The early work in fuzzy process control by Mamdani’s group was focused on the control of a small steam engine in a laboratory environment. This work paved the way for large-scale process control methods. The first large-scale industrial application of fuzzy control was to a cement kiln (Holmblad and Ostergaard, 1982). The development of the cement kiln controller was facilitated by the availability of an operator’s handbook containing rules for controlling the system. This work of Holmblad and Ostergaard laid the foundation for subsequent rule-based fuzzy process control systems. Particularly, it represents the starting point for the research described in this book. We were attracted to these fuzzy systems because they were simple and linguistic in nature; we could control nonlinear systems with simple linguistic rules. A fundamental flaw with this control system remained. It was not adaptive; it could not change when the process changed.

Early on in the fuzzy process control effort, researchers discussed primitive adaptive fuzzy control systems. Procyk and Mamdani (1979) extended their initial fuzzy control system to form a self-organizing process controller that used a linguistic description of the control strategy as a basis for adaptation. It implemented a derivative-based search to discover effective linguistic rules. The research effort presented in this book extends this initial effort in adaptive control by employing new and developing tools from the field of computational intelligence including genetic algorithms and neural networks. We felt that we could use adaptive linguistic systems to learn very precise control rules and that human operators might accept such linguistic controllers that use the kind of linguistic rules they understand better than they have accepted mathematical “black boxes.” However, we are getting a little ahead of ourselves.

1.3 Where We Got Involved

Our initial thesis was that traditional control techniques were unnecessarily complex and that expert systems could be used to implement the strategies employed by effective operators. However, as we discovered, traditional expert systems were not the answer by themselves.

Our initial expert system was a process control advisor for a phosphate flotation plant (Davis, Jordan, and Stanley, 1990). (Chapter 16 addresses column flotation. Flotation is a process through which economically valuable minerals are separated in a water suspension from sand sized valueless material.) This prototype expert system was developed to systematically offer advice on the control of a commercial Florida phosphate flotation plant operation. The PC-based system was designed to receive input from remote sensors for circuit parameters such as feed rate, reagent addition, and pH and also accept input of operator supplied information. This information described the quality of the concentrate and tailings in each of the coarse, fine, and amine flotation circuits. The computer evaluated the information using rules obtained from industry representatives and Bureau of Mines flotation experts. The expert system then recommended actions to the operator based on problems identified in the flotation circuit. This expert system was designed to provide more uniformity among the flotation operators and to serve as a trainer for new operators. In addition, it represented an initial step toward fully automated systems for phosphate flotation.

As effective as the phosphate flotation advisor was, it did have some inadequacies. Most notably, the traditional production rules it used were not adequate to accomplish accurate control. To illustrate this shortcoming, let’s consider an example situation in which non-fuzzy, if-then, production rules are used.

Consider the task of capturing the characteristics of a simple system represented by the function shown in Figure 1.1. This figure can be thought of as presenting a relationship between input and output parameters, and captures the essence of the task associated with both process control and modeling. The goal in control is to provide a desired value of the output variables based on the current values of the input variables.

Interestingly enough, this figure also represents the modeling problem. In a computer modeling problem, the goal is to use independent variables to determine dependent variables. When there is but one independent and one dependent variable, Figure 1.1 is sufficient. However, as in the control problem, when there are multiple input and output parameters, the curve in Figure 1.1 must be expanded into a higher dimensional surface. Both control and modeling problems can be thought of as surface fitting problems.

Figure 1.1  A general functional relationship can be used to represent both process control and modeling applications.

Consider the task of representing the control/modeling problem represented by the curve in Figure 1.1 with production rules. And, realize that although this curve exists, it is generally identified with data points; we do not know the form of the equation that describes f(x). One production rule representation of the curve might consist of the following rules:

1.  If { 0 < x ≤ 1 } then { f(x) = 3.0 }

2.  If { 1 < x ≤ 2 } then { f(x) = 2.0 }

3.  If { 2 < x ≤ 3 } then { f(x) = 1.0 }

4.  If { 3 < x ≤ 4 } then { f(x) = 2.0 }

5.  If { 4 < x ≤ 5 } then { f(x) = 3.0 }