As an example, we showed how our heuristic knowledge can be used to design a fuzzy controller for the rotational inverted pendulum. However, we also showed 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 control"(MRAC) 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 Following this, in Section 4.4 we show several ways to "dynamically focus"the learning activities of an adaptive fuzzy controller. A simple magnetic levitation control problem is used to introduce the methods, and we compare the performance of the methods to a conventional adaptive control technique. Design and implementation case studies are provided for the rotational inverted pendulum(with a sloshing liquid in a bottle at the endpoint) Adaptation mechani sm controller plant Figure 4.1 direct adaptive controlAs an example, we showed how our heuristic knowledge can be used to design a fuzzy controller for the rotational inverted pendulum. However, we also showed 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 control" (MRAC). 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. Following this, in Section 4.4 we show several ways to "dynamically focus" the learning activities of an adaptive fuzzy controller. A simple magnetic levitation control problem is used to introduce the methods, and we compare the performance of the methods to a conventional adaptive control technique. Design and implementation case studies are provided for the rotational inverted pendulum (with a sloshing liquid in a bottle at the endpoint). Figure 4.1 direct adaptive controls