郑州大学电气工程学院：《智能控制》课程教学资源（PPT课件）Chapter 04 Adaptive Fuzzy Control

Chapter 4 Adaptive Fuzzy Control

1 Chapter 4 Adaptive Fuzzy Control

4.1 Overview The design process for fuzzy controllers that is based on the use of heuristic information from human experts has found success in many industrial applications. Moreover, the approach to constructing fuzzy controllers via numerical input-output data is increasingly finding use

2 4.1 Overview The design process for fuzzy controllers that is based on the use of heuristic information from human experts has found success in many industrial applications. Moreover, the approach to constructing fuzzy controllers via numerical input-output data is increasingly finding use

Regardless of which approach is used, however, there are certain problems that are encountered for practical control problems, including the following: (1)The design of fuzzy controllers is performed in an ad hoc manner so it is often difficult to choose at least some of the controller parameters. For example, it is sometimes difficult to know how to pick the membership functions and rule-base to meet a specific desired level of performance. (2) The fuzzy controller constructed for the nominal plant may later perform inadequately if significant and unpredictable plant parameter variations occur, or if there is noise or some type of disturbance or some other environmental effect. Hence, it may be difficult to perform the initial synthesis of the fuzzy controller, and if the plant changes while the closed loop system is operating we may not be able to maintain adequate performance levels

3 Regardless of which approach is used, however, there are certain problems that are encountered for practical control problems, including the following: (1) The design of fuzzy controllers is performed in an ad hoc manner so it is often difficult to choose at least some of the controller parameters. For example, it is sometimes difficult to know how to pick the membership functions and rule-base to meet a specific desired level of performance. (2) The fuzzy controller constructed for the nominal plant may later perform inadequately if significant and unpredictable plant parameter variations occur, or if there is noise or some type of disturbance or some other environmental effect. Hence, it may be difficult to perform the initial synthesis of the fuzzy controller, and if the plant changes while the closed￾loop system is operating we may not be able to maintain adequate performance levels

With our heuristic knowledge we could design a fuzzy controller for the rotational inverted pendulum. However, we could also do that if a bottle half-filled with water is attached to the endpoint, the performance of the fuzzy controller degraded, While we certainly could have tuned the controller for this new situation it would not then perform as well without a bottle of liquid at the endpoint. It is for this reason that we need a way to automatically tune the fuzzy controller so that it can adapt to different plant conditions. Indeed, it would be nice if we had a method that could automatically perform the whole design task for us initially so that it would also synthesize the fuzzy controller for the nominal condition. In this chapter we study systems that can automatically synthesize and tune( direct) fuzzy controllers

4 With our heuristic knowledge we could design a fuzzy controller for the rotational inverted pendulum. However, we could also do that if a bottle half-filled with water is attached to the endpoint, the performance of the fuzzy controller degraded. While we certainly could have tuned the controller for this new situation, it would not then perform as well without a bottle of liquid at the endpoint. It is for this reason that we need a way to automatically tune the fuzzy controller so that it can adapt to different plant conditions. Indeed, it would be nice if we had a method that could automatically perform the whole design task for us initially so that it would also synthesize the fuzzy controller for the nominal condition. In this chapter we study systems that can automatically synthesize and tune (direct) fuzzy controllers

There are two general approaches to adaptive control, the first of which is depicted in Figure 4.1. In this approach the adaptation mechanism"observes the signals from the control system and adapts the parameters of the controller to maintain performance even if there are changes in the plant. Sometimes, the desired performance is characterized with a reference model. and the controller then seeks to make the closed-loop system behave as the reference model would even if the plant changes. This is called"model reference adaptive controlMRAC)

5 There are two general approaches to adaptive control, the first of which is depicted in Figure 4.1. In this approach the "adaptation mechanism" observes the signals from the control system and adapts the parameters of the controller to maintain performance even if there are changes in the plant. Sometimes, the desired performance is characterized with a "reference model," and the controller then seeks to make the closed-loop system behave as the reference model would even if the plant changes. This is called "model reference adaptive control" (MRAC)

Adaptation 凵 mechanlsm r(t) u(t controller plant FIGURE 4.1 direct adaptive controls 6

6 FIGURE 4.1 direct adaptive controls. Adaptation mechanism controller plant r(t) u(t) y(t)

In Section 4.2 we use a simple example to introduce a method for direct (model reference) adaptive fuzzy control where the controller that is tuned is a fuzzy controller. Next, we provide several design and implementation case studies to show how it compares to conventional adaptive control for a ship steering application, how to make it work for a multi-input multi-output MIMO) fault-tolerant aircraft control problem, and how it can perform in implementation for the two-link flexible robot

7 In Section 4.2 we use a simple example to introduce a method for direct (model reference) adaptive fuzzy control where the controller that is tuned is a fuzzy controller. Next, we provide several design and implementation case studies to show how it compares to conventional adaptive control for a ship steering application, how to make it work for a multi-input multi-output (MIMO) fault-tolerant aircraft control problem, and how it can perform in implementation for the two-link flexible robot

In the second general approach to adaptive control, which is shown in Figure 4.2, we use an on-line system identification method to estimate the parameters of the plant and a"controller designer module to subsequently specify the parameters of the controller

8 In the second general approach to adaptive control, which is shown in Figure 4.2, we use an on-line system identification method to estimate the parameters of the plant and a "controller designer" module to subsequently specify the parameters of the controller

If the plant parameters change, the identifier will provide estimates of these and the controller designer will subsequently tune the controller. It is inherently assumed that we are certain that the estimated plant parameters are equivalent to the actual ones at all times(this is called the certainty equivalence principle Then if the controller designer can specify a controller for each set of plant parameter estimates, it will succeed in controlling the plant. The overall approach is called"indirect adaptive control since we tune the controller indirectly by first estimating the plant parameters(as opposed to direct adaptive control, where the controller parameters are estimated directly without first identifying the plant parameters

9 If the plant parameters change, the identifier will provide estimates of these and the controller designer will subsequently tune the controller. It is inherently assumed that we are certain that the estimated plant parameters are equivalent to the actual ones at all times (this is called the "certainty equivalence principle"). Then if the controller designer can specify a controller for each set of plant parameter estimates, it will succeed in controlling the plant. The overall approach is called "indirect adaptive control" since we tune the controller indirectly by first estimating the plant parameters (as opposed to direct adaptive control, where the controller parameters are estimated directly without first identifying the plant parameters)

Plant Controller parameters System designer identification Controller parameters r(t y controller plant FIGURE 4.2 indirect adaptive controls

10 FIGURE 4.2 indirect adaptive controls. System identification controller plant r(t) u(t) y(t) Controller designer Plant parameters Controller parameters