Chapter 2 Fuzzy Control
1 Chapter 2 Fuzzy Control
Fuzzy Control: The Basics ■ Overview a Fuzzy Control: A Tutorial Introduction General Fuzzy System a Simple Design Example: The Inverted Pendulum Simulation of fuzzy control System 2
2 Fuzzy Control: The Basics ◼ Overview ◼ Fuzzy Control: A Tutorial Introduction ◼ General Fuzzy System ◼ Simple Design Example: The Inverted Pendulum ◼ Simulation of Fuzzy Control System
Qu uestions Why do we select fuzzy controllers in many real- world systems? How much of the success can be attributed to the use of the mathematical model and conventional control design approach? How much should be attributed to the clever heuristic tuning that the control engineer uses upon implementation? If we exploit the use of heuristic information throughout the entire design process, can we obtain higher performance control systems? How do we design a fuzzy controller 3
3 Questions ◼ Why do we select fuzzy controllers in many realworld systems? ◼ How much of the success can be attributed to the use of the mathematical model and conventional control design approach? ◼ How much should be attributed to the clever heuristic tuning that the control engineer uses upon implementation? ◼ If we exploit the use of heuristic information throughout the entire design process, can we obtain higher performance control systems? ◼ How do we design a fuzzy controller?
uestions Whether do we need a model in fuzzy control? a What are the performance evaluation of fuzzy control? What should we pay attention in fuzzy controller design 4
4 Questions ◼ Whether do we need a model in fuzzy control? ◼ What are the performance evaluation of fuzzy control? ◼ What should we pay attention in fuzzy controller design?
2.1 Overview What is the motivation for turning to fuzzy control? Basically, the difficult task of modeling and simulating complex real world systems for control systems development, especially when implementation issues are considered, is well documented. Even if a relatively accurate model of a dynamic system can be developed it is often too complex to use in controller development, especially for many conventional control design procedures that require restrictive assumptions for the plant (e.g, linearity)
5 2.1 Overview What is the motivation for turning to fuzzy control? Basically, the difficult task of modeling and simulating complex real world systems for control systems development, especially when implementation issues are considered, is well documented. Even if a relatively accurate model of a dynamic system can be developed, it is often too complex to use in controller development, especially for many conventional control design procedures that require restrictive assumptions for the plant (e.g., linearity)
It is for this reason that in practice conventional controllers are often developed via simple models of the plant behavior that satisfy the necessary assumptions, and via the ad hoc(special) tuning of relatively simple linear or nonlinear controllers Regardless, it is well understood (although sometimes forgotten) that heuristics enter the conventional control design process as long as you are concerned with the actual implementation of the control system. It must be acknowledged, moreover, that conventional control engineering approaches that use appropriate heuristics to tune the design have been relatively successful
6 It is for this reason that in practice conventional controllers are often developed via simple models of the plant behavior that satisfy the necessary assumptions, and via the ad hoc(special) tuning of relatively simple linear or nonlinear controllers. Regardless, it is well understood (although sometimes forgotten) that heuristics enter the conventional control design process as long as you are concerned with the actual implementation of the control system. It must be acknowledged, moreover, that conventional control engineering approaches that use appropriate heuristics to tune the design have been relatively successful
You may ask the following questions: How much of the success can be attributed to the use of the mathematical model and conventional control design approach, and how much should be attributed to the clever heuristic tuning that the control engineer uses upon implementation? And if we exploit the use of heuristic information throughout the entire design process, can we obtain higher performance control systems? Fuzy control provides a formal methodology for representing, manipulating, and implementing a human's heuristic knowledge about how to control a system 7
7 You may ask the following questions: How much of the success can be attributed to the use of the mathematical model and conventional control design approach, and how much should be attributed to the clever heuristic tuning that the control engineer uses upon implementation? And if we exploit the use of heuristic information throughout the entire design process, can we obtain higher performance control systems? Fuzzy control provides a formal methodology for representing, manipulating, and implementing a human's heuristic knowledge about how to control a system
In this section we seek to provide a philosophy of how to approach the design of fuzzy controllers. The fuzzy controller block diagram is given in Figure 2.1, where we show a fuzzy controller embedded in a closed-loop control system. The plant outputs are denoted by y(t), its inputs are denoted by u(, and the reference input to the fuzzy controller is denoted by r(t
8 In this section we seek to provide a philosophy of how to approach the design of fuzzy controllers. The fuzzy controller block diagram is given in Figure 2.1, where we show a fuzzy controller embedded in a closed-loop control system. The plant outputs are denoted by y(t), its inputs are denoted by u (t), and the reference input to the fuzzy controller is denoted by r (t)
Fuzzy controller Reference input Inference Inputs Outputs r(t) mechani sm u(t) y(t Proces Rule-base Figure 2. 1 Fuzzy controller architecture
9 Fuzzy controller Fuzzification Defuzzification Inference mechanism Rule-base Process Inputs u(t) Outputs y(t) Reference input r(t) Figure 2.1 Fuzzy controller architecture
Basically, you should view the fuzzy controller as an artificial decision maker that operates in a closed-loop system in real time. It gathers plant output data y(, compares it to the reference input r(t, and then decides what the plant input u(t should be to ensure that the performance objectives, will be met 10
10 Basically, you should view the fuzzy controller as an artificial decision maker that operates in a closed-loop system in real time. It gathers plant output data y(t), compares it to the reference input r (t), and then decides what the plant input u(t) should be to ensure that the performance objectives, will be met
