Compute and Simulate Linear Quadratic Regulator (LQR) in MATLAB for Nonzero Set Points

#controltheory #controlengineering #control #optimalcontrol #pidcontrol #matlab #matlab_assignments #matlabsimulation #programmingtutorials #matlab #matlabsimulation
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The post accompanying this video can be found here:

In this video and in the accompanying post, we explain how to simulate and compute Linear Quadratic Regulator (LQR) in MATLAB. We use the MATLAB function lqr(). We explain in detail how to compute the feedback control gain and how to simulate the closed-loop system.

[aleksandarhaber]

It takes a significant amount of time and energy to create these free video tutorials. You can support my efforts by making a PayPal donation or by becoming a Patreon:

[NoNameFound--years-ago]

thanks for the video, just a small and a quick tip, in case the LQR is used with set points that are not zero, it has another name based on it's nature in this case and that is LQT ( linear quadratic tracker).

[aleksandarhaber]

The post accompanying this video can be found here:

[hitman]

Hi .. an awesome tutorial on the LQR controller. Can you also suggest some more references to select the Q and R weighting matrices for the best optimisation.

[biteraman]

Hi sir, I have no idea how I stumbled across your channel but it has certainly increased my curiosity and interest in control theory. I'm currently a student from india and am looking to get myself into learning control theory. If you could advice me on how to start for an absolute beginner and work my way through intermediate and advanced concepts. I'm looking to get started with a strong foundation and basics. Thanks in advance :)

[sohaibullahzarghoon]

hello, nice video but one question, if we add integral action to the lqr control how would the close loop system code in Matlab.

[chengmao]

Hello sir, here is a question. Since Ud is only the leat square solution, it can not guarantee AXd+BUd = =0. Then the dot of X is not zero at final. Could you explain this?

[kevingeraldsitanggang]

Excuse me sir, i want to ask another question. If i want to control the rpm on dc motor using lqr control. What i want to ask is :

1. How to control the speed steady on 500rpm?
2. if we got the optimum gain matrix K = [10.648 415.01](after getting the dc motor state space and using lqr = (A, B, Q, R) function on matlab) what is the X1 and the X2 to control the rpm of the DC motor?

I hope your response ASAP sir. Thank you

[kevingeraldsitanggang]

Excuse me sir, i want to ask another question. How do we know that X1 and X2 from the state are the distance from the equilibrium (X1), and Velocity (X2)? how do we specify X1 and X2?

[zachdaniel]

I love this video and it's extremely helpful! I have a question though: what if my desired state is not a constant value (like in this case a position of 3 and a velocity of zero), but instead a function of time, for example 4sin(t)?

[kevingeraldsitanggang]

Excuse me sir, I want to ask how do I use the matrix value K? Because the results of the LQR control search will produce the matrix value K with the matrices order 1x2, but I don't understand what the meaning of K11 and K12 on the matrices