1.) convert z domain transfer function to time delay equations
suppose you have the following Z transform
sys = tf([1 2],[1 5 10],0.1,'Variable','z^-1')
So the above transfer function converts to the following equation in time domain
y[n] + 5y[n-1] + 10y[n-2] = x[n] + 2x[n-1]
the numerator of transfer function corresponds to the delays in input and the denominator polynomial represents the delays in the output
2.) How to apply a discrete PID controller ?
you can use the following code snippet to generate the pid controller values
sys = tf(1,[1 1])
pidtune(c2d(sys,0.1),'pid') % c2d converts from continuous domain to discrete domain
Thank you
