If the rectangular integrator [see below (8-38)] is used in the PID transfer function in (8-52), the

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If the rectangular integrator [see below (8-38)] is used in the PID transfer function in (8-52), the resulting controller is described by
\[
\frac{M(z)}{E(z)}=D(z)=K_{p}+K_{I}\left[\frac{T z}{z-1}ight]+K_{D}\left[\frac{z-1}{T z}ight]
\]
This transfer function is implemented in many commercial digital controllers. Write a difference equation required to realize this controller.

Equation 8-52z + az + b z(z - 1) K = Kp + KT/2 + Kp/T a = (K,T/2Kp-2Kp/T)/Kd b = Kpl (TKd) D(z) = K

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Digital Control System Analysis And Design

ISBN: 9780132938310

4th Edition

Authors: Charles Phillips, H. Nagle, Aranya Chakrabortty

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