How to get the desired range of eigenvalues of a control system?
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I want to solve the control system with the desired range of eigenvalues. The control system is given in simulink as follows:
The controller S is given in DT as(you can implement it on simulink):
where the matrices and sample time are:
The controller has the eigenvalues K=[k1,k2] such that following requirements are satisfied.
- The rise time is tr <= 1.3 seconds.
- Maximum overshoot s <= 0.17
- absolute(K1) <= 0.9333 , absolute(K2)<=26.6 *by absolute I mean neglect the sign . The requirement can be satisfied y decreasing the desired damping and natural frequency or the values of Q matrix.
- Please indicate to me which inequality is satisfied.
- k2 >= -0.000k1 + 3.920 and k2 >= -19.745k1 + 3.920
- k2 <= -0.000k1 + 3.920 and k2 >= -19.745k1 + 3.920
- k2 >= -0.000k1 + 3.920 and k2 <= -19.745k1 + 3.920
also indicate if system is controllable. I shall be very thankful if someone can solve this problem.I have provided the sample code below.
if true
K=place(A,B,[....place...eigenvalues])
eig(A-(B*K))
L=acker(A',C',5*eig(A-B*K))'
Ao=A-L*C
Bo=[L B]
Co=eye(2)
Do=zeros(2,2)
eig(Ao)
end
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