%Discrete Reaching Law VSS Control
clear all;
close all;

a=25;b=133;

ts=0.001;
A1=[0,1;0,-a];
B1=[0;b];
C1=[1,0];
D1=0;
[A,B,C,D]=c2dm(A1,B1,C1,D1,ts,'z');

x=[-0.5;-0.5];
r_1=0;r_2=0;

for k=1:1:2000
   
time(k)=k*ts;
   
   r(k)=0.5*sin(3*2*pi*k*ts);
   c=10;eq=5;q=30;
   Ce=[c,1];
   
   %Using Waitui method   
   dr(k)=(r(k)-r_1)/ts;
   dr_1=(r_1-r_2)/ts;
   r1(k)=2*r(k)-r_1;
   dr1(k)=2*dr(k)-dr_1;
  
   R=[r(k);dr(k)];
   R1=[r1(k);dr1(k)];
   
   E=R-x;
   e(k)=E(1);
   de(k)=E(2);
   
   s(k)=Ce*E;
   
   ds(k)=-eq*ts*sign(s(k))-q*ts*s(k);
	u(k)=inv(Ce*B)*(Ce*R1-Ce*A*x-s(k)-ds(k));   

	x=A*x+B*u(k);
	y(k)=x(1);

%Update Parameters
r_2=r_1;
r_1=r(k);
end
figure(1)
plot(time,r,'r',time,y,'b');
xlabel('Time(second)');ylabel('(r and y)');
figure(2)
plot(time,s,'r');
xlabel('Time(second)');ylabel('Switch function s');
figure(3)
plot(e,de,'r',e,-c*e,'b');
xlabel('e');ylabel('de');
figure(4)
plot(time,u,'r');
xlabel('Time(second)');ylabel('u');