z domain to delay difference equations and applying pid controller

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i want to convert z domain transfer function to time delay equations and then apply a discrete PID controller for it?
how can i code this?

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Sarvesh Kale
Sarvesh Kale am 6 Mär. 2023
Bearbeitet: Sarvesh Kale am 6 Mär. 2023
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')
sys = 1 + 2 z^-1 -------------------- 1 + 5 z^-1 + 10 z^-2 Sample time: 0.1 seconds Discrete-time transfer function.
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])
sys = 1 ----- s + 1 Continuous-time transfer function.
pidtune(c2d(sys,0.1),'pid') % c2d converts from continuous domain to discrete domain
ans = Ts z-1 Kp + Ki * ------ + Kd * ------ z-1 Ts with Kp = 1.69, Ki = 2.59, Kd = 0.0779, Ts = 0.1 Sample time: 0.1 seconds Discrete-time PID controller in parallel form.
get more information on pidtune, tf and c2d by clicking on them
Thank you

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