[ODE] Servo to reach a target position

[Royce3]

I got a chance to look at my PID algos at work here, and here are
the algos...

These are PID algos were in use by "Think & Do" ( now www.entivity.com )
back in 1999.


Control Error

CE = SP - (PV + Bias)


Gains

Kc = ProportionalGain * OutputSpan / InputSpan

Ki = Kc / Ti

Kd = Kc * Td


Proportional Output

Position: Op = Kc * CEt0
Velocity: dOp = Kc * ( CEt0 - CEt1 )


Integral Output

Position: Oi = Oi1 + ( Ki * CEt0 * dT )
Velocity: dOi = Ki * CEt0 * dT


Derivative Output

Position: Od = Kd ( CEt0 - CEt1 ) / dT
Velocity: dOd = Kd ( ( CEt0-CEt1 ) / dT0 - ( CEt1 - CEt2 ) / dT1 )


Output Variable

Position: OV = Op + Oi + Od
Velocity: OV = OV1 + dOp + dOi + dOd


So, they do use dT in integral and derivative terms. Typing this
in I realized another mistake in my PID code. The speed loop should
not be accumulating the D term like it is.