Supervisory control using fuzzy set theory

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There is a strong economic incentive for designing supervisory controllers to optimize the performance of complex industrial processes. However, relatively few industrial examples have been reported. This is attributed to the lack of good mathematical models which are needed to implement the existing techniques based on modern control theory. By relaxing the constraint on the mathematical nature of the model, a whole range of techniques adapted from decision and game theory become available. These techniques use the operator's linguistic process model which relates cause and effect e.g. IF the flow is increased THEN the temperature will decrease. Usually these relationships are phrased in vague imprecise terms. in previous attempts to develop controllers from this type of model, classical set theory has been used to represent the concepts being expressed. This takes no account of the imprecision of the statement. It has been shown that a more successful representation of these concepts is achieved if fuzzy sets are used to model the imprecise concepts. This thesis is concerned with the development of supervisory controllers using these linguistic models. Three methods are described: (a) The heuristic controller (HO consists of a set of linguistic control rules. These rules are developed by the operator a priori and so represent his solution to the control problem given an implicit understanding of the process and its objectives. The rules relate the state of the process to the control action needed to optimize it e.g. IF the temperature is low THEN increase the flowrate. It is shown that when the linguistic concepts of this controller are represented by fuzzy rather than classical sets, controller performance is more robust and reliable. (b) Control actions can also be generated from an explicit formulation of the linguistic model and the process objectives. Using this method, the model-based controller (MBC) does not rely on the operator to produce the rules set. It does, however, require that the process objectives can be represented as fuzzy sets on the domains of the constraint and manipulated variables. Once the goals and constraints are defined, a priority assignment technique is used to reflect the importance of each objective. Consequently, at each control instant, the control action is selected so that the fuzzy performance function is improved. Two alternative decision mechanisms (MIN and MULT) have been assessed. It is shown that the MIN decision maker produces a controller which is more versatile and robust. In the MIN decision maker, the decision is controlled by the objective that Is furthest from Its desired state. (c) The development of the above methods led to the design of a self-organizing controller. This incorporates the best aspects of the heuristic and model-based controllers by allowing the operator to specify (i) an explicit linguistic model (ii) an explicit set of fuzzy objectives; and (iii) an initial set of control rules The control action is normally calculated from the heuristic rule set. However, when the performance of these rules is unsatisfactory, they are modified by reference to the model and process objectives. Thus, even though the original set of control rules may not cover the full variable space or may contain rules that are inconsistent with the process objectives, the self-organizing controller can cope with these problems by changing its own structure. The controller design procedures developed here were tested and evaluated on the control of a computer simulated cement kiln and also on a laboratory-scale heat recovery unit. To implement the fuzzy control scheme, a fuzzy compiler was required. This was developed so that linguistic algorithms and models could be written and altered without reference to their detailed fuzzy implementation. The results show that linguistic models can be used to design supervisory controllers and that the controller performance is enhanced when the linguistic concepts are represented by fuzzy sets. The methods developed here appear to have considerable potential for industrial implementation.