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 = -0.000k1 + 3.920 and k2 >= -19.745k1 + 3.920 # 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

How to get the desired range of eigenvalues of a control system?

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Usman 2016-2-11

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.

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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