Module 6. First-Order + Time-Delay Processes

The most commonly used model to describe the dynamics of chemical processes is first order + time delay. In this module, we relate the stability of feedback control of these processes to frequency-response analysis. The important principles that we wish to illustrate are as follows:

• Gain margin is a measure of gain uncertainty that can be tolerated

• Phase margin is a measure of the time-delay uncertainty that can be tolerated

• The "cross-over frequency" is related to the ultimate period from the closed-loop Ziegler-Nichols approach

• Ziegler-Nichols recommended tuning values do not provide adequate gain and phase margins

• IMC-based PI is easier to tune for robustness than are the other approaches

The sections of this module are as follows:

M6.1 Motivation

M6.2 Closed-Loop Time-Domain Simulation

M6.3 Bode Analysis

M6.4 Ziegler-Nichols Tuning

M6.5 IMC-Based PID Control

M6.6 Summary

It is assumed that the reader has the MATLAB Control Toolbox, which has the Bode and Nyquist functions.