function dx=Model(t,x)
global w A alfa J Ce R Km Ku S a1 Fm Fc M kv
persistent aa
dx=zeros(3,1);
a1=1.0; %Effect on the shape of friction curve
Fm=20;
Fc=15;
kv=2.0;
F=J*x(3);
if t==0
aa=0;
end
dF=J*aa;
if abs(x(2)) if F>Fm
Ff=Fm;
dFf=0;
elseif F Ff=-Fm;
dFf=0;
else
Ff=F;
dFf=dF;
end
end
if x(2)>alfa
Ff=Fc+(Fm-Fc)*exp(-a1*x(2))+kv*x(2);
dFf=(Fm-Fc)*exp(-a1*x(2))*(-a1)*x(3)+kv*x(3);
elseif x(2) Ff=-Fc-(Fm-Fc)*exp(a1*x(2))+kv*x(2);
dFf=-(Fm-Fc)*exp(a1*x(2))*a1*x(3)+kv*x(3);
end
if S==1
rin=A*sin(w*t);
drin=A*w*cos(w*t);
ddrin=-A*w*w*sin(w*t);
dddrin=-A*w*w*w*cos(w*t);
end
if S==2
rin=1;
drin=0;
ddrin=0;
dddrin=0;
end
if S==3
rin=A*sign(sin(0.4*2*pi*t));
drin=0;
ddrin=0;
dddrin=0;
end
error=rin-x(1);
derror=drin-x(2);
dderror=ddrin-x(3);
u=200*error+40*derror; %PID
du=200*derror+40*dderror;
if u>=110
u=110;
end
if u u=-110;
end
if M==0
Ff=0;dFf=0; %No Friction
end
dx(1)=x(2);
dx(2)=-Km*Ce/(J*R)*x(2)+Ku*Km*u/(J*R)-Ff/J;
dx(3)=-Km*Ce/(J*R)*x(3)+Ku*Km*du/(J*R)-dFf/J;
aa=dx(3);
