Matlab_Simulink: PID gains optimization program_input consideration (free program release)

What we want to achieve
Matlab version
Toolbox
Download URL
Folder Structure
How to run the program
Simulink File（PID_fmin.slx）
m-file code (Main_PID_fmin_input.m)
m-file code (func_fmin_input.m)
Simulation result
Discussions
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What we want to achieve

Construction of a PID control simulator using Simulink and m-files
Optimization of PID gains for the above program
Optimization using fminsearch
Optimization to prevent excessive input

Matlab version

Matlab2021a
*Past versions also available as downloadable formats

Toolbox

Simulink

Download URL

PID_Control_fmin_input - Google drive

*Download the folder for the Matlab version you are using.
Example: If you are using the 2021a version, select "2021a" from the link above.
*We are not responsible for any problems caused by the use of the above programs.

Folder Structure

Download and extract the above.

How to run the program

Run "Main_PID_fmin_input.m"

Simulink File（PID_fmin.slx）

m-file code (Main_PID_fmin_input.m)

%% Initialization

clc % Initialize command window

clear % Initialize workspace

close all % Close all graphs

%% Variable Declaration

% ===== Controlled system =====

K = 1;

A = 1;

B = 1;

C = 1;

% ===== reference signal =====

r_val = 10; % step reference signal

% ===== Simulink =====

N_File = 'PID_fmin.slx'; % simulink filne name

FinalTime = 30; % Simulation end time [s]

SamplingTime = 0.1; % Sampling time [s]

% ===== Estimated system gain =====

K_hat = 0.1*K; % It is used in fminsearch

%% fminsearch

ini_x = [0.5 0.5, 0.5]; % Initial PID gains

[x, fval] = fminsearch(@(x) func_fmin_input(x,N_File,K_hat),ini_x);

%% Run the Simulink

open(N_File); % Open Simulink file

sim(N_File); % Run the Simulink

%% Output Figures

% ===== Store the Simulink data =====

t = ScopeData.time; % Time

y = ScopeData.signals(1).values(:, 1); % Output

r = ScopeData.signals(1).values(:, 2); % Reference signal

u = ScopeData.signals(2).values(:, 1); % Input

% ===== output figures =====

% ----- y -----

figure;

subplot(211);

plot(t,y);

hold on;

plot(t,r,'--');

grid on;

xlabel('$ t {\rm [s]} $', 'interpreter', 'latex');

ylabel('$ y(t) $', 'interpreter', 'latex');

legend('$ y(t) $', '$ r(t) $', 'interpreter', 'latex');

% ----- u -----

subplot(212);

plot(t,u);

hold on;

grid on;

xlabel('$ t {\rm [s]} $', 'interpreter', 'latex');

ylabel('$ u(t) $', 'interpreter', 'latex');

m-file code (func_fmin_input.m)

function f = func_fmin_input(x,N_File,K_hat)

%% Variable Declaration

Kp = x(1);

Ki = x(2);

Kd = x(3);

assignin('base','Kp',Kp);

assignin('base','Ki',Ki);

assignin('base','Kd',Kd);

% Run the Simulink

sim(N_File);

%% Store the Simulink data

t = ScopeData.time; % Time

y = ScopeData.signals(1).values(:, 1); % Output

r = ScopeData.signals(1).values(:, 2); % Reference signal

u = ScopeData.signals(2).values(:, 1); % Input

%% 評価規範
% To make the same order between error and input, intrduce a K_hat

f = sum*1.^2);

%% output optimization results in command window

fprintf('[Kp, Ki, Kd, fval] = %.3g, %.3g, %.3g, %.3g\n',Kp, Ki, Kd, f);