A computational approach to fuzzy logic controller design
Nonlinearities inherent in practical control problems make closed form solutions difficult. Using computational and empirical methods, a multi-disciplinary approach is presented for the design of a nonlinear real time controller of industrial processes. The state space is quantized into cells creating a discrete state space model of system behavior. Using a form of dynamic programming, an optimal control algorithm based on this cellular structure generates a discrete optimal control table. To avoid the problems associated with quantized control actions, a fuzzy logic controller (FLC) with parametrized rule output functions is tuned to fit, in a least squares sense, the control policy embodied in the control table. The output of the fuzzy logic controller is a smooth nonlinear function of its inputs and is amenable to real time implementation on a digital processor. This approach constitutes a systematic procedure for FLC design.
This work led to improved versions of the cell-to-cell mapping and optimal control algorithms through variable time step sizes, nonuniform cell sizes, and adjusted cost functions. A derivation is given for the application of the Widrow-Hoff LMS algorithm to the selection of FLC output parameters. The approach is verified with two examples, the time optimal position control of a DC motor and the time optimal angular position control of an inverted pendulum.