# Thread: feedback coefficient , K

1. ## 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];

2. ## Re: feedback coefficient , K

Originally Posted by ain
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

3. ## 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.