ex8_17.m

华东理工大学自动化系《控制系统分析、设计和应用》教材配套程序实例,有关说明： 1. 安装MATLAB软件。安装时

% ex8_17
% 设计降阶观测器
a=[0 1 0;0 -1 1;0 0 -5];b=[0 0 5]';c=[1 0 0 ];d=0;
syms s f11 f12 f21 f22 t11 t21 l11 l21 p1 p2 Iphe;pp1=-20;pp2=-20;
F=[f11 f12;f21 f22];L=[l11;l21];T=[t11 1 0;t21 0 1];
SD=subs((s-p1)*(s-p2),{p1,p2},{pp1,pp2});S0=subs(SD,'s',0);
S1=subs(jacobian(SD,'s'),'s',0);S2=subs(jacobian(jacobian(SD,'s'),'s')/2,'s',0);
SF=det(s*eye(size(F,1))-F);F0=subs(SF,'s',0);F1=subs(jacobian(SF,'s'),'s',0);
F2=subs(jacobian(jacobian(SF,'s'),'s')/2,'s',0);SG=F*T-T*a+L*c;
[f11,f12,f21,f22,l11,l21,t11,t21]=solve(S0-F0,S1-F1,SG(1,1),SG(1,2),SG(1,3),...
  SG(2,1),SG(2,2),SG(2,3),'f11','f12','f21','f22','l11','l21','t11','t21');
f11=sym2poly(f11);f12=sym2poly(f12);f21=sym2poly(f21);f22=sym2poly(f22);
l11=sym2poly(l11);l21=sym2poly(l21);t11=sym2poly(t11);t21=sym2poly(t21);
L=[l11;l21],T=[t11 1 0;t21 0 1],F=[f11 f12;f21 f22],J=T*b,Iphe=inv([c;T])
p=[-10 -1+2*j -1-2*j];syms s k1 k2 k3 K KI;K=[k1,k2,k3];
S=sym2poly((s-p(1))*(s-p(2))*(s-p(3)));Acl=[a-b*K];
DS=det(s*eye(size(Acl,1))-Acl);SD4=subs(DS,'s',0);
SD3=subs(jacobian((DS-SD4),s),'s',0);SD2=subs(jacobian(jacobian(DS,s),s)/2,'s',0);
[k1,k2,k3]=solve(S(4)-SD4,S(3)-SD3,S(2)-SD2);
k1=sym2poly(k1);k2=sym2poly(k2);k3=sym2poly(k3);K=[k1,k2,k3];kx=K*Iphe