Standard HW Problem #1: PID and Root Locus
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- เผยแพร่เมื่อ 12 เม.ย. 2014
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A walkthrough of a typical homework problem using the root locus method to tune a PID controller. This is the first in what may be a series of homework style problems I'll cover. This is a long and drawn-out way of solving this particular problem but I hope that the background will make this problem a little more realistic for you.
Errata:
Just some random misspellings so far! Let me know if you find anything and I'll add it here.
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Brian, I just want you know that you are the only reason anybody at the University of Central Florida is currently passing our Feedback Control class. Our lecturer is terrible and you bring the only sense to the topic. Everyone knows to go to your lectures to learn.
that engine drawing tho
You are alive it is great! It was so sad not to have new videos from you for such a big amount of time.
Just reached the end of your vidoes and I can't wait for more! I'm a controls engineer (well, sorta) and your videos have helped me more than anything in school or anything I've learned on the job. Please keep making videos!
My test is tomorrow and the lecturer suddenly throws in an "oh btw, there will be questions on PID controllers" despite knowing we only learnt the MOST BASIC principle of what PID controllers do in the lab. This vid saved my bacon. Thanks Brian!
One of the very best explanations I have watched on YT! Excellent work!
Hi Brian, just want to say its nice to see you back :)
Brian Douglas Hi! first things first i am a big fan of yours and maybe all of my Indian Institute mates.The moment I started going through these videos i am not able to resist myself for next ones, I have reached your last video and maybe all of other people too and we are eagerly waiting for your next update.Just out of curiosity I wanted to know whether you have planned to put any video in these following weeks.
And last but not the least: Keep sharing your knowledge and Keep making the world more intelligent place!
Thank you Brian. Watching your videos makes control theory almost fun to do :D
Awesome video...thanks so much for all these control systems videos Brian...really love them!
Great work .. can't wait to see your future videos.
i really hope your a professor, cause this is good. oh so good. How you relate the control model to what is actually being control is amazingly helpful and makes all this solid in my mind
Welcome back, Brian!
Your videos made me very interested in Control engineering: I'm actually considering it for my MSc studies. I'll be doing my BSc thesis in the control field as well (rotorcrafts). Thanks for showing me the fun part of control engineering :)
Great! We need more enthusiastic and capable controls engineers. Especially with all the buzz lately with unmanned vehicles it's going to be important. Safety with automated systems is important and you can only get there by understanding your problem and the ways it can fail.
thank you sir u made complex world so simple................ u gave me wings...... now i will learn to fly.........
Sir please post videos as soon as possible. I see your every video regularly. And they are completely helpful in remembering for viva exams and brushing up purposes. my control systems vivas will arrive soon. please upload as soon as you can sir. thank you :)
Excellent presentation Brian, you have a great ability in conveying complex issues in easy to understand terms. If only my crusty old control lecturer back in the early 80’s when I went through University had a fraction of your ability 😂
Great thanks, very easy to follow and understand
Thank you for your clear explanation! It was very helpful : )
Very elegantly explained....thanks a lot!
amazing vid!! :) great refresher and helped to cement a lot of concepts thanks again Brian! Do you think you would be able to do a vid on State-space models in the future?
Loving your videos, they have been a big help even for my graduate level course. Would you be able to do a video on state space representations? Thanks for it all.
Hey Brian, glad to see you back on here! Sounds like you might be moving these lectures toward modern control topics. Any possibility that LQG control might be covered in a practical sense? How about H-infinity (or any other optimal control methods/design)? Thanks!
9 years ago but so good . Thanks for your videos
I definitely like the video. However, one key explanation is missing around 10:20, when the characteristic equation (CE) is re-arranged round t. Because the goal is to find t to achieve the desired closed-loop requirement, the re-arranged CE can be regarded as t being the open loop gain of the new open loop transfer function L(s) = (0.01s^3+0.41s^2+5.1s)/5. Now, this becomes the standard root locus problem, but L(s) does not contain the representation of the PID controller or the engine plant.
