PID Controllers, 2nd Edition

Chapter 2.1 - Process Models: Introduction

A block diagram of a simple control loop is shown in Figure 2.1. The system has two major components, the process and the controller, represented as boxes with arrows denoting the causal relation between inputs and outputs. The process has one input, the manipulated variable, also called the control variable. It is denoted by u. The process output is called process variable (PV) and is denoted by y. This variable is measured by a sensor. The desired value of the process variable is called the setpoint (SP) or the reference value. It is denoted by y_sp. The control error e is the difference between the setpoint and the process variable, i.e., e = y_sp - y. The controller in Figure 2.1 has one input, the error, and one output, the control variable. The figure shows that the process and the controller are connected in a closed feedback loop.

The purpose of the system is to keep the process variable close to the desired value in spite of disturbances. This is achieved by the feedback loop, which works as follows. Assume that the system is in equilibrium and that a disturbance occurs so that the process variable becomes larger than the setpoint. The error is then negative and the controller output decreases which in turn causes the process output to decrease. This type of feedback is called negative feedback, because the manipulated variable moves in direction opposite to the process variable.

The controller has several parameters that can be adjusted. The control loop performs well if the parameters are chosen properly. It performs poorly otherwise, e.g., the system may become unstable. The procedure of finding the controller parameters is called tuning. This can be done in two different ways. One approach is to choose some controller parameters, to observe the behavior of the feedback system, and to modify the parameters until the desired behavior is obtained. Another approach is to first develop a mathematical model that describes the behavior of the process. The parameters of the controller are then determined using some method for control design.

Figure 2.1 Block diagram of a simple feedback system.

An understanding of techniques for determining process dynamics is a necessary background for both methods for controller tuning. This chapter will present such techniques.

Static models are discussed in the next section. Dynamic models are discussed in Section 2.3. Transient response methods, which are useful for determining simple dynamic models of the process, are presented in Section 2.4. Section 2.5 treats methods based on moments. These methods are less sensitive to measurement noise and, furthermore, are not restricted to any specific input signal. The frequency response methods, described in Section 2.6, can be used to obtain both simple models and more detailed descriptions. Methods based on estimation of parametric models are more complex methods that require more computations but less restrictions on the experiments. These methods are presented in Section 2.7. The models discussed so far describe the relation between the process input and output. It is also important to model the disturbances acting on the system. This is discussed in Section 2.8. Section 2.9 treats methods to simplify a complex model and the problem of unmodeled dynamics and modeling errors. Conclusions and references are given in Sections 2.10 and 2.11.

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Chapter 2.1 - Process Models: Introduction

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