p1=-2+2i;
p2=-2-2i;
p3=-20;
p4=-80;
P=[p1,p2,p3,p4];
m=0.111;
R=0.015;
g=-9.8;
J=9.99e-6;
H=-m*g/(J/(R^2)+m);
A=[0 1 0 0;0 0 H 0; 0 0 0 1;0 0 0 0];
B=[0;0;0;1];
C=[1 0 0 0];
D=[0];
%求狀態
K=acker(A,B,P)
%alphas=poly(A);
%betas=(conv(1,-p1),conv(1,-p2),conv(1,-p3),conv(1,-p4));
%i=length(alphas):-1:2;
%diff=alphas(i)-betas(i);
%L=hankel([alphas(length(alphas)-1:-12);1]);
%K=diff*inv(L)*inv(Q);
%disp('The state-feedback matrix are:')
%K
%disp('The close-loop poles are:');
%eig(A-B*K)
T=0:0.01:5;
U=0.25*ones(size(T));
[Y,X]=lsim(A-B*K,B,C,D,U,T);
plot(T,Y);
title('ball-beam system step response');
xlabel('Time-sec');
ylabel('Response-value');
grid