Man Scilab

stabil - stabilization

Calling Sequence

F=stabil(A,B,alfa)

K=stabil(Sys,alfa,beta)

Parameters

• A : square real matrix ( nx x nx )
• B : real matrix ( nx x nu )
• alfa, beta : real or complex vector (in conjugate pairs) or real number.
• F : real matrix ( nx x nu )
• Sys : linear system ( syslin list) ( m inputs, p outputs).
• K : linear system ( p inputs, m outputs)

Description

F=stabil(A,B,alfa) returns a gain matrix F such that A+B*F is stable if pair (A,B) is stabilizable. Assignable poles are set to alfa(1),alfa(2),... . If (A,B) is not stabilizable a warning is given and assignable poles are set to alfa(1),alfa(2),... . If alfa is a number all eigenvalues are set to this alfa (default value is alfa=-1 ).

K=stabil(Sys,alfa,beta) returns K , a compensator for Sys such that (A,B) -controllable eigenvalues are set to alfa and (C,A) -observable eigenvalues are set to beta .

All assignable closed loop poles (which are given by the eigenvalues of Aclosed=h_cl(Sys,K) are set to alfa(i) 's and beta(j) 's.

Examples

// Gain:
Sys=ssrand(0,2,5,list('st',2,3,3));
A=Sys('A');B=Sys('B');F=stabil(A,B);
spec(A) //2 controllable modes 2 unstable uncontrollable modes
//and one stable uncontrollable mode
spec(A+B*F) //the two controllable modes are set to -1.
// Compensator:
Sys=ssrand(3,2,5,list('st',2,3,3)); //3 outputs, 2 inputs, 5 states
//2 controllables modes, 3 controllable or stabilizable modes.
K=stabil(Sys,-2,-3);  //Compensator for Sys.
spec(Sys('A'))
spec(h_cl(Sys,K))   //K Stabilizes what can be stabilized.
 
  

See Also

st_ility ,   contr ,   ppol ,  

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