8.2.2 Stability and Performance Analysis Next we will discuss several issues related to the performance analysis of fuzzy control systems o 1. Is verification and certification of fuzzy control systems important? Yes, especially for safety-critical systems(e.g, an aircraft). It may not be as important for certain applications (e. g, a washing machine with a fuzzy control system) 42. What are the roles of simulation and implementation in evaluating the performance of fuzzy control systems? They play exactly the same role as for conventional control systems
8.2.2 Stability and Performance Analysis Next, we will discuss several issues related to the performance analysis of fuzzy control systems. ❖ 1. Is verification and certification of fuzzy control systems important? Yes, especially for safety-critical systems (e.g., an aircraft). It may not be as important for certain applications (e.g., a washing machine with a fuzzy control system). ❖ 2. What are the roles of simulation and implementation in evaluating the performance of fuzzy control systems? They play exactly the same role as for conventional control systems
3. What are the roles of the following nonlinear analysis approaches in fuzzy control system design? so(a)Phase plane analysis .s(b)Describing function analysis so(c)Stability analysis: Lyapunov's first and second methods; absolute stability and the small gain theorem o( d)Analysis of steady-state errors .o() Method of equivalent gains 冷() Cell-to-ce‖ mapping approaches Several of these approaches may apply to the analysis of the behavior of the fuzzy control system you design
3. What are the roles of the following nonlinear analysis approaches in fuzzy control system design? ❖ (a) Phase plane analysis . ❖ (b) Describing function analysis. ❖ (c) Stability analysis: Lyapunov's first and second methods; absolute stability; and the small gain theorem . ❖ (d) Analysis of steady-state errors. ❖ (e) Method of equivalent gains. ❖ (f) Cell-to-cell mapping approaches. Several of these approaches may apply to the analysis of the behavior of the fuzzy control system you design
4. What are the problems with utilizing mathematical analysis for fuzzy control system verification? The techniques take time to learn the problems for which fuzzy control are particularly well suited, and where there is often very good motivation to use fuzzy rather than conventional control are the control problems where the plant has complex nonlinear behavior, and where a model is hard to derive due to inherent uncertainties. Each of these characteristics often makes the assumptions that are needed for the nonlinear analysis techniques invalid, so the theory often does not end up offering much when it is really needed 5. Does fuzzy control provide robust control"? If so, can this be demonstrated mathematically or experimentally? There has been a recent focus in research on stability analysis to show that fuzzy control does provide robust control. It is very difficult, of course, to show robustness via experimentation since by its very definition robustness verification requires extensive experimentation
❖ 4. What are the problems with utilizing mathematical analysis for fuzzy control system verification? The techniques take time to learn. The problems for which fuzzy control are particularly well suited, and where there is often very good motivation to use fuzzy rather than conventional control, are the control problems where the plant has complex nonlinear behavior, and where a model is hard to derive due to inherent uncertainties. Each of these characteristics often makes the assumptions that are needed for the nonlinear analysis techniques invalid, so the theory often does not end up offering much when it is really needed. ❖ 5. Does fuzzy control provide "robust control"? If so, can this be demonstrated mathematically or experimentally? There has been a recent focus in research on stability analysis to show that fuzzy control does provide robust control. It is very difficult, of course, to show robustness via experimentation since by its very definition robustness verification requires extensive experimentation
8.2.3 Implementation and General issues Finally, we will discuss several issues related to implementation and the overall fuzzy controller design methodology .o 1. Are there computational advantages in using fuzzy control as compared to conventional control? Not always PID control is simpler than fuzzy control; however, there are some types of conventional control that are very difficult to implement where a fuzzy controller can be simpler. It depends on the application and the methods you choose o 2. Should I use a conventional or "fuzzy processor"for implementation? We have typically found that our needs can be met if we use a conventional processor that has a better track record with reliability; however, there may be some advantages to fuzzy processors when large rule bases are used and fast sampling times are needed
8.2.3 Implementation and General Issues Finally, we will discuss several issues related to implementation and the overall fuzzy controller design methodology. ❖ 1. Are there computational advantages in using fuzzy control as compared to conventional control? Not always. PID control is simpler than fuzzy control; however, there are some types of conventional control that are very difficult to implement where a fuzzy controller can be simpler. It depends on the application and the methods you choose. ❖ 2. Should I use a conventional or "fuzzy processor" for implementation? We have typically found that our needs can be met if we use a conventional processor that has a better track record with reliability; however, there may be some advantages to fuzzy processors when large rulebases are used and fast sampling times are needed
33. Are there special"tricks of the trade"in the implementation of fuzzy controllers that have many rules? Yes. Several of these are listed in Chapter 2, in Section 2.6 beginning on page 91 .o 4. Does fuzzy control provide for a user-friendly way to tune the controller during implementation studies? Often it does, We have found in field studies that when you know generally what to do to get a controller to work, it is sometimes hard to get this information into the gains of a conventional controller and easier to express it in rules and load them into a fuzzy controller or fuzzy supervisor
❖ 3. Are there special "tricks of the trade" in the implementation of fuzzy controllers that have many rules? Yes. Several of these are listed in Chapter 2, in Section 2.6 beginning on page 91. ❖ 4. Does fuzzy control provide for a user-friendly way to tune the controller during implementation studies? Often it does. We have found in field studies that when you know generally what to do to get a controller to work, it is sometimes hard to get this information into the gains of a conventional controller and easier to express it in rules and load them into a fuzzy controller or fuzzy supervisor