Sliding Mode Control Part II

[@johnathonstreet619]

Great lecture! Subscribed. I hope you have more lectures coming

[@jx4864]

You explain this sliding mode control so well. Thank you so much 😊

[@jimmylu9156]

Instead of relying on intuition to explain your choice of the sliding surface in your first example, you can rigorously prove that S=0 achieves the desired property by showing that the eigenvalues of the resulting system, x_dd + x_d + x = 0, has a negative real-part, and x therefore converges to 0 asymptotically.

[@ibrahimhalilteke4399]

Dear Sir Prof. Dr. Ali Thank you for making this beautiful instructional video. I had two questions, if you could answer them, I would appreciate it. 1- When I examine different sources or videos, I see that the expression x'' is written in two different ways. I see that in some sources the term control rule (u) is multiplied by the expression b(x), while in some sources the term u is written separately, which statement is correct? 2- While writing the control rule of the 2nd or 3rd order systems, I see that the term u is obtained with assumptions, how logical is it to establish a control system based on the control rule (u) obtained with the assumptions?

[@cset]

Dear Ibrahim, Thank you for your kind remarks. Here is my take on your questions. 1) Multiplying the control u with b(x) or writing the control u separately, both methods are correct. There are many types and forms of control system design and hence there are many different ways in which you will find the expression for u. Usually, if you are a beginner, you start with linear control systems. 2) There are two main purposes of obtaining u with assumptions. First, the assumptions are taken to make the problem of designing u to become easy. Here, the care must be taken that the assumptions must not be unrealistic. Second, the assumptions are related to some realistic constraints. In this case, the options for designing of u become limited but it is something that needs to be taken into account. Overall, it is logical to make assumptions as long as the assumptions are sensible.

[@abderahmanealioua9291]

thank you so much sir it's really helpful and we are waiting more from you

[@treasaseb]

Sir, thank u for highly informative lectures on SMC...I have a doubt...is the chattering in x3 us due to control input u....will there be chattering in other states x1 x2..which are independent of u

[@cset]

Thank you for the encouraging remarks. The chattering is indeed due to the switching of the control input u. Since the rate of change of x3 is directly proportional to u, there is maximum chattering in x3. x1 and x2 will also have chattering because of indirect dependence on u but chattering will be less compared to that in x3. So the sequence (for the given example) is, switching of u affects x3 (directly), now chattering in x3 affects x2, and finally, chattering in x2 affects x1 (hence x1 is least affected).

[@treasaseb]

@@cset Thank u sir😊

[@alikanaan584]

thank u so much, such a great lecture. i hope to get the PDF of the two parts

[@menouerdjillali2358]

I need to applay the SMC with seconde ordre système define by transfert function seconde ordre

[@cset]

A second order system is discussed here kzbin.info/www/bejne/Z3_NmpKpf9B_rNk maybe its better to convert transfer function into state space and then apply SMC

[@منوعاتثقافيةتعليمية]

Dear Dr. Ali Nasir I have a question about design sliding surface function Is the sliding surface function depend on number of states or the order of the system equation? I have system with 6 states but the second derivative and first derivative. In this case how can I select the sliding surface function?? Thanks

[@cset]

There are two rules of thumb for selecting the sliding surface. 1) S = 0 must be useful in terms of achievement of the control objective. 2) The control input “u” should appear in the S_dot So, the sliding surface depends upon the states that are being controlled (to achieve a certain value) and the states whose derivative involves the control input “u”. But again the equation for S shall be crafted in such a way that whenever S = 0, the objective of the control is achieved.

[@arrow4redemption]

Thank you Prof. Please why does the first code has plus one (u = -x(2)-(-b*x(1)+a*x(2)^2+1)*sign(s);) and there is no control gain after the sign.

[@cset]

Thank you, that is a mistake. Plus one should be replaced with sign(s)-->u = -x(2)-(-b*x(1)+a*x(2)^2+sign(s)) instead of sign(s) being a multiplier of (-b*x(1)+a*x(2)^2+1).

[@arrow4redemption]

@@cset Thank you so much Prof. Please Prof., can you do one for active magnet bearing control using nonlinear controller

[@cset]

@@arrow4redemption this one may be useful for you kzbin.info/www/bejne/ona4gmWZpLF3qbssi=fdhcaqYX-wUhEo0y

[@arrow4redemption]

@@cset Thank you so much Prof. Please Prof, how can external disturbance be introduced to the active magnet bearing system to check for controller robustness ?

