% ***************************************************************************\
%    PID Function
%
%  This program has been written by the Technical Support Staff at Z-World in
%  response to several customer requests.  As such, it has NOT had the testing and
%  validation procedures which our "standard" software products have.  It is being
%  made available as a sample.  There is no warranty, implied or otherwise.
%
%  The PID (Proportional Integral Derivative) function is used in mainly
%  control applications. PIDCalc performs one iteration of the PID
%  algorithm.
%
%  While the PID function works, main is just a dummy program showing
%  a typical usage.
%***************************************************************************/
% function ISE = PID(Proportion,Integral,Derivative) 
clc;
clear;
Proportion = 4.8269;%2.591;       % Proportional Const
Integral = 4.0806;%1.4079;        % Integral Const
Derivative = 3.899;%1.1921;      % Derivative Const
dt = 0.01;                % 每一次迭代時間
Epock = 2000;             % 所用時間20秒
PlantOut(1) = 0;          % 初始輸出 0 

for i =1:Epock
    
    % 參考輸入
    input(i)  = 1;
    
    % 傳感器輸出
    if i==1
        output(1) = 0;
    else
        output(i) = PlantOut(i);
    end
    
    % 計算偏差
    Error(i) = input(i) - output(i);
    
    % 指標(biāo)計算誤差累積
    CumulateError(i) = Error(i)^2*dt;
    
    % PID計算  用面積法近似積分  用變化量近似微分
    ErrorArea(i) = Error(i)*dt;
    if i == 1
        dError = Error(i);
    else
        dError = Error(i) - Error(i-1);
    end
    PIDout(i) = Proportion * Error(i) +  Integral * sum(ErrorArea) + Derivative * dError;

    % 裝置輸出計算
    gs(i) = 2/5*exp(-1/5*i*dt)*dt;
    PlantOut(i+1) = PIDout*fliplr(gs)';
end

ISE = sum(CumulateError);
% 輸出響應(yīng)曲線
plot((0:dt:20),PlantOut);
hold on
plot((0:dt:20),1,':')

xlabel('t/s')
axis([0 20 0 1.4])