CHAPTER 4

FUZZY CONTROL WITH MAMDANI SYSTEMS

The basic idea of control is to command a system to perform as desired by monitoring the system’s performance and adjusting its input in such a way as to force the performance to be as desired. The output or states of the system are measured and fed back to the controller. On the basis of this information, the controller decides how to change the system input in order to improve the system performance.

Much of conventional control is “model based,” which means the controller design is based on a mathematical model of the system. Examples of model-based controllers are linear state feedback controllers, optimal controllers, H_{∞} controllers, and proportional-integral-derivative (PID) controllers (although a skilled expert can tune a PID controller to improve system performance even when there is no mathematical model of the system).

In some cases, however, these methods fail because a sufficiently accurate mathematical model of the system is not known. In such cases, if sufficient knowledge about how to control the system is available from a human “expert,” a fuzzy system can be designed to effectively control the system even if the mathematical model is completely unknown [13,16–18]. In fact, one of the main uses for fuzzy systems is in closed-loop control of nonlinear systems whose mathematical models are unknown or poorly known.

4.1 TRACKING CONTROL WITH A MAMDANI FUZZY CASCADE COMPENSATOR

Mamdani fuzzy systems can be used to formulate ...