Abstract
This paper deals with stability of a fuzzy control system designed using the direct fuzzy inference. The describing function method is applied to the stability analysis.
A fuzzy controller has two inputs (the error and the change in error) and one output (the change in manipulating variable). The input variable is divided into three fuzzy partitions, that is Positive, Zero and Negative. The output value has three singletons as fuzzy partitions: Positive, Zero and Negative.
The describing function of this fuzzy controller is analytically obtained. Using the relationship between the locus of inverse describing function and Nyquist locus of the controlled object, the asymptotically stable condition of the fuzzy control system is analyzed.
Using this condition, stability bounds of the loop gain for the first order lag system with dead time and the second order linear system are calculated analytically. Those stability bounds are founds to be nearly equal to those obtained by a simulation study.
This fact indicates that the describing function method is useful for analyzing the stability of fuzzy control systems with direct fuzzy inference.
