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Part IV Nonadaptive Fuzzy Control

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Part IV Nonadaptive Fuzzy Control Part IV Nonadaptive Fuzzy Control When fuzzy systems are used as controllers, they are called fuzzy controllers. If fuzzy systems are used to model the process and controllers are designed based on the model, then the resulting controllers also are called fuzzy controllers. Therefore, fuzzy controllers are nonlinear controllers with a special structure. Fuzzy control has represented the most successful applications of fuzzy theory to practical problems. Fuzzy control can be classified into nonadaptive fuzzy control and adaptive fuzzy control. In nonadaptive fuzzy control, the structure and parameters of the fuzzy controller are fixed and do not change during real-time operation. In adaptive fuzzy control, the structure orland parameters of the fuzzy controller change during real- time operation. Nonadaptive fuzzy control is simpler than adaptive fuzzy control, but requires more knowledge of the process model or heuristic rules. Adaptive fuzzy control, on the other hand, is more expensive to implement, but requires less information and may perform better. In this part (Chapters 16-22), we will study nonadaptive fuzzy control. In Chapter 16, we will exam the trial-and-error approach to fuzzy controller design through two case studies: fuzzy control of a cement kiln and fuzzy control of a wastewater treatment process. In Chapters 17 and 18, stable and optimal fuzzy controllers for linear plants will be designed, respectively. In Chapters 19 and 20, fuzzy controllers for nonlinear plants will be developed in such a way that stability is guaranteed by using the ideas of sliding control and supervisory control. A fuzzy gain scheduling for PID controllers also will be studied in Chapter 20. In Chapter 21, both the plant and the controller will be modeled by the Takagi-Sugeno-Kang fuzzy systems and we will show how to choose the parameters such that the closed- loop system is guaranteed to be stable. Finally, Chapter 22 will introduce a few robustness indices for fuzzy control systems and show the basics of the hierarchical fuzzy systems. Chapter 16 The Trial-and- Error Approach to Fuzzy Controller Design 16.1 Fuzzy Control Versus Conventional Control Fuzzy control and conventional control have similarities and differences. They are similar in the following aspects: They try to solve the same kind of problems, that is, control problems. There- fore, they must address the same issues that are common to any control prob- lem, for example, stability and performance. The mathematical tools used to analyze the designed control systems are similar, because they are studying the same issues (stability, convergence, etc.) for the same kind of systems. However, there is a fundamental difference between fuzzy control and conven- tional control: Conventional control starts with a mathematical model of the process and con- trollers are designed for the model; fuzzy control, on the other hand, starts with heuristics and human expertise (in terms of fuzzy IF-THEN rules) and controllers are designed by synthesizing these rules. That is, the information used to construct the two types of controllers are different; see Fig.lG.1. Ad- vanced fuzzy controllers can make use of both heuristics and mathematical models; see Chapter 24. For many practical control problems (for example, industrial process control), it is difficult to obtain an accurate yet simple mathematical model, but there are experienced human experts who can provide heuristics and rule-of-thumb that are very useful for controlling the process. Fuzzy control is most useful for these kinds Sec. 16.1. Fuzzy Control Versus Conventional Control 207 fuzzy control conventional control heuristics and mathematical human expertise I I model I nonlinear controller I nonlinear control theory Figure 16.1. Fuzzy control versus conventional control. of problems. As we will learn in this and the next few chapters, if the mathemat- ical model of the process is unknown or partially unknown, we can design fuzzy controllers in a systematic manner that guarantee certain key performance criteria. We classify the design methodologies for fuzzy controllers into two categories: the trial-and-error approach and the theoretical approach. In the trial-and-error approach, a set of fuzzy IF-THEN rules are collected from an introspective ver- balization of experience-based knowledge (for example, an operating manual) and by asking the domain experts to answer a carefully organized questionnaire; then, fuzzy controllers are constructed from these fuzzy IF-THEN rules; finally, the fuzzy controllers are tested in the real system and if the performance is not satisfactory, the rules are fine-tuned or redesigned in a number of trial-and-error cycles until the performance is satisfactory. In the theoretical approach, the structure and param- eters of the fuzzy controller are designed in such a way that certain performance criteria (for example, stability) are guaranteed. Of course, in designing fuzzy con- trollers for practical systems we should combine both approaches whenever possible to get the best fuzzy controllers. In this chapter, we will illustrate the trial-and-error approach through two practical examples-a cement kiln fuzzy control system, and a wastewater treatment fuzzy control system. The theoretical approaches will be studied in Chapters 17-21. 