1 内容介绍
讨论了一阶倒立摆控制系统的数学模型及其建立方法,并通过MATLAB的Simulink模型整定出一阶倒立摆双闭环PID控制系统的最优控制参数,最后对该系统的鲁棒性进行了仿真分析.
2 部分代码
%% The reference Papers
% Mehran Mazandarani, L. Xiu,Interval Type-2 Fractional Fuzzy Inference
% Before using FFIS.m read please carefully watch the video files and read
% the help file, Help_FFIS201210_updated.pdf.
%% The example of control of inverted pendulum system using FFIS
% This program is the first version of the function FFIS.m (FFIS_201210)
% The algorith of this function has not been written in an optimal manner.
% Thus, naturally, it may take more time than that one may expect for
% getting the output.
% Based on the settings in this example, it takes several minutes to get
% the output.
%% Initialize the Fuzzy system structure (Initialization Section)
clc
clear
% close all
fis=readfis('fis');
%% Fractional Indices
% Fids={value_1,form_1, value_2,form_2,...,value_m,form_m}
% Read the help_FFIS.pdf for more information about the cell arraye Fids.
% fis.Outputs.MembershipFunctions
% In this example the following indices have been considered arbitrary.
Fids={0.5, 'a', 0.5, 'a', 1,'a', 0.5, 'b', 0.5,'b'};
% For Mamdani's FIS
% Fids={1, 'a', 1, 'b', 1,'a', 1, 'b', 1,'b'};
%% Model (The main section)
T=3;
n=3000;
tspan=linspace(0,T,n+1);
h=tspan(2)-tspan(1);
% % This is the gain of control signal based on the control structure.
Kgain=220;
% % % % Pendulum parameters
g=9.8;
m=2;
M=8;
l=2;
% x1 is the angle of the pendulum and is used as the error
% x2 is the derivative of the x1, i.e. the derivative of the error
% % % % % % % % % % % % % % % % % %
% x1=theta;
% x2=theta_dot;
x1=zeros(1,n+1);
x2=zeros(1,n+1);
u=zeros(1,n);
x1(1)=0.3; % the initial condition
x2(1)=0.1; % the initial condition
a=1/(M+m);
% Model part
for cnt=1:n
Inputs=[x1(cnt); x2(cnt)];
% % % the control signal
u(cnt)=FFIS(fis,Inputs,Fids);
u(cnt)=Kgain*u(cnt);
% % The model has been considered in a descrete form by the use of
% % forward approximation of the derivative definition.
x1(cnt+1)=x1(cnt)+h*x2(cnt);
k1=g*sin(x1(cnt))-a*m*l*x2(cnt)^2*sin(2*x1(cnt))/2-a*cos(x1(cnt))*u(cnt);
k2=4*l/3-a*m*l*cos(x1(cnt))^2;
x2(cnt+1)=x2(cnt)+h*k1/k2;
end
figure(1)
plot(tspan(1:numel(x1)),x1,'LineWidth',2)
grid on
hold on
figure(2)
plot(tspan(1:numel(u)),u/Kgain,'LineWidth',2)
grid on
hold on
3 运行结果
4 参考文献
[1]胡全义, 黄士涛, 李洪洲,等. 自适应神经模糊推理系统在倒立摆控制中的应用[J]. 机电工程, 2007, 24(1):4.
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