Control: Model Reference Adaptive Control (Lectures on Advanced Control Systems)

Model reference adaptive control (MRAC) is a control technique used to regulate an uncertain system's behavior based on a desired reference model. It involves comparing the state/output of the system being controlled to the state/output of a reference model, and then adjusting the controller parameters to minimize the error between the two. This video will teach you MRAC.

[@MAjmal-qc8gb]

One of the best of teachers, particularly for researchers, you are the north star

[@tyucelen]

I appreciate your kind feedback ☺️🙏

[@MAjmal-qc8gb]

@@tyucelen I was struggling to find the gap as I have recently started my Ph.D., but you have helped me to get a new guideline on how we can use adaptive controllers in power systems; I want to know if it is more complicated to implement reference model-based adaptive controller as compare to reference point based.

[@sa1dana]

this is a concise and gentle introduction, thanks!!

[@metehangul1164]

Thank you for the clear explanations and presentation which I found really helpful for me to get started with MRAC. Im voting for the "Transient Performance Recovery".

[@tyucelen]

Thanks Metehan. Yes, transient performance recovery is on my top list as MRAC designs can have unpredictable learning performance especially when they are first turned on.

[@anneoni691]

Dear professor, thank you for your videos, especially on nonlinear systems and adaptive control. it is changing lives. Kindly make a video on lyapunov equations and quadratic regulators. thank you.

[@tyucelen]

Thank you very much! I appreciate the feedback. Linear Quadratic Regulator video will be released on April 10 and a Matlab example study will be released on April 12 on this topic. Lyapunov equation is a great suggestion. Just to clarify: About Lyapunov equation, do you want to understand A'*P+P*A+R=0 equation?

[@anneoni691]

@Tansel Yucelen yes professor. Also a Matlab coding example of adaptive control is highly requested too. Thank you.

[@thanhlephuong7687]

​@@tyucelenGreat! Please

[@lyapunov8972]

Hello Professor, thank you for producing videos on these interesting control engineering topics. The topics you present are on point. For me, this channel is currently the most interesting in the field of control engineering on KZbin. The programming examples are very helpful for a deeper understanding. I would be happy to see videos on the topics "Transient Performance Recovery" , "Enforcing Performance Guarantees". I would also be interested in the topic of LMI for stability studies of gain scheduling controllers. What problems can occur when the gain scheduling parameter is the controlled variable, especially for very dynamic systems? Many thanks

[@tyucelen]

Thank you very much :) I will try to make videos on transient performance recovery and enforcing performance guarantees. I will first post a video on MRAC example in Matlab on April 14th. About gain scheduling, check this video please: kzbin.info/www/bejne/iWbcnaOMibN9m68

[@daredevil652]

digital control application example especially for embedded systems would be so informative. generally one may not easily apply these theories to any device such as microcontroller. How do we program considering practical implementation issues. It would be so helpful doctor. Thank you for perfect video giving the essence of the subject👍

[@tyucelen]

Good suggestion, noted ;)

[@leinadshAlpha]

Great lectures! You opened me to the possibilities of adaptive control! I'm custom to work in a S-domain /Z-domain representation, and not SS representation. I especially use Z domain because I implement the controller in FPGA. Do you have recommendation/ references on how to apply these method in the Laplace domain? thank you again for the lectures.

[@daredevil652]

Doctor, as far as i know we re using time domain analysis and design for model reference adaptive control here. In addition there are some books that use frequency domain, Laplace, anaylsis and design and it looks scary :) when i try to follow it. when to use each of them? I think we consider here the case thatuncertainty is in the dynamics what about we have uncertianty in the input part B matrix as well. by the way i am voting for transient improvement video :) thank you again best wishes

[@tyucelen]

Thanks for this comment. I will try to post a video on transient performance recovery. About the consideration on the uncertainty in the B matrix, please watch this longer video: kzbin.info/www/bejne/mWq5qJSJetRoqpo - It also covers this case and presents a more in depth lecture on MRAC. Finally, about frequency domain formulations, it is possible. Yet, most modern adaptive control designs these days follow a state space approach similar to I do in this video. I hope you will find this reply helpful.