208 The Trial-and-Error Approach to Fuzzy Controller Design Ch. 16 16.2 The Trial-and-Error Approach to Fuzzy Controller Design The trial-and-error approach to fuzzy controller design can be roughly summarized in the following three steps: Step 1: Analyze the real system and choose state and control vari- ables. The state variables should characterize the key features of the system and the control variables should be able to influence the states of the system. The state variables are the inputs to the fuzzy controller and the control vari- ables are the outputs of the fuzzy controller. Essentially, this step defines the domain in which the fuzzy controller is going to operate. Step 2. Derive fuzzy IF-THEN rules that relate the state variables with the control variables. The formulation of these rules can be achieved by means of two heuristic approaches. The most common approach involves an introspective verbalization of human expertise. A typical example of such verbalization is the operating manual for the cement kiln, which we will show in the next section. Another approach includes an interrogation of experienced experts or operators using a carefully organized questionnaire. In these ways, we can obtain a prototype of fuzzy control rules. Step 3. Combine these derived fuzzy IF-THEN rules into a fuzzy system and test the closed-loop system with this fuzzy system as the controller. That is, run the closed-loop system with the fuzzy controller and if the performance is not satisfactory, fine-tune or redesign the fuzzy controller by trial and error and repeat the procedure until the performance is satisfactory. We now show how to design fuzzy controllers for two practical systems using this approach-a cement kiln system and a wastewater treatment process. 16.3 Case Study I: Fuzzy Control of Cement Kiln As we mentioned in Chapter 1, fuzzy control of cement kiln was one of the first successful applications of fuzzy control to full-scale industrial systems. In this sec- tion, we summarize the cement kiln fuzzy control system developed by Holmblad and Bsterguard [I9821 in the late '70s. 16.3.1 The Cement Kiln Process Cement is manufactured by fine grinding of cement clinkers. The clinkers are pro- duced in the cement kiln by heating a mixture of limestone, clay, and sand com- ponents. For a wet process cement kiln, the raw material mixture is prepared in a slurry; see Fig.16.2. Then four processing stages follow. In the first stage, the water Sec. 16.3. Case Studv I: Fuzzv Control of Cement Kiln 209 is driven off; this is called preheating. In the second stage, the raw mix is heated up and calcination (COz is driven off) takes place. The third stage comprises burning of the material at a temperature of approximately 1430°C, where free lime (CaO) combines with the other components to form the clinker minerals. In the final stage, the clinkers are cooled by air. coal from mill m burning slurry calcining feeder / I preheating clinker zone W I I I I cooler I I xn burner I pipe hot air exhaust/ gas Figure 16.2. The cement kiln process. The kiln is a steel tube about 165 meters long and 5 meters in diameter. The kiln tube is mounted slightly inclined from horizontal and rotates 1-2 rev/min. The clinker production is a continuous process. The slurry is fed to the upper (back) end of the kiln, whereas heat is provided to the lower (front) end of the kiln; see Fig. 16.2. Due to the inclination and the rotation of the kiln tube, the material is transported slowly through the kiln in 3-4 hours and heated with hot gases. The hot combustion gases are pulled through the kiln by an exhaust gas fan and controlled by a damper that is in the upper end of the kiln as shown in Fig. 16.2. Cement kilns exhibit time-varying nonlinear behavior and experience indicates that mathematical models for the process become either too simple to be of any practical value, or too comprehensive and needled into the specific process to possess 210 The Trial-and-Error Approach to Fuzzy Controller Design Ch. 16 any general applicability. However, humans can be trained and in a relatively short time become skilled kiln operators. Consequently, cement kilns are specially suitable for fuzzy control. 16.3.2 Fuzzy Controller Design for the Cement Kiln Process First, we determine the state and control variables for this system. The state variables must characterize the main functioning of the cement kiln process and their values can be determined from sensory measurements.
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