Demanded velocity vdem = * (target - x). Input u = 100*(vdem - v)
Velocity demand limit = Initial position =
The drive is now limited in magnitude to 1. The plot is red when u is on a limit.

<![CDATA[ //Setup window tmax=10; ScaleWindow(-1.5,-0.9,0.5,1.1); DrawAxes(-1.5,-1,0.5,1); kx=document.getElementById("posgain").value; x=document.getElementById("pos0").value*1.0; kv=100; vdemlim=eval(document.buttons.vellim.value); b=1; dt=.01; t=0; x=eval(document.buttons.pos0.value); //Initial position veldem=0; v=0; u=0; //Input motor current MoveTo (x, v); 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");} MoveTo(x,v); x = x + v*dt; //This is the simulation v = v + b*u*dt; t = t + dt; LineTo(x, v); MoveBlock(x); if(t<tmax){setTimeout("loop();", 1000*dt);} ]]>