Great Video!! BTW, could you give some suggestions about the sequence to complete all your control system videos to have a systematic learning experience? Thanks a lot.
That last 7 minutes went straight over my head lol
Welcome back, Brian!
Beyond the actual content of the videos, I think your sketching skills are also among the best lecturers in the world. lol
Thank you for the video. Its great!
Hey Brian - welcome back. I have an interest in fuzzy logic and neural networks as control architectures. Do you plan to address these areas in the future?
This is ultra high end content. My goodness!
+Brian
Can you please talk about optimal control problems?
Thanks.
Thanks Brian, your videos are of top quality & brilliantly composed. Just a quick question: When massaging the open loop system into 1+k.G(s) = 0, do you not require G(s) to be in monic form as well? I've noticed some texts state this, but am not too sure why. If you have a quick yes/no answer that'd be great! Thanks for the video again ;)
Welcome back! exam time soon, videos will be very handy
Thanks! Good luck on your exams.
Bro you are a god send. Thank you, for your helpful videos. :) and you included Matlab which I needed help on. ;-; thanks
Holy Bode Plots! A pleasant surprise video.
amazing, keep these videos coming ;)
nice video, and we can observe that the center of mass does not change for the same system when designing a new controller
superb content
Just as a general terminology question - "Critically damped" as I was always taught, and always refer to it, is when a system only overshoots once - and then asymptotically approaches the steady-state from the other side. Damping without overshoot was called "over-damped", and multiple oscillations was "under-damped", with unending steady-state oscillations being 'un-damped'.
Where did you learn your terminology from, Mr. Douglas. And do you see an advantage to one naming convention over the other?
Mimiko Liba Uh oh, did I? I don't think I meant to if I did. Could you point me to the time in the video where I said that? I meant to say that zeta = 0.7 is an under damped system. Thanks for the comment!
Mimiko Liba I think I misunderstood your question at first. A critically damped system does have a damping ratio of 1 (so perfectly damped with no oscillation). The roots for a perfectly damped system exist on the real line. When the roots are on the imaginary axis the damping ratio is 0 and this system is undamped. What I said in the video is correct. Let me know if this is confusing or if I've once again completely missed your question. Thanks!
I hope I understand English very well, because I believe you explain it very well and very wonderful
And I also hope that when solving problems that you put points to solve then solve it sequentially
Finally, thank you very much for this work
Thanks for the awesome video!
you are the king! :) thank you
Can you make a more detailed video about how you derive characteristic equation and find value of tau? Perhaps with a system that has multiple parameters?
This is soooo good!!!
So once you get the characteristic equation into the denominator of the transfer function, you use the OLTF to find the zeroes even if the numerator is no longer equal to the OLTF?
best...can you please make some tutorials on matlab simulink basics... how to make a real life simulation environment...and it would be nice if you start modern control theories soon... i know people demand much, but you compelled us because you are too good...good to see you back....
What's the name of the font used ? Congratiulations for the work. Nice job.
Hey Brian or someone else; If you have an openloop TF that does not have the standard form, with 2 complex poles, but maybe two real poles, or 3 and a zero, how do you calculate the damping factor?
Can you do an example of unstable system that has right hand pole? Thanks a lot.
Wouldn’t the center of más be +13.7 ? My logic is that when you have poles and zeroes you substract the zeroes.
side question: how do you manage such a great hand writing , drawing and managing colors? what device are you using? how much practice? I am amazed on what you are doing here....
I think he records the drawing, and then record the explanation controlling the drawing velocity. IDK
@11:20 can someone kindly clarify why is it positive 3 in the denominator for the centroid? Isn't it n-m, and since we have no poles and three zeroes, shouldn't it be 0-3 = -3 instead of positive 3 or am I missing something?
how do you solve when you are not given the parameters for your PID controller
+Brian Douglas
When solving for where the third pole should be (15:28), the formula is (Sum of finite poles - Sum of finite zeros)/(#poles - #zeros).
