hinfsyn controller not reducing error

Question

toolazy2care 2021-6-9

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/851615-hinfsyn-controller-not-reducing-error

hinfsyn_work.m

Hello everybody,

I am currently getting into H-infinity synthesis. I implemented the synthesis procedure for gain-scheduled LPV-controller for discrete-time systems by Apkarian et al., unfortunately the controller did not behave as expected. So I tried Matlab's hinfsyn() and basically encountered the same problem, which is that the controller does almost nothing. This leads me to the conclusion that I am doing somethin wrong when setting up my control problem.

For starters I wanted to implement a very simple tracking problem, i.e.

I chose P to be a simple second order SISO system:

The control system must be provided in the general representation (described here)

In my case

, i.e. the performance signal to be minimized is the control error, and

, i.e. the measurement vector to the controller is the control error, so i defined P as

with

as above. The synthesis with hinfsyn() returns a controller with performance

. However, inspecting the step response of the closed loop system (w --> e) shows, that the control error is not reduced at all:

I assume I defined my control problem wrong, but can't see how. A working example is in the file attached to this post, I am really thankfull for any ideas on this.

Cheers