PID Controllers, 2nd Edition

Chapter 4.1 - Controller Design: Introduction

This chapter describes some methods for determining the parameters of a PID controller. To obtain rational methods for designing controllers it is necessary to define the main purpose of the control system. This is done in Section 4.2.

The design methods differ with respect to the knowledge of the process dynamics they require. A PI controller is described by two parameters (K and T_i) and a PID controller by three or four parameters (K, T_i, T_d, and N). The classical Ziegler-Nichols methods are discussed in Section 4.3. In these methods process dynamics are characterized by two parameters. One parameter is related to the process gain and the other describes how fast the process is. In the step response method, the parameters are simple characteristics obtained from the step response. In the frequency response method, the parameters are the ultimate gain and the ultimate frequency.

An obvious extension of the frequency response method is to develop methods that are based on more knowledge of the open-loop transfer function, e.g., the slope of the transfer function or its values at two or more frequencies. In Section 4.4 we discuss various methods that are based on attempts to shape the loop transfer function. Section 4.5 treats analytical design methods, where the controller transfer function is obtained from the specifications and the process transfer function by a direct calculation.

One possibility for compromise between several different criteria is to use optimization methods. This is discussed in Section 4.6. Another way to characterize process dynamics with few parameters is to use low-order dynamic models with few parameters. Such methods are discussed in Section 4.7 where the design goal is to position all the poles of the closed-loop system. It is shown that methods based on dynamic models of first and second order lead to PI and PID controllers.

Instead of attempting to position all closed-loop poles, it can be attempted to assign only a few dominating poles. Such methods are discussed in Section 4.8. The approach leads to systematic design methods and a unification of many other techniques. New simple design methods based on the dominant pole design method are presented in Chapter 5.

In Section 4.9, design methods based on disturbance rejection are presented. Finally, conclusions and references are given in Sections 4.10 and 4.11.

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Chapter 4.1 - Controller Design: Introduction

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