Interval type-2 fuzzy pid controllers

The aim of this chapter is to present a general overview about interval type-2 fuzzy PID (proportional-integral-derivative) controller structures. We will focus on the standard double input direct action type fuzzy PID controller structures and their present design methods. It has been shown in various works that the type-1 fuzzy PID controllers, using crisp type-1 fuzzy sets, might not be able to fully handle the high levels of uncertainties associated with control applications while the type-2 fuzzy PID controller using type-2 fuzzy sets might be able to handle such uncertainties to produce a better control performance. Thus, we will classify and examine the handled fuzzy PID controllers within two groups with respect to the fuzzy sets they employ, namely type-1 and interval type-2 fuzzy sets. We will present and examine the controller structures of the direct action type-1 fuzzy PID and interval type-2 fuzzy PID controllers on a generic, a symmetrical 3x3 rule base. We will present general information about the type-1 fuzzy PID and interval type-2 fuzzy PID controllers tuning parameters and design strategies. Finally, we will present a simulation study to evaluate the control performance of the type-1 fuzzy PID and interval type-2 fuzzy PID on a first-order plus time-delay benchmark process.