Designing a Lead Compensator with Bode Plot
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- čas přidán 21. 05. 2013
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This video walks through a phase lead compensator example using the Bode Plot method.
A great reference to read if you're interested in learning more on this topic: teal.gmu.edu/~gbeale/ece_421/c...
Errata:
Around 7:00 I added an additional '+1' in the denominator of the Ess equation. The denominator should be 0.2s^2 + s + k.
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Thanks for the comment! My background is dynamics and controls in aerospace engineering from university. But the majority of my working experience is with satellite guidance, navigation, and control.
You're an amazing teacher. And video editor. The fact that I don't have to wait to see you write something down, and you're writing it down as you're saying it, along with one fluid document and nice colors, makes this series amazing. Thank you so much
I just realised I'm never impatient and skipping forward because he is always going at a great pace. The editing really is spot on
Brian, I am a ME grad student with one of my concentrations focused on controls. I just want to say without your videos I would not fully understand the concepts that are being fully covered in class. Thank you very much you are awesome!
120k views and I'm responsible for at least a half of them
Thank you so much for posting these videos! On behalf of a large portion of the UBC engineering students in the control system class we are soooo grateful!! You are awesome!!
wow 8 years down the line and you're still as amazing as ever. You have my respect
I just want to say, thank you for all of your videos. I'm taking controls this summer and it has been a very fast pace class to be in. Your videos and step by step instructions have made studying 10x easier. Thank you!
This is more of a trip than a video. Really solid knowledge you've been putting out man!
Brian , if there is an equivalent of the oscars for control engineering you should get an oscar for this a series of videos . These videos are a masterclass in control engineering !
Wonderful video! I have been struggling with compensator design for a while now and this is a tremendous resource.
Thank you so much, you have told me everything I need to solve my projects at Faculty. Keep making videos like this one. Best regards. From Mexico
Really excellent Brian ! You’re videos are awesome!
all of the videos are very helpful for my exam
super big thanks Brian
Not only have you saved my exam, you got me like the subject too. Big thanks
Hello again! Yes you are correct it is obvious from the graph that the DC gain is +6dB :-) Thanks for pointing that out. I'll add an annotation to correct it. And you are right that you wouldn't have a gain crossover frequency in your case. And that means that your system (assuming this was a Bode plot for an open loop system that you were planning on closing) would have infinite phase margin! Or no matter how much delay the system had it would still be stable.
Brian, thank you so much for this video, really concise and informative.
Thank you.You saved me.I had a project about this but the lecturer told us to find out by ourselves how to find the compensator.
You are the best. I got this so fluently. I wish we had prof like you.
Man, you really deserve that money on patreon, i will start to danate, you're so good in this!
Your videos are fantastic, I am currently doing my maters in Controls Engineering and all we do is complex math to solve these. Which takes away from the application and process. Thank you !
TOP tier videos Brian!
thankyou very much for this good explaination. i have to translate a little here and there to the way my teacher thought me but basically what he explains in 6 hours., you explain more clearly in 15 minutes! so thanks for that!
Once again you saved my bacon on a control systems assignment. Awesome video. Awesome.
Dude do more of these! so helpful
man your are awsome, thank you very much. you explain better that a lot of professor I had
You can use the command margin(sys) in the command window to bring up a Bode plot with the gain and phase margins in the title. Another way to show margins is to type bode(sys) and right click on the graph, -> Characteristics, -> All Stability Margins.
Thanks for the example. I always need an example to understand anything I am trying to learn.
i love this content. thank you so much!
Thank you for your elaboration!
Thank you SOOO much !! This video helped me a lot :)
Awesome video man! Thank you!
Nice i'm about to start electrical soon and watching is helping get a grasp on whats ahead so thanks!!!!
Thank you Brian
Super helpful! Thank you so much
Best video i ever seen for control system 🔥🔥🔥🔥
hey you referenced a professor at my school! awesome!
Very good lecture man
THIS IS GOLD!!!
You kinda sound like Ben Wyatt from Parks and Rec, which is awesome btw
Thanks for making these videos they are superb!
Amazing job👍👍 .. thanks alot
Oh my god could you please teach my university professor how to teach the course? You are just amazing
amazing lectture!
i think you meant to say +6dB:) Awesome videos BTW.
@ 3:33 for other's reference :)
thank you it' very helpful
you are the best !
Excuse me. I have a comment.
Brian Douglas.
You're an American hero.
Thank you Brian! The reference link in the description seems to be dead though.
Also, the -3dB gain, which can be called the bandwidth of a system, is the frequency at which the output signal is sqrt(2)/2 times smaller than the input. This is traditionally thought of the as the frequency above which the system effectively attenuates the signal so much that it doesn't pass it through. Of course there is a little attenuation at lower frequencies and some passing at higher frequencies but it gives a good measure. So if your signal cut all gains in half at all frequencies ...
