Heuristic design of a fuzzy controller for a flexible robot

A ratio is identified as a heuristic to assist in designing fuzzy logic system (FLS) controllers with a low number of membership functions (MFs), high tracking precision, and fast execution time for the control of a two-link flexible space robot. Comparing simulation results for an FLS with three, five, seven, and nine triangular and Gaussian membership functions provides a combination of type and number of MF for optimal tracking control and execution time. Optimal control occurs when the ratio of the FLS output scaling gain to the number of MFs is equal to the output variable universe of discourse. The optimal FLS design is chosen with three triangular membership functions at an output scaling gain of 15, giving a design ratio of five and execution time of 1 min 40 s while tracking a square trajectory.