1. A rule-base(a set of If-Then rules), which contains a fuzzy logic quantification of the expert's linguistic description of how to achieve good control 2. An inference mechanism(also called an"inference engineor fuzzy inference"module), which emulates the expert's decision making in interpreting and applying knowledge about how best to control the plant. 3. Fuzzification interface, which converts controller inputs into information that the inference mechanism can easily use to activate and apply rules. 4. A defuzzification interface, which converts the conclusions of the inference mechanism into actual Inputs for the e process. 36
36 1. A rule-base (a set of If-Then rules), which contains a fuzzy logic quantification of the expert's linguistic description of how to achieve good control. 2. An inference mechanism (also called an "inference engine" or "fuzzy inference" module), which emulates the expert's decision making in interpreting and applying knowledge about how best to control the plant. 3. A fuzzification interface, which converts controller inputs into information that the inference mechanism can easily use to activate and apply rules. 4. A defuzzification interface, which converts the conclusions of the inference mechanism into actual inputs for the process
We introduce each of the components of the fuzzy controller for a simple problem of balancing an inverted pendulum on a cart, as shown in Figure 1.3. Here, y denotes the angle that the pendulum makes with the vertical (in radians), l is the half- pendulum length(in meters), and u is the force input that moves the cart (in Newtons ). we will use r to denote the desired angular position of the pendulum. The goal is to balance the pendulum in the upright position (i.e, r=0 when it initially starts with some nonzero angle off the vertical e,y≠0) 37
37 We introduce each of the components of the fuzzy controller for a simple problem of balancing an inverted pendulum on a cart, as shown in Figure 1.3. Here, y denotes the angle that the pendulum makes with the vertical (in radians), l is the halfpendulum length (in meters), and u is the force input that moves the cart (in Newtons). We will use r to denote the desired angular position of the pendulum. The goal is to balance the pendulum in the upright position (i.e., r = 0) when it initially starts with some nonzero angle off the vertical (i.e., y≠0)
Figure2.3 Inverted pendulum on a cart 38
38 Figure2.3 Inverted pendulum on a cart
This is a very simple and academic nonlinear control problem, and many good techniques already exist for its solution. Indeed, for this standard configuration, a simple PID controller works well even in implementation. In the remainder of this section we will use the inverted pendulum as a convenient problem to illustrate the design and basic mechanics of the operation of a fuzy control system. We will also use this problem in Section 2. 4 to discuss much more general issues in fuzzy control system design that the reader will find useful for more challenging applications(e.g the ones in the next chapter) 39
39 This is a very simple and academic nonlinear control problem, and many good techniques already exist for its solution. Indeed, for this standard configuration, a simple PID controller works well even in implementation. In the remainder of this section, we will use the inverted pendulum as a convenient problem to illustrate the design and basic mechanics of the operation of a fuzzy control system. We will also use this problem in Section 2.4 to discuss much more general issues in fuzzy control system design that the reader will find useful for more challenging applications (e.g., the ones in the next chapter)
2.2.1 Choosing Fuzzy Controller Inputs and Outputs How do we choose fuzzy controller inputs and outputs to control the pendulum, as shown in Figure 2 o Consider a human-in-the-loop whose responsibility The fuzzy controller is to be designed to automate how a human expert who is successful at this task would control the system. First, the expert tells us (the designers of the fuzy controller) what information she or he will use as inputs to the decision-ma king process 40
40 2.2.1 Choosing Fuzzy Controller Inputs and Outputs How do we choose fuzzy controller inputs and outputs ? Consider a human-in-the-loop whose responsibility is to control the pendulum, as shown in Figure 2.3. The fuzzy controller is to be designed to automate how a human expert who is successful at this task would control the system. First, the expert tells us (the designers of the fuzzy controller) what information she or he will use as inputs to the decision-making process