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How to choose the desired poles for this system[MIMO closed system] (Controller and observer design) ?

Asked by HAITHAM AL SATAI on 31 May 2019
Latest activity Commented on by HAITHAM AL SATAI on 31 May 2019
Select the desired poles according to your requirements. If possible, calculate the feedback matrix K to place the poles to the desired poles. Could I get help By suggesting any poles or the proper way to choose them for the system in the below picture?.

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1 Answer

Answer by Raj
on 31 May 2019
 Accepted Answer

Your problem is basically a set path tracking problem.
Capture.JPG
In you case the 'r' is nothing but 'v' and N is the third matrix given in your system equation. You know where you are (x) and where you want to go (v). Now basically HOW you want to go is what will determine your desired pole locations i.e. your system's performance criteria/timing characteristics. This generic plot should help:
Capture.JPG
Few other generic guidelines (available in literature) that you can keep in mind are:
1) Do not choose the closed loop poles far away from the open loop poles. Otherwise, it will demand high control effort.
2) Do not choose the closed loop poles very negative. Otherwise, the system will be fast reacting (i.e. it will have a small time constant) In frequency domain it leads to a large bandwidth, which in turn leads to amplification of noise.
Hope this helps. Good luck!!

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@Raj I didn't get it too much Sir. This is a closed loop system and When I want to show the characteristics like troubleshoot, rise time I have to choose poles. I tried with many poles I got the troubleshoot either zero or Inf. If you were in my place with any poles you start.

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