控制对象为：

采样时间为1ms，采用z变换进行离散化，经过z变换后的离散化对象为：

y(k)=-den(2)y(k -1)- den(3)y(k -2)- den(4)y(k-3)+num(2)u(k -1)+ num(3)u(k -2)+ num(4)u(k-3)

设计离散PID控制器。其中，S为信号选择变量，S=1时为阶跃跟踪，S=2时为方波跟踪，S=3时为正弦跟踪。PID阶跃跟踪结果如图所示。

仿真程序：

%PID Controller

clear all;

close all;

ts=0.001;

sys=tf(5.235e005,[1,87.35,1.047004,0]);

dsys=c2d(sys,ts,'z');

[num,den]=tfdata(dsys,'v');

u_1=0.0;u_2=0.0;u_3=0.0;

y1=0.0;y2=0.0;y_3=0.0;

X-[0,0,0);

error_1=0;

for k=1:1:500

time(k)=k *ts;

S=3;

if S==1

kp=0.50;ki=0.001;kd=0.001;

yd(k)=1; %Step Signal

elseif S==2

kp=0.50;ki=0.001:;kd-0.001;

yd(k)=sign(sin(2*2*pi*k*ts)); %Square Wave Signal

elseif S==3

kp=1.5;ki=1.0;kd=0.01; %Sine Signal

yd(k)=0.5*sin(2*2*pi*k*ts);

end

u(k)=kp*x(1)+kd*x(2)+ki*x(3); %PID Controller

%Restricting the output of controller

if u(k)>-10

u(k)=10;

end

ifu(k)<=-10

u(k)=-10;

end

%Linear model

y(k)=-den(2)*y_1-den(3)*y_2-den(4)y_3+num(2)*u_l+num(3)*u_2+num(4)*u_3;

crror(k)=yd(k)-y(k);

%Return of parameters

u_3=u_2;u_2=u_1;u_1=u(k);y_3=y_2;y_2=y_l:y_I=y(k);

x(1)=error(k); %Calculating P

x(2)=(error(k)-error_1)/ts; %Calculating D

X(3)=x(3)+error(k)*ts; %Calculating I

error_1=error(k);

end

figure(1);

plot(time,yd,'r' time,y,'k:1 linewidth',2);xlabel('time(s));ylabel('yd,y');

legend('ldeal position signal','Position tracking');