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Fuzzy Control and Modeling: Analytical Foundations and Applications

Hao Ying

Chapter 4

Mamdani Fuzzy Controllers of Non-PID Type - all with Video Answers

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Chapter Questions

Problem 1

Is a fuzzy controller that uses linear fuzzy rules always a linear fuzzy controller?

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Problem 2

Find some fuzzy control or fuzzy modeling papers in the literature that include complete information on the Mamdani fuzzy rules used. Compare these fuzzy rules with the corresponding linear fuzzy rules to see how different they can be. Are the differences significant?

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Problem 3

Generate nonlinear fuzzy rules using some nonlinear functions of your choice. (See Section 4.3.) What are the limit controllers for fuzzy controllers using these nonlinear fuzzy rules?

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Problem 4

Verify the analytical structures of the fuzzy controllers derived in this chapter.

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Problem 5

Use computer simulation to compare control performance between the fuzzy controllers with linear fuzzy rules in this chapter and their respective limit controllers (i.e., linear PI, PD and PID controllers). Use different system models. Are the fuzzy controllers better than the linear controllers?

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Problem 6

. The fuzzy controllers in this chapter are non-PID type, whereas those in the previous chapter are PID-type. What are the causes?

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Problem 7

Section 4.7 shows that a fuzzy controller with linear fuzzy rules and three input variables does not necessarily become the sum of a global three-dimensional multilevel relay and a local nonlinear PID controller. Can you configure a fuzzy controller so that this is the case?

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Problem 8

Use the results in Section 4.9 .2 to directly generate the analytical structures of some fuzzy controllers that interest you. See Section 4.9 .5 for examples.

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Problem 9

Build a nonlinear fuzzy controller with linear fuzzy rules. Conduct a simulation study, using different system models, to explore how the degree of nonlinearity of the fuzzy controller, determined by the number of input fuzzy sets, affects the performance of the fuzzy control systems.

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Problem 10

. Compare the fuzzy control performances in Problem 8 with those achieved by the linear limit controller.

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Problem 11

Is it possible to quantify the degree of nonlinearity for fuzzy controllers with nonlinear fuzzy rules? If yes, how can you do it? If no, why?

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