Yes.. this is a homework-- I think I've figured out part of the problem but
can't find any info on how to do the second. I would appreciate a hint or
clue..

The system:

A = [0 1; 1 0] B = [0; 1]

Q = [q 0; 0 q] R = [r 0; 0 r]

I have to solve the problem symbollically.

I have determined the P matrix, and Kc as a function of (r,q) r,q undetermined constants

I have

Kc = [ g g]

where g = -1+ sqrt[1-(q/r)]

and P = [w f; 0 f]

where:

w = r(1+sqrt(1-q/r))-q f = r(1+sqrt(1-q/r))

How can I find omega and zi for the closed loop system?

I do not know for certain if my expressions for P matrix and Kc are correct or not.

Perhaps a better question is can I feed matlab symbolic expressions into it's LQR function to check my work? I tried using symbolic math to compute all of this in matlab, but had some troubles since I'm not that familiar with symbolic package in matlab.

Now part of the problem is to compute damping factor and natural freq. The prof didn't give us ANY notes or info on how to compute these values for an LQR design.

Thanks,

Bo

The system:

A = [0 1; 1 0] B = [0; 1]

Q = [q 0; 0 q] R = [r 0; 0 r]

I have to solve the problem symbollically.

I have determined the P matrix, and Kc as a function of (r,q) r,q undetermined constants

I have

Kc = [ g g]

where g = -1+ sqrt[1-(q/r)]

and P = [w f; 0 f]

where:

w = r(1+sqrt(1-q/r))-q f = r(1+sqrt(1-q/r))

How can I find omega and zi for the closed loop system?

I do not know for certain if my expressions for P matrix and Kc are correct or not.

Perhaps a better question is can I feed matlab symbolic expressions into it's LQR function to check my work? I tried using symbolic math to compute all of this in matlab, but had some troubles since I'm not that familiar with symbolic package in matlab.

Now part of the problem is to compute damping factor and natural freq. The prof didn't give us ANY notes or info on how to compute these values for an LQR design.

Thanks,

Bo