在连续系统的数字PID控制仿真-2的基础上，利用S函数实现PID离散控制器的Simulink仿真。

在S函数中，采用初始化函数、更新函数和输出函数，即 mdlInitializeSizes函数、mdIUpdates函数和mdlOutputs函数。在初始化中采用sizes 结构，选择1个输出、2个输入。其中一个输入为误差信号，另一个输入为误差信号上一时刻的值。S函数嵌入在Simulink程序中，采样时间为1ms。仿真结果如图所示。

仿真图：

PID控制器程序：chap1_8s.m

function [sys,x0,str,ts]=exp_pidf(t,x,u,flag)

switch flag,

case 0 % initializations

[sys,x0,str,ts] =mdllnitializeSizes;

case 2 % discrete states updates

sys = mdIUpdates(x,u);

case 3 %computation of control signal

% sys = mdlOutputs(t,x,u,kp,ki,kd,MTab);

sys=mdlOutputs(t,x,u);

case{1,4,9} %unused flag values

sys= [ ];

otherwise %error handling

error(['Unhandled flag=',num2str(flag)]);

end;

% when flag=0, perform system initialization.%

function [sys,x0,str,ts] =mdllnitializeSizes

sizes = simsizes; % read default control variables

sizes.NumContStates= 0: % no continuous states

sizes.NumDiscStates = 3; % 3 states and assume they are the P/I/Dcomponents

sizes.NumOutputs=1; % 2 output variables: control u(t) and state x(3)

sizes.NumInputs = 2; % 4 input signals

sizes.DirFeedthrough=1: % input reflected directly in output

sizes.NumSampleTimes=1; % single sampling period

sys = simsizes(sizes);

x0=[0; 0;0]; % zero initial states

str =[];

ts=[-1 0]; % sampling period

% when flag=2,updates the discrete states%

function sys = mdlUpdates(x,u)

T=0.001;

sys=[ u(1);

x(2)+u(1)*T;

(u(1)-u(2)/T];

% when flag-3, computates the output signals

function sys = mdlOutputs(t,x,u,kp,ki,kd,MTab)

kp=1.5;ki=2.0;kd=0.05;

%sys=[kp,ki,kd]*x;

sys=kp*x(1)+ki*x(2)+kd*x(3);

作图程序：chap1_8plot.m

close all;

plot(t,y(:,1),r',ty(:,2),k:',linewidth’,2);

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

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