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Math Help - feedback coefficient , K

  1. #1
    ain
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    feedback coefficient , K

    Dear all,

    I have an equation to solve like below:

    xdot= Ax+Bu + D
    u=Kx

    How to find the feedback coefficient K?

    A=[1 0 0 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0;...
    0 0 1 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0];

    B=[0 0 0;...
    0 0 0;...
    0 0 0;...
    0 0 0;...
    0 0 0;...
    0 0 0;...
    1 0 0;...
    0 0 0;...
    0 1 0;...
    0 0 0;...
    0 0 1];

    u=[u2;u3;u4];

    D = [0; 0; x1*x4; 0; x6; 0 x8; 0; x10; 0; x11];
    x = [x1; x2; x3; x4; x5; x6; x7; x8; x9; x10; x11];
    Last edited by ain; June 14th 2011 at 03:18 AM.
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  2. #2
    Grand Panjandrum
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    Re: feedback coefficient , K

    Quote Originally Posted by ain View Post
    Dear all,

    I have an equation to solve like below:

    xdot= Ax+Bu + D
    u=Kx

    How to find the feedback coefficient K?

    A=[1 0 0 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0;...
    0 0 1 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0;...
    0 0 0 0 0 0 0 0 0 0 0];

    B=[0 0 0;...
    0 0 0;...
    0 0 0;...
    0 0 0;...
    0 0 0;...
    0 0 0;...
    1 0 0;...
    0 0 0;...
    0 1 0;...
    0 0 0;...
    0 0 1];

    u=[u2;u3;u4];

    D = [0; 0; x1*x4; 0; x6; 0 x8; 0; x10; 0; x11];
    x = [x1; x2; x3; x4; x5; x6; x7; x8; x9; x10; x11];
    Is what you post for u correct?

    CB
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  3. #3
    ain
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    Re: feedback coefficient , K

    yes, actually i want to find the value of u. I read some of example but most of it not have D matrix just like xdot=Ax+Bu , so from u=Kx, we can find the K through pole placement or orther method and we will get the u value. But I not have an idea how to solve this equation when we have another matrix D.
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