Why don't we include the zero locations?
Yes, I don't understand that
because in the original denominator, there are only poles and no zeros.
Can you please explain how to design a controller for non linear time varying systems
Hi Brian,
Thank you so much for helping all of us with controls concepts. I know this is a really really old video and I don't know if you're still seeing these comments. Could you please explain how you figured that the compensated system had 3 zeros and no poles, and then drew a rootlocus with 5 branches for a 3-zero system? It seemed to me that the forward loop TF of the compensated system had 2 zeros and 3 poles. 2 zeros from the PID controller, 1 pole from the PID controller and 2 original poles. That would make for a total of 5 CL poles and 2 CL zeros
Hi, the first one has to do is write the transfer function of the system in standard form i.e. G(s)/(1 + KG(s)). So what Brian did was he multiplied the transfer function of the PID controller with that of the OL plant, then rearranged the resulting expression. If you pause the video at around 10:25, you will see that he multiplied both sides of the characteristic equation with the denominator and grouped all the terms with tau, which in this case is the variable parameter K. As for the number of critical frequencies (poles and zeros), at 10:35 you can see the standard form of the system's transfer function; the numerator is a third-degree polynomial so the overall system has 3 zeros but no poles since the denominator is just a constant. It's been a long time since you posted the question but I hope this helps anyone out there.
@@ricomorasata3227 Potentially Dumb question, but how are we finding zeros using the characteristic equation. I thought the characteristic equation gives us the poles of the closed loop transfer function.
I am trying to learn control system for a PMSM motor Position control using Cascaded torque and position loop. Could you please make some videos on motor position control topic. Thanks for posting good info on TH-cam.
Brilliant
At 14:56 how do you sub in the 's'? I can't get the same answer
U got it? I can't do it
That was a tricky problem this subject takes practice
Instead of using a transfer function, could a state space model be used?
Heyy , I have question about PID . How we can design a PID ? is it using tuning PID methods?
"First Ill set the Diesel engine transfer function", G = tf(1, [0.01 0.11 0.1]). How do you get at this transfer function? Where did the 0.01, 0.11 or 0.1 come from? Why not 5, 17 and 0.0001? I've read about control theory, had classes about the Fourrier transform, s-transform, z-transform. I've worked with over a 50 systems that can be describes by a transfer function. But I've never been able to ever relate a real system to a transfer function. How?
how could i keep a ball jumping at the same hight ?
Please,help
Can you make some videos on Digital control system?
Hi Brian,
What am I missing!?
It looks like you did not solve for the roots of the characteristic equation. You got -20.5 and +/-9.5i (at approx 11:00mins)
It looks like you ignored the 1 in the characteristic equation.
Hi Tom, I wasn't solving for the roots of the characteristic equation, I was solving for the poles and zeros of the open loop transfer function. The closed loop transfer function has the characteristic equation (1 + open_loop_system), and if I solved for the roots that would give me the poles of the closed loop system. However, the root locus plot works off of the open loop system, which was everything but the 1 +. The open loop system didn't have any poles, but it did have three zeros, one at the origin and two at -20.5 +/-9.5i. Does that clear it up? If not, my videos on root locus might help. Cheers!
OK - yes I understand now. Thanks!
when you will post another problem,thank you
This may be a stupid question but can you turn the relation a(x(t))^2 + bx(t) + c = f(t) into a transfer function?
Unfortunately no, because it is not a linear system. The problem occurs with the squaring of x(t) in the first term.
