z domain to delay difference equations and applying pid controller

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?

Answer 1

[Sarvesh Kale]

Hi kruthika u,

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