Question

Given the following specification:

P.O. ≤4.6%;Ts1%​≤3.28sec;3 samples in Tr​.
and a process with a z-transform of:
Z{G(s)}= z / (z−0.8)(z−0.1)
Design a discrete PID controller in the z-domain (think zero-pole matching to generate D(z) ) which have a second order response and will meet the specifications.
- Generate the z-transform of the controller D(z)

Answer 1

A discrete PID controller using zero-pole matching technique to meet certain specifications of overshoot and settling time, but without additional context or desired closed-loop characteristics, a specific transfer function D(z) cannot be provided.

Step-by-step explanation:

A discrete PID controller in the z-domain for a given process with the z-transform provided. To achieve the given specifications, we would need to apply control theory techniques such as zero-pole matching to generate the transfer function D(z) for the PID controller.

Unfortunately, without additional information on the desired closed-loop system or design constraints beyond what is provided, we cannot give a specific D(z). However, generally, a discrete PID controller in the z-domain would aim to place zeros to cancel the process poles or to shape the response, and place poles to obtain a desired dynamical behavior that meets the overshoot and settling time specifications.