H_infinity controll

Hello,

my task is to design a H_infinity controller for a ss-model. I have all matrices A,B,C,D an the only goal of the controller is to stabilize the system arround the 0-vector with a sinusoidal disturbance.

My question is, how do I figure out my P-matrix ? So how do i have to set my weighting filters? How can i simulate it in simulink ?

This is my Simulink model of the plant, and I have allready linearized arround 0. F ist the iput for my disturbance and tau ist my input for u. On the right side you can see alle the 4 states.

These are my differential equations:

So from ther I got my linearized SSM:

This is what I got so far, but the Matlab documentation could not help me with the H_infinity-controller

Thank you for your help!!

Manuel

[Alon Brook-Ray]

@Manuel Hess , can you please upload the simulink/matlab file/s of this controller of yours?

I know that 4 years have passed since this post of yours, but your files can help me in my project.

Thanks!

[Umar]

Hi Manuel,

Your task is to design an H_infinity controller for a state-space model with given matrices A, B, C, and D and the goal is to stabilize the system around the 0-vector in the presence of a sinusoidal disturbance. Also, you have specific questions about determining the P-matrix, setting weighting filters, and simulating the system in Simulink.

First, let’s figure out determining the P-Matrix, which is a key component in H_infinity control design and represents the desired closed-loop poles of the system. In order to solve this, choose the poles based on the desired system response, stability margins, and performance requirements. Then, use the hinfsyn function in MATLAB to compute the H_infinity controller. This function automatically determines the P-matrix based on the system and weighting filters. For more information on this function, please refer to

https://www.mathworks.com/help/robust/ref/dynamicsystem.hinfsyn.html

Now, setting weighting filters can be achieved by defining your weighting filters using the w1 and w2 parameters in the hinfsyn function. These filters should be chosen based on the frequency characteristics of the disturbance and the control input and to simulate the system with the H_infinity controller in Simulink, you need to implement the controller along with the plant model which you already have done and then use the ss function in MATLAB to create a state-space model of the closed-loop system with the H_infinity controller. For more information on ss function, please refer to

https://www.mathworks.com/help/control/ref/ss.html

Please let me know if you have any further questions.