Demanded velocity vdem = * (target - x). Input u = 100 * (vdem - v)
Velocity demand limit = Initial position =
The drive is now limited in magnitude to 1.
You can change the position target,
target = 0
<![CDATA[ //Setup window tmax=10; ScaleWindow(-1,-1.5,tmax,1.5); DrawAxes(0,-1.5,tmax,1.5); for(t=1;t<tmax;t+=1){Spot(t,-0.02);} kx=eval(document.buttons.posgain.value); kv=100; vdemlim=eval(document.buttons.vellim.value); disturbance=0; b=1; dt=.01; t=0; x=eval(document.buttons.pos0.value); //Initial position veldem=0; v=0; u=0; //Input motor current Colour("blue"); Label("Velocity",5,1); Colour("gray"); Label("Drive u",5,0.8); MoveTo (t, x); Colour("black"); loop(); ]]>
<![CDATA[ //Loop window xtarget=0; veldem=kx*(xtarget-x); //This calculates the velocity demand if(veldem>vdemlim){veldem=vdemlim;} if(veldem<-vdemlim){veldem=-vdemlim;} u=kv*(veldem-v); Colour("black"); if (u>1){u=1; Colour("red");} //This applies the limit if (u<-1){u=-1; Colour("red");} x = x + v*dt; //This is the simulation v = v + b*(u+disturbance)*dt; t = t + dt; Spot(t, x); Colour("gray"); Spot(t,u); Colour("blue"); Spot(t,v); if(t<tmax){setTimeout("loop();", 1000*dt);} ]]>