is not written down, some type of model is used"in your head. 6. Since most people claim that no formal model is used in the fuzzy control design methodology, the following questions a(a) Is it not true that there are few, if any, assumptions to be violated by fuzzy control and that the technique can be indiscriminately applied? Yes, and sometimes it is applied to systems where it is clear that a Pid controller or look-up table would be just as effective. So, if this is the case, then why not use fuzzy control? Because it is more computationally complex than a Pid controller and the pid controller is much more widely (b) Are heuristics all that are available to perform fuzzy controller design? No. any good models that can be used, probably should be (c) By ignoring a formal model, if it is available, is it not the case that a significant amount of information about how to control the plant is ignored? Yes. If, for example, you have a model of a complex process, we ofter use simulations to gain an understanding of how best to control the plant-and this knowledge can be used to design a fuzzy controller a(d) Can standard control theoretic analysis be used to verify the operation of the resulting control system? Sometimes, if the fuzzy control system satisfies the assumptions needed for the mathematical analysis. This will (e) Will it be difficult to clearly characterize the limitations of various fuzzy control techniques(i.e, to classify which plants can be controlled best with different fuzzy or conventional controllers)? Yes (f) Will it be difficult to clearly relate the results of using the fuzzy controller to previous work in conventional control to definitively show that contributions are being made to the field of control? Yes 7. Is there always a formal model available for control design? No, but for most systems there is at least an approximate model available. This information is often valuable and should not be ignore 8. Does the use of fuzzy controllers limit the design methodology as compared to the use of more general expert controllers? Expert controllers use more general knowledge-representation schemes and inference strategies(see more details in Section 5.5.1), so for some plants it may be advantageous to use the expert controller. It is, however, not clear at this point what class of plants call for the use of expert control 5.2.2 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 lay 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? (a) Phase plane analy (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 approachesis not written down, some type of model is used "in your head." 6. Since most people claim that no formal model is used in the fuzzy control design methodology, the following questions arise: ƒ (a) Is it not true that there are few, if any, assumptions to be violated by fuzzy control and that the technique can be indiscriminately applied? Yes, and sometimes it is applied to systems where it is clear that a PID controller or look-up table would be just as effective. So, if this is the case, then why not use fuzzy control? Because it is more computationally complex than a PID controller and the PID controller is much more widely understood. ƒ (b) Are heuristics all that are available to perform fuzzy controller design? No. Any good models that can be used, probably should be. ƒ (c) By ignoring a formal model, if it is available, is it not the case that a significant amount of information about how to control the plant is ignored? Yes. If, for example, you have a model of a complex process, we often use simulations to gain an understanding of how best to control the plant—and this knowledge can be used to design a fuzzy controller. ƒ (d) Can standard control theoretic analysis be used to verify the operation of the resulting control system? Sometimes, if the fuzzy control system satisfies the assumptions needed for the mathematical analysis. This will be discussed in more detail in the next section. ƒ (e) Will it be difficult to clearly characterize the limitations of various fuzzy control techniques (i.e., to classify which plants can be controlled best with different fuzzy or conventional controllers)? Yes. ƒ (f) Will it be difficult to clearly relate the results of using the fuzzy controller to previous work in conventional control to definitively show that contributions are being made to the field of control? Yes. 7. Is there always a formal model available for control design? No, but for most systems there is at least an approximate model available. This information is often valuable and should not be ignored. 8. Does the use of fuzzy controllers limit the design methodology as compared to the use of more general expert controllers? Expert controllers use more general knowledge-representation schemes and inference strategies (see more details in Section 5.5.1), so for some plants it may be advantageous to use the expert controller. It is, however, not clear at this point what class of plants call for the use of expert control. 5.2.2 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? ƒ (a) Phase plane analysis. ƒ (b) Describing function analysis. ƒ (c) Stability analysis: Lyapunov's first and second methods; absolute stability; and the small gain theorem. ƒ (d) Analysis of steady-state errors. ƒ (e) Method of equivalent gains. ƒ (f) Cell-to-cell mapping approaches