Hi Brian, Thanks for the great lecture! You mentioned some disadvantages of adding a double integrator to the controller design to get zero Ess. Could you please justify those with an example if possible?
Did you plot the bode plot for Plant G(s), or did you include K/s as well while plotting?
Brian, the lead compensator has anything to do with type 2 compensator used in Power Electronics Control, for example?
hi, Brian, one more question: how do we determine phase margin requirements if we only have some settling time specifications?
Hey Brian. Gain Margin and Phase margins are defined for the "closed-loop" using the "open-loop transfer function's" Bode plot. And for the finding the bandwidth we need to see the bode plot of Closed-loop transfer function. But in the video (at 3:36) you mention the Gain margin, Phase margin, and Bandwidth on the same bode plot. I think Bandwidth should be found from the Bode plot of the Closed-loop transfer function. Just a thought. Could you please help me with this question?
Is it possible to go with step input instead of ramp input, and leave the system as type ( 0 ) ?? which means without adding an integrator ?
seriously good work, recommending you to all my friends.
Brian's mentioned a couple of times that component values become too big or too small to be practical, can someone give me a resource that shows how you would select component values and actually implement a continuous controller?
at 6:57 you have 0.2s^2 + s + K + 1 in the denominator. When I do the math the 1 is not there. Am I doing something wrong?
Im 6 years late but yes, he made mistake. He mentions it in the description box.
@@aki_gunting4644 Better late than never. I had the same question.
amazing!
Hello! Thanks for great tutorial. if there is also requirement on settling time. should we just change Wm?
where ts = 3pi/Wm
This makes so much more sense now then only in the time domain. xD
Your videos really are incredible. Extremely informative, clear and easy to understand.
Just makes it so blatantly obvious how backwards our higher education system is. We are taught by people who don't know how to teach. Most of my professors may be extremely knowledgeable in their field, but their method of conveying information and teaching is stale. And that is because, unfortunately,, our system favours those with more publications rather than ability to teach. The primary interest and focus of my professors lies in their research - lecturing to them is a thing they do on the side. They strive to improve their research and produce more publications, but few of them strive to improve their teaching methods.
Dear Brian, tnx for the video, as a question:
Is this problem (we cannot add more than 55 deg of Phase Margin using lead compensator, otherwise the components become unrealistic and big) also includes digital implementation? Because in digital control, we do not use capacitors and opamps anymore, and therefore the implementation of phase margins larger than 55 might be easy.... what is your opinion about this?
How did you get wm to equal 22.2?? Thank you for all you help! I love your videos.
Based on the color he used (yellow) to write the phase margin he chose, I assume he also chose wm at that value. If I'm not wrong, usually there are constraints, like the sensitive of the closed-loop system to variations, that will guide us to chose the right value for the wm frequency. Please someone correct me if this is not correct.
Great instructor....Slute You Brian
Brian Hi , I am an Electrical student , I really appreciate your videos and work your are doing , BUT can you please sort and number all your lectures in order , so when you recall in your particular video(some others , when you say for e.g. "in the previous video") we could easier find it .
Thanks again,
Ron from Boston , (Ma)
.
@Brian Douglas Is the Gain @Wm in dB or is this the K-Factor? And is this Formula really correct?
Hey brian, I have question about finding the wimax for the phase lead. Coul you elaborate on that more please.
You could invert colors and print in pdf your classes! Would be great for study have all that you write in paper =D
By the way, congratulations for your classes! It saved my semester in control.
Greatings of Brazil!
I'm not familiar with the lead compensator equation you used in solving your example. can anyone tell how it was derived? I only know the equation presented in the previous video, the one with wz and wp. thanks in advance :D
Brian , say you have a particular piece of hardware , how do you derive the transfer function for the plant . You assume the transfer function for the plant but how can this be derived experimentally ?
I work with a system that is a PI controller and we use lead and lag to tune. It has always confused me why the lead and lag don't cancle eachother out. Do you have a video that explains use of both lead and lag in the same control loop or can you make one?
Hi Brian, I'm a teacher, and really fascinated me the tool you use to make your presentation, I would like to know what program or tools do you use to produce them??
thanks you so much. I got a weird question, what if the reference signal is 0? For example we want hold a rob on a moving car always straight up by a motor on the bottom of the rob and thus the reference is 0 degree
Could you add videos for compensator design using matlab or could you provide the codes in the description below. It would be great!!!
Does that changes the transient response,that we have seen in lead compensator using root locus?
What is your background if you dont mind me asking? Very interesting videos!!
Hi everyone. Why in 7:15 has been taken the open loop function G(s) to project the regulator for closed loop function ? Is the bode diagram in 12:43 belonging to closed loop function ? Thanks
Thanks for doing these videos Brian they are awesome and very helpful! I was wondering though how did you derive K > 49?