[@cset]

@@arrow4redemption you can add a small random number to "u". That is called matched disturbance. For example if u = -k*x, with disturbance, it becomes u = -kx+d where d is a small random number e.g., d = 0.1*randn(1) etc. As for the state space model, without disturbance, it is like x_dot = Ax + Bu. With matched disturbance, it would be x_dot = Ax + Bu + Ed where E = B

[@100rabhkr_India]

Why you dont consider the Error (Eta) when you write the equation for Sliding variable. like S= (Eta dot)+ (Lamda x Eta)

[@cset]

That is a good point. I have presented the sliding surface as a linear combination of the output and its derivative because I am demonstrating the control design for the stability problem. So error itself is equal to the value of the output. In general, however, when dealing with reference tracking problems, we use eta and eta_dot

[@100rabhkr_India]

@@cset another doubt. For sliding mode, if I chose my input with the uncertainty, for example x2 dot= x3 + x2+ (1 + theta) u where theta is my uncertainty with which the input is associated, how to chose my input signal in the form of u and v

[@cset]

@@100rabhkr_India There is no special method for such a situation that I am aware of. The main objective is to make S*S_dot

[@melesmengistu4045]

nice tutorial, please how can i design sliding surface for an anderactuated system?

[@ayoogun5004]

Please can you also teach us on writing the codes for this particular examples?... So we could learn and confirm the results by ourselves.

[@cset]

Absolutely, I have a whole playlist on teaching implementation of Control using MATLAB kzbin.info/aero/PLmwDtdfGY3-brehZArGHUeWCcq1-wHozA You can get started from here: kzbin.info/www/bejne/d5KTZYZpeMxgjMU

[@souravde6116]

SIr can you provide the matlab code or any matlab tutorial that explains the concept.

[@alisyal9570]

Sir how in last example in Sdot +Thita 2 (x1) is convert into -Thita 2 (x1)

[@cset]

That must be a typo. Keep the + sign in the subsequent step.

[@iqragul136]

Assalum o alikum Professor. Can you please make and upload lectures on Integral SMC, double Integral SMC, terminal SMC, Supertwisting SMC.

[@cset]

Thank you for your suggestion, please refer to the following playlist kzbin.info/aero/PLmwDtdfGY3-brehZArGHUeWCcq1-wHozA It has multiple videos on various types of SMC. Hope that it will be useful.

[@menouerdjillali2358]

Please l need an exemple to use sliding mode control with seconde ordre système

[@RajnishPO]

Kindly give an theoretical /non mathematical overview of the controller in general as an introduction with specific refrence of Sliding Mode Controller

[@cset]

Dear Sir, I do have an introductory lecture (non-mathematical) kzbin.info/www/bejne/iZLOnq2Xd9iiY8k but I guess it is not biased towards SMC. For SMC, I have this lecture that covers the basic concept (kzbin.info/www/bejne/Z3_NmpKpf9B_rNk)

[@RajnishPO]

Thank you very much Sir..

[@pengyoucn7847]

Sir, could you explain the sliding mode controller for electric load simulator?

[@منوعاتثقافيةتعليمية]

hello, why v is positive? and theta X2 is negative why? can you correct the lecture with one page? Sdot times S, I don't understand why S not multiplied with other terms?

[@cset]

Thank you for pointing this out. I have posted the corrections in the description of the video. 1) v is positive (that should not be an issue although taking v as negative would not make any difference in the final expression for u) 2) theta2*x1 is negative by mistake. It should be positive 3) S is multiplied with all the terms. In fact that is how we get (after cancellations) -S*sign(S) on the right-hand side. I hope that I have clarified enough. If you need more explanation, let me know.

[@منوعاتثقافيةتعليمية]

@@cset thank you very much Dr Ali It's very clear now.

[@sushantpatil2816]

Sliding surface S = x3 is also possible.. right?

[@cset]

Yes, that is possible under specific control objectives. For example, x3 = 0 ensures x2 to be constant and x1 to be linear... if that is desirable, then S=x3 is okay. But if you need all of x1, x2, x3 to go to zero, then S = x1 + x2 + x3 (for the dynamics given in example) is better because S = x3 would not work.

[@honesttalks4149]

Sir i need some assistance of yours in my research thesis?? How can I contact you? Please i need your help.

[@lifesgood5665]

plz provide code

[@cset]

added in the description of the video

[@lifesgood5665]

@@cset sor can we get ur contact

[@shamsusalehkwalli8071]

immensely helpful

[@medarametlapraveen]

sir continue lecture for solving in convergence in prescribed time.

[@raymondzhao9557]

Could you please share the MATLAB file ？ Thank you very much！

[@cset]

Even better, I have shared the videos on how to write the code for feedback control systems (including a video on MATLAB code for higher-order sliding mode control) kzbin.info/www/bejne/d5KTZYZpeMxgjMU kzbin.info/www/bejne/baDVaaSkqdmlers