MATLAB Program for SLIDING MODE CONTROL

clc

clear all

x1(1)=0.1;%Initial condition for the first state i:e theta

x2(1)=0.1;%Initial condition for the second state i.e angular velocity theta_dot

h=0.01;% integration step size

M=0.5;%PENDULUM MASS

k=10;%controller gain

L=2.5;%length of cord

g=9.81;%gravitation constant

a=5;

t=0:h:20;%simulation time

for n=1:length(t) %loop for integrating the pendulum equation

    s(n)=a*x1(n)+x2(n);%defining the linear sliding surface

    u(n)=(M*L^2)*(-a*x2(n)+(L/g)*sin(x1(n)))-k*sign(s(n)); %Equivalent control, k is control gain, sign is signum function

   

    x1(n+1)=x1(n)+h*x2(n);%USING EULER APPROXIMATION OF INTEGRATION FOR EQUATION 1 x1_dot=x2

    x2(n+1)=x2(n)+h*(-(L/g)*sin(x1(n))+(1/(M*L^2))*u(n));%integrating second equation

   

end  %ending the running loop

figure(1)

plot(t,x1(1:end-1),'r')% Angle

figure(2)

plot(t,x2(1:end-1),'k')%Rate of change of angle

figure(3)

plot(t,u,'b')% Control input