设计离散PID控制器，各信号的跟踪结果如图所示，其中S代表输入指令信号的类型。通过取余指令 mod实现三角波和锯齿波。当S=1时为三角波，S=2时为锯齿波，S=3时为随机信号。在仿真过程中，如果 D=1，则通过 pause命令实现动态演示仿真。在随机信号跟踪中,对随机信号的变化速率进行了限制。

仿真程序：

%PID Controller

clear all;

close all;

tS=0.001;

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

u_1=0.0;

u_2=0.0;

u_3=0.0;

yd_1=rand;

y_1=0；

y_2=0;

y_3=0;

x=[0,0.,0]';

error_ 1=0;

for k=1: 1:3000

time(k)=k*ts;

kp=1.0;ki=2.0;kd=0.01;

S=3;

if S==1 %Triangle Signal

if mod(time(k),2)<1

yd(k)=mod(time(k).1);

else

yd(k)=1-mod(time(k),1);

end

yd(k)=yd(k)-0.5;

end

if S==2 %Sawtooth Signal

yd(k)=mod(time(k),1.0);

end

if S==3 %Random Signal

yd(k)=rand;

dyd(k)=(yd(k)-yd_1)/ts; %Max speed is 5.0

while abs(dyd(k))>=5.0

yd(k)=rand;

dyd(k)-abs((yd(k)-yd_ 1Vts);

end

end

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

%Restricting the output of

if u(k)>=10

u(k)=10;

end

if u(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_1+num(3)*u_2+num(4)*u_3;

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

yd_1=yd(k);

u_3=u_2;u_2=u_l;u_I=u(k);

y_3=y_2:y_2=y_1:y_1=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 1

xi(k)-x(3);

error_l=error(k);

D=0;

if D=-1 %Dynamic Simulation Display

plot(time,yd,'b' ,time,y,r);

pause(0.00000000000000000);

end

end

figure(1);

plot(time,yd.'r',time,y,'k:" 'linewidth' ,2);

xlabel('time(s));ylabel('yd,y);

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