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//------------------------------------------------------------------
//------------------------------------------------------------------
//A function written by Deepti Khimani.
//Usage:-
//[K, lambda]=acker_dk(a, b, pl)
//K=acker_dk(a, b, pl)
//a:- System matrix.
//b:- input matrix.
//p:- Desired poles.
//K:-State feedback gain for the control law u=-Kx.
//lambda:- Eigen values of (a-b*k)
//------------------------------------------------------------------
//------------------------------------------------------------------
function [K, lambda]=acker_dk(a, b, pl)
[lhs,rhs]=argn(0)
if rhs == 0 then
disp(["K=acker_dk(a, b, pl)";"[K, lambda]=acker_dk(a, b, pl)"]);
disp(["a:- System matrix";"b:- input matrix";"p:- Desired poles"]);
disp(["K:-State feedback gain for the control law u=-Kx";...
"lambda:- Eigen values of (a-b*k)"]);
return;
end
[ra ca]=size(a);
[rb cb]=size(b);
l=length(pl);
CO=cont_mat(a,b);
if ra~=l then
error(["Dimension error:";"number of desired poles must equal...
to order of the system"]);
elseif ra~=ca then
error(["Dimension error:";"system matrix should be...
a sqaure matrix"]);
elseif rb~=ra then
error (["Dimension error:","Input matrix should have...
as many rows as a system matrix."]);
elseif rank(CO)<ra then
error("system is not controllable");
end
//------------------------------------------------------------------
//controllable canonical form
[Ac,Bc,T,ind]=canon(a,b);
//CO=zeros(ra,cb);
for i=1:ra
CO(:,ra+1-i)=Ac^(i-1)*Bc;
end
//------------------------------------------------------------------
chr_eq=poly(pl,'s');
des_chr_coeff=coeff(chr_eq);
des_chr_coeff=des_chr_coeff(1:ra);
alpha_c=Ac^ra;
for k=1:ra
alpha_c=alpha_c + des_chr_coeff(k)*Ac^(k-1)
end
//------------------------------------------------------------------
//State feedback gain
temp=zeros(1,ra);
temp(1)=1;
K=temp*inv(CO)*alpha_c;
K=K/T;
lambda=spec(a-b*K);
endfunction
//------------------------------------------------------------------
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