Inverse function of "place function" - State Feedback Control

Hello!

Is there a function in which the value of the gain constant (K) is a paramenter and the result are the poles?

Example:

1) As it is: p1 = a + b*1i (any set point i've chosen) p2 = a - b*1i (any set point i've chosen) A and B are canonical controlable state feedback matrices (no problems here)

K = place(A,B,[p1 p2]);

K = gain of the feedback to produce the control efect (no problem here)

2) What i want to do:

[pa pb] = (place)^-1(A,B,K); I want to discover pa and pb values, as A, B and K are already determined.

(i know i can solve that just by doing the inverse eqs., but i want to know if there's any fast-usage-matlab-made function!)

Thx all.

Fávero

Answer 1

[Azzi Abdelmalek]

eig(A-B*K)

Answer 2

[Fávero]

Hi. Thx for the answer. K = [k1 k2], so

[pa, pb] = eig (A-B*K)

returns me pa = [0.9942 -0.9942; -0.1075 1] pb = [-0.0072 0; 0 -5.3855]*10^6.

I'm sorry, but i cannot see how those values works as poles for me. If you please help me providing further info, i'll be greatfull.

Fávero

[Azzi Abdelmalek]

Can you provide an example of A,B and K

[Arkadiy Turevskiy]

Take a look at doc for eig.

I think what you want is:

[V,D]=eig(A-B*K);
p=diag(D);