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Introduction
Fuzzy control uses sentences, in the form of rules, to control a process. The controller can take many inputs, and the advantage of fuzzy control is the ability to include expert knowledge. The interface to the controller is more or less natural language, and that is what distinguishes fuzzy control from other control methods. It is generally a nonlinear controller. There are, however, very few design procedures in the nonlinear domain compared to the linear domain. This book proposes to stay as long as possible in the linear domain, on the solid foundations of linear control theory, before moving into the nonlinear domain with the design. The design method consists accordingly of four steps: design a PID controller, replace it with a linear fuzzy controller, make it nonlinear, and fine-tune the resulting controller. A nonlinear process may have several equilibrium points, and the local behaviour can be different from the behaviour far from an equilibrium, which makes it difficult to control. In order to demonstrate various aspects of nonlinear control, the book uses a simulator of a train car on a hilly track.
Fuzzy controllers appear in consumer products such as washing machines, video cameras, and cars. Industrial applications include cement kilns, underground trains, and robots. A fuzzy controller is an automatic controller, that is, a self-acting or self-regulating mechanism that controls an object in accordance with a desired behaviour. The object can be, for instance, a robot set to follow a certain path. A fuzzy controller acts or regulates by means of rules in a more or less natural language, based on the distinguishing feature: fuzzy logic. The rules are invented by plant operators or design engineers, and fuzzy control is thus a branch of artificial intelligence.
1.1 What Is Fuzzy Control?
Conventionally, computer programs make rigid yes or no decisions by means of decision rules based on two-valued logic: true/false, yes/no, or one/zero. An example is an air conditioner with a thermostatic controller that recognizes just two states: above the desired temperature or below the desired temperature. Fuzzy logic, on the other hand, allows intermediate truth-values between true and false.
A fuzzy air conditioner may thus recognize ‘warm’ and ‘cold’ room temperatures. The rules behind are less precise, for instance:
- Rule. If the room temperature is warm and slightly increasing, then increase the cooling.
Many classes or sets have fuzzy rather than sharp boundaries, and this is the mathematical basis of fuzzy logic: the set of ‘warm’ temperature measurements is one example of a fuzzy set.
The core of a fuzzy controller is a collection of linguistic (verbal) rules of the if–then form. Several variables may appear in each rule, both on the if side and on the then side. The rules can bring the reasoning used by computers closer to that of human beings.
In the example of the fuzzy air conditioner, the controller works on the basis of a temperature measurement. The room temperature is just a number, and more information is necessary to decide whether the room is warm. Therefore, the designer must incorporate a human being’s perception of warm room temperatures. A straightforward approach is to evaluate beforehand all possible temperature measurements. For example, on a scale from 0 to 1, truly warm corresponds to 1 and definitely not warm corresponds to 0,
This example uses discrete temperature measurements, whereas Figure 1.1 shows the same idea graphically, in the form of a continuous mapping of temperature measurements to truth-values. The mapping is arbitrary, that is, based on preference, not mathematical reason.
1.2 Why Fuzzy Control?
If PID control (proportional-integral-derivative control) is inadequate – for example, in the case of higher-order processes, systems with a long deadtime, or systems with oscillatory modes (Åström and Hägglund 2006) – fuzzy control is an option. But first, let us consider why one would not use a fuzzy controller:
- The PID controller is well understood, easy to implement – both in its digital and analogue forms – and it is widely used. By contrast, the fuzzy controller requires some knowledge of fuzzy logic. It also involves building arbitrary membership functions.
- The fuzzy controller is generally nonlinear. It does not have a simple equation like the PID, and it is more difficult to analyse mathematically; approximations are required, and it follows that stability is more difficult to guarantee.
- The fuzzy controller has more tuning parameters than the PID controller. Furthermore, it is difficult to trace the data flow during execution, which makes error correction more difficult.
On the other hand, fuzzy controllers are used in industry with success. There are several possible reasons:
- Since the control strategy consists of if–then rules, it is easy for a process operator to read. The rules can be built from a vocabulary containing everyday words such as ‘high’, ‘low’, and ‘increasing’. Process operators can e...