I think it is sad that students are given problems like this. In reality, I have NEVER been provided a transfer function for the plant so learning how to do system identification is a must to get the plant /open loop transfer function. Next the restriction on gains is wrong. The problem puts a restriction on the gains because root locus in only good for determining ONE gain, not three. In reality one would use pole placement to place the closed loop poles where you want. It is possible to place the closed loop poles on the negative real axis in the s-plane so there is no overshoot. It is still possible for overshoot to occur due to the zeros caused by the PID. In this case it is necessary to modify the PID so the forward gains are different from the feedback gains to place the zeros too. It is possible place all the closed loop poles and zeros to get the response you you want but the results may not be a standard PID.
One thing that NO one says is that the break away point is important.
I never use root locus. I have written many auto tuning programs. System identification and pole placement are my main tools. I don't see why root locus is still taught given there are better methods.
Now that I have thrown enough stones, Brian does do a good job of solving the problem as stated but the problem isn't realistic.
can someone explain intuitively please ? for electrical engineering, poles would represent an open cct output (infinite impendence) and zero would represent a short cct output (zero impendence) , how would that modeled on a diesel engine ?
How you are drawing the root locus? I think it's wrong. BTW great videos. Love it.
have the same question. Why does Brian decide to "crash" all the trajectories into each other, when there are easy "straight" paths to the poles. I guess it is some sort of intuition gained through experience. Doesn't seem to matter for the final conclusion though.
Hi Brian, Why did you stop to make videos?
What are dominant pole(s) and zero(s) ?
+Milan Shah The ones that are closest to the imaginary axis (i.e. less negative). If poles/zeros are much more negative than previous ones (ex. s = -100 v/s s = -3) then they can be considered negligible poles/zeros.
+Jason Angoh thanks Jason and sorry for late reply !
And if you can brief about, "Don't addition of dominant pole(s) and zero(s) change the behavior of the system as those are nearer to imaginary axis w.r.t. system pole(s) and zero(s) ? " , I will be thankful to you.
+Milan Shah The further from the imaginary axis (towards -infinity), the faster that particular pole attenuates. On the positive side (positive poles), the particular poles expand faster and faster.
Can someone explain where the 45 degrees is coming from?
The approximated value of cos(45°) is 0.7, so that's the region on the plane we want
+Maciek Makopol cos(45 degree) = 0.7
I geagled it but don't know if you can see the image
www.google.co.uk/search?q=damping+ratio+root+locus&espv=2&biw=1920&bih=971&site=webhp&tbm=isch&imgil=5AhJ8CDXIy2vAM%253A%253BmCW4yWgYW2wSmM%253Bhttp%25253A%25252F%25252Fvirtual.cvut.cz%25252Fcourse%25252Fsyscontrol%25252Fnode69.html&source=iu&pf=m&fir=5AhJ8CDXIy2vAM%253A%252CmCW4yWgYW2wSmM%252C_&usg=__ZinoGYbhyPYC9iMLPRbqo18NefQ%3D&ved=0ahUKEwjI0vepo8vMAhUSOsAKHXVKBWIQyjcIJQ&ei=8ZsvV4iWD5L0gAb1lJWQBg#imgrc=DgRWur0N1CIwkM%3A
cos(theta)=zeeta
Hey Brian, I was wondering if you could suggest books on control theory (for engineering preferably) that have a focus on the historical aspect and how its evolved to present day?
Vikram Udyawer sorry for my interference. I think the book which I`m using may fit your needs. The name is Feedback Control of Dynamic Systems from Gene F. Franklin. It covers all the control theory and presents a little bit of historical bakground at the end of each chapter.
Hope it helps.
Best Regards.
Did you mean zero every time you said pole after 12 mins?
Zeros of the characteristic equations -> poles of the transfer function ;)
I got the same issue !
Sir i really appreciate your work your lecture are just awesome . But i have a suggestion can you please slow down the speed of you teaching i think you are too fast to catch for beginners .
Thank you for lectures
wow ..!!! :)
You found a pole (8.7i -8.7)after stating there were not poles. Please explain.
can i reach you through email? I need some help regarding my masters thesis...!!
Good video but math is wrong, chiefly the trig mathematics. Sin(75)/13.7 is not = sin(60)12.2