Hi everyone:

How would a discrete smith predictor code be written in time domain or implemeted with a simple discrete pid control. How would the equation look like in time domain. Also have any references to PIP discrete control.

Thanks a bunch

 

The general form for the PID analog controller written in terms of the La Place variable s is
K[1+1/sTi+sTd]
note the differentiator term is not augmneted with a low pass filter
to implement the diff with low pass filter we use the following Transfer function
K[1+1/sTi+sTd/(1+0.1Tds)]
now to generate the correspoding difference equation with the same filtering properties as the differential equation replace s with

s = (z-1)/Tz in the derivative term
s = 2(z-1)/T(z+1) in the integral term
T = Sampling Time of Digital Network
or else simply replace s every where with one of the above transfromations.

define Y(Z) = Z transfrom of the output
controller
U(Z) = Z transform of the input to
controller

when you replace the analog version of the PID with its disrete form you will have a transfer function written in terms of z

to solve simply use Y(z) = H(z).U(z)