How to choose the desired poles for this system[MIMO closed system

Illustration
HAITHAM AL SATAI - 2022-03-23T12:25:36+00:00
Question: How to choose the desired poles for this system[MIMO closed system

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

    Profile picture of Prashant Kumar Prashant Kumar answered . 2025-11-20

    Your problem is basically a set path tracking problem. 

     

    observer design

    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:

    observer design

    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.


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