6:30
Brian, At 3:35 in the video, you say DC gain is about -6dB, did you mean to say positive +6dB?
That's so cool! Could you tell me what subjects you feel would be the most important for me to grasp during uni, in order to be successful at space engineering?/Do you have any advice for becoming a succesful aerospace engineer :)
Very strong and very dense video. I find my self not able to absorb the amount of info in one video in single session.
Hi
I am designing the lead compensator for the 12V to 5V buck converter when i draw the bode plot of my buck converter the phase margin curve is touching the -180 an any point how can i find the crossover frequency.
help , i dont understand. for the servo motor system , if gain is negative, this means input>feedback amplitude? but what is amplitude stand for in servo case? isnt frequency is the main concern (to change the speed)?
You're an amazing teacher.....Really thank you for sharing the videos....I have a doubt....K > 50 right?
First of All Thanks a lot for the videos. I really admire your effort and I'm very grateful for these lectures. At 6:54 Step 2, Where's that extra 1 (adding with K) in the denominator is coming from ( right most equation in white colour), when trying to find the value K.
You are the best
There is a disconnect where you write the equation for the lead compensator in a different format . How is this equation derived ?
Hey Brian. At 6:59, shouldn't the equation be (0.2s^2 + 1)/(0.2s^2+s+k)? how comes there is an additional "+1" in the denominator?
Im 6 years late but yes, he made mistake. He mentions it in the description box.
@@aki_gunting4644 well I am 8 years late but thanks for your comment. I thought that I made a mistake somewhere when I try to calculate myself.
@@aki_gunting4644 Thank you, I was wondering the same.
Thank you! Was about to comment, been wracking my brain with finding out where that '+1' came from. Glad to see i'm not alone.
Used both Lead compensator to further improve 10% of current phase margin of the response.
(You can used Scilab to draw the bode plot).
Hello and thanks for the video, at 9:43, you write the upper cutoff freq. eq. and marked it on the lower side on the phase plot, and you marked the upper side for the lower cutoff, shouldn't it be the reverse ? :)
Hello Ersin, you are quite right! I accidentally called the upper cutoff frequency the lower one and vice versa. I placed an annotation in the video there so others aren't confused. Thanks for catching that and pointing it out.
When simulating by matlab, I found that by adding many many lead compensators, like 7 compensators, can meet almost all requirments of a system, but is there any cost to add too many lead compensators?
There's a subtle difference between the two ways I presented the data and so I can see now that it is very confusing. In this video I am talking about the steady state ERROR to a ramp input. If you have a type 0 system with a ramp input the final ERROR in the system will be inf, which means your system does a poor job of tracking that input. In the other video I was talking about the steady state value of the OUTPUT, not the error. In a type 0 stable system the final output is 0 to an impulse.
Thank you. I've posted a video on how I make a control system video just for that purpose. Just search for that video title with my name and it should come up. I hope your own presentations turn out well!
Are you using your mouse to write all this???? If yes, I am in complete awe.
Can you make some vides on filters area? kalman, particle filter.. Thanks! Keep working on this beautiful classes!
Whats the numerical method to find the variable T? and what does it signify?
at 12:10 the value of wm is selected as 22.2 rad/sec how it is selected and second thing how is this table over a2 id built
Too late but might help some other people - you can find that value by calculating the extra gain:
extra gain = 20*log(1/sqrt(alpha))
and then finding its corresponding frequency in the bode plot of the uncompensated system :)
@@666blablablabla666 Is alpha a2?
When we use phase lag and phase lead method in bode plot to design compensator?
Hey Brian,
I think you have an error in the phi max relation w/ Alpha equation at 10:50. it should be:
phimax = sin^-1(1-a/1+a)
no because he uses a > 1
why to add to lead compensators for phase margin above 55degrees ,how to manage gain margin along with pahse margin in lead compensator. pls help with these asap..
I have a linear system O(s)/F(s) = -alpha/(s^2 - beta^2), where alpha = 6 / l(4M+m) and beta^2= (6*g/l)*((M+m)/(4M+m)). M= 2 ; m= 0.1 and l=0.4 . What kind of compensator should I use? What is the compensator value? another parameters I should know? how could I know the response is satisfactory?
Thanks
Dear Brian, Thanks for sharing such a nice and easy way presentation.
1. Can you correct me that in the first 2 steps you actually introduce an Integral I controller by placing the pole at origin and adjusting the required Gain "Ki" ?
2. Can we say a lead compensator is actually a PD controller ? if so then you first introduced Integral controller and then PD so would that mean it is indeed some how a PID controller design video ?
3. Can we say PD = Lead compensator, and PI = Lag compensator so they are just two different names of the same controllers if not than what are the difference actually ?
Thanks
Regards