Real-Time Simulations

//Setup window


  ScaleWindow(-1,-1,tmax,1);
  DrawAxes(0,-1,tmax,1);

  xtarget=0;
  
  x=0;
  xest=0;
  v=0;
  vest=0;
  theta=0;
  omega=0;
  phi=4;
  phirate=0;
  phitarget=0;
  u=0;            //Input motor current
  
  Colour("black");
  Label("Position/10",tmax/2,.7);
  Colour("blue");
  Label("Velocity/10",tmax/2,.6);
  Colour("red");
  Label("Tilt*10",tmax/2,.5);
  Colour("green");
  Label("Tilt-rate",tmax/2,0.4);  
  Colour("gray");
  Label("Drive u",tmax/2,0.3);  
  
  MoveTo (t, x);
  Colour("black");
  loop();

   u=kphi*(phi-phitarget)+kphidot*phirate+ktheta*theta+komega*omega;
  Colour("black");
  if (u>1){u=1; Colour("red");}    //This applies the limit
  if (u<-1){u=-1; Colour("red");}

theta=theta+omega*dt;
omega=omega+(80*theta+2*phirate-50*u)*dt;
phi=phi+phirate*dt
phirate=phirate+(-4*phirate+100*u)*dt
x=(theta+phi)*r;
v=(omega+phirate)*r;

  t=t+dt;

  Colour("black");
  Spot(t,x/10);
  Colour("blue");
  Spot(t,v/10);
  Colour("red");
  Spot(t,theta*10);  
  Colour("green");
  Spot(t,omega);
  Colour("gray");
  Spot(t,u);   
  if(t<tmax){setTimeout("loop();",10);}