts to attach the ball bearing on to the rotating disc?

@blownuppumpkin95 3 года назад

Shouldn't it be a real pole at -a at minute 41:00?

@ChristopherLum 3 года назад

Yes, you are absolutely correct, thank you for pointing this out. I've listed this in the errata section.

@gideonprior4842 2 года назад

Around 41:07 you say real zero at -a, but its a real pole at -a

@Minji_Hanni_Dani_Haerin_Hyein Год назад

33:26

@Minji_Hanni_Dani_Haerin_Hyein Год назад

1:01:50

@hichamlhachimi9594 3 года назад

that garbage P only controller LOL

@pnachtwey 20 дней назад

There are a couple of very important things that are neglected. If the set point for the motor changes abruptly, the control output will saturate. Servo motors to not change position in steps. Overshoot should be avoided. Where does the open loop model come from? Lum's real motor must have a lot of friction. Why? Lum must have added the friction to make it easier to control with only a PI controller. My motor has little friction, so a derivative gain is required to provide damping. Mechanical friction is not energy efficient. Something must provide damping, or it will oscillate a lot. There is no mention of where best to move the zeros. The worst part of this is the students can't see the math to do all of this as it is all hidden in the Matlab libraries.

@vaibhavsinghgaharwar1397 2 года назад

@ChristopherLum 2 года назад

Hi Viabhav, Thanks for reaching out, I'm glad you enjoyed the video. Unfortunately I'm unable to respond to questions on RU-vid due to the sheer volume of inquiries that I receive. That being said, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum as I'll be able to answer questions there. Given your interest in the topic, I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching! -Chris