Hi @Mikel
You can try the two approaches in the code.
However, the step value should not exceed fs = 130, or else your designed SMC cannot track 
well (unless you increase r).
well (unless you increase r). % solving the ode
t0 = 0;
tfinal = 20;
tspan = linspace(t0, tfinal, 20001);
x0 = [0 0 0];
[t, x] = ode45(@(t, x) SMCf(t, x), tspan, x0);
% plotting the output
plot(t, 2*cos(t), t, x(:,1)), grid on
xlabel('t')
legend('\omega_{d}(t)', 'y(t)')
% describing the ode
function [dot,s,u,wd,dwd,ddwd] = SMCf(t, x)
%variables
c = 5;
r = 10;
% perturbation
ts = 4; % step time
fs = 139/1.08; % step output value (shouldn't exceed 130 or it cannot track)
f = fs*(t > ts); % step function (not a math expression, but a program syntax)
% f = fs*heaviside(t - ts); % Heaviside function (an acceptable math function for step)
% yc, desired track
wd = 2*cos(t);
% compute desired velocity and acceleration
% dyc = gradient(yc,t);
dwd = - 2*sin(t);
ddwd = - 2*cos(t);
%sliding variable
s = dwd + c*wd - c*x(1) - x(2);
%control law U to satisfy ss'<0
u = r*tanh(s/0.01);
x1dot = x(2);
x2dot = - 5.648*x(2) - 1.609*x(1) + 13.89*u + f;
x3dot = x(1);
dot = [x1dot x2dot x3dot]';
end
