The Composition of Heterogeneous Control Laws

To design a control system to operate over a wide range of conditions, it may be necessary to combine control laws which are appropriate to the different operating regions of the system. The fuzzy control literature, and industrial practice, provide certain non-linear methods for combining heterogeneous control laws, but these methods have been very difficult to analyze theoretically. We provide an alternate formulation and extension of this approach that has several practical and theoretical benefits. First, the elements to be combined are classical control laws, which provide high-resolution control and can be analyzed by classical methods. Second, operating regions are characterized by fuzzy set membership functions. The global heterogeneous control law is defined as the weighted average of the local control laws, where the weights are the values returned by the membership functions, thereby providing smooth transitions between regions. Third, the heterogeneous control system may be described by a qualitative differential equation, which allows it to be analyzed by qualitative simulation, even in the face of incomplete knowledge of the underlying system or the operating region membership functions. An example of heterogeneous control is given for level control of a water tank and two alternate analysis methods are presented.