[@daredevil652]

@@tyucelen thank you hocam

[@user-jk6pw8fl1y]

Thank you! I would like to inquire about selecting a reference model. For instance, if I derive a model through system identification, with force as the input and displacement as the output, within a spring-mass-damper system context, could this model serve as a reference model? While configuring, I noticed that both the reference input and output seem to share the same physical properties (e.g., displacement). However, in a spring-mass-damper system, the input is typically force, and the output is displacement. How should I approach designing the reference model? Thank you in advance for your guidance.

[@suleozkurt1819]

Is there an example available where the nominal control input is generated by a PID or PI controller to track a reference input? I would like to validate my calculations for an adaptive comfort mode of flight vehicles? Best regards Süleyman

[@tyucelen]

I will post about this soon. Stay tuned. If you want to learn about this now, you can check: onlinelibrary.wiley.com/doi/abs/10.1002/047134608X.W1022.pub2

[@suleozkurt1819]

@@tyucelen Thank you very much. I would like to buy the book, but there is actually a buying stop at my University due to changes in the financial system. I am interested more in the derivation of the adjustment mechanism for a given control architecture such as PID control architecture. I hope you will post something regarding this. Probably I will buy your book by my own. Best regards to Florida from Stuttgart, Germany :) Selamlar Süleyman :)

[@suleozkurt1819]

@@tyucelen I actually tried to implement this for a PID controller as nominal control input. But I am unsure how to handle the derivative part. Do you have literature or suggestiongs regarding that? Best regards Süleyman

[@tyucelen]

I will post a video tomorrow morning, where PID is used as the nominal controller@@suleozkurt1819

[@suleozkurt1819]

@@tyucelen thank you very much :)

[@ivanfurlan6544]

Hello Professor. I have a question. dV/dt is a negative number since R>0 (excluding e=0). So why it is necessary to use Barbalat's lemma? Isn't R>0 enough to imply V->0 for t->inf? Thank you

[@tyucelen]

It is not enough. To understand this point, please watch kzbin.info/www/bejne/fl7Yq4B9prF-irc 👀

[@ivanfurlan6544]

I watched the video. My understanding is that if R>0 (like in this video about MRAC) then we are in the case 2 of the Lyapunov video. So we should have aymtoptic stab. without the need of any other check. Where am I wrong? Thanks for your help.

[@tyucelen]

@@ivanfurlan6544 So, V depends on e and \tilde{W}. But, dV/dt only depends on e according to dV/dt=-e^T*P*e. Since it does not depend on a quadratic term involving \tilde{W}, the best we can say is Lyapunov stability/boundedness. If we have had, dV/dt=-e^T*P*e-\tilde{W}^T*\tilde{W}, then you are right about asymptotic stability. But we only have dV/dt=-e^T*P*e ;)

[@ivanfurlan6544]

Thank you 😊

[@berkinan1496]

Hi sir. How can i find to “K2” for Bm? 5:58

[@tyucelen]

Please check 5:30 of this video: kzbin.info/www/bejne/e4jId6upmrppnZY&lc=UgwdP1drExLYObgzBPB4AaABAg

[@daredevil652]

hocam, could you please recommend some books and other materials in order to gain a better insight about adaptive control and its mathematical background both in theory and stability proofs

[@tyucelen]

One of my personal recommendation is the adaptive control book by Kevin Wise and Eugene Lavretsky 👀

[@BTanControls]

Hocam, here we set up a control law that guarantees the convergence of the error dynamics to 0 and compensates for the uncertainties, but did these control parameters converge to their correct values? Is it possible to set up a control structure that can guarantee this as well? It would be great if there is a video about LQR, by the way, iyi çalışmalar 🙂

[@zzZ-xxX-ccC]

In general, they cannot unless the PE condition is satisfied.

[@tyucelen]

Not necessarily. As mentioned, it requires Persistent Excitation (PE). Check this out: www.tandfonline.com/doi/pdf/10.1080/00207178708933715 as an example. I will post LQR video by the way next week. Thanks :)