A new integrated fuzzy bang–bang relay control system

In this paper, we propose a new fuzzy bang–bang relay controller (FBBRC). The bang–bang control systems use switching relays or hard limiter saturation functions with fixed parameters, and their input does not have the flexibility to control the non-linear system over its entire range of operation. The conventional fuzzy bang–bang controllers have an analog output and an external hard limiting device to convert the output to bang–bang action. The new integrated FBBRC proposed here directly output two-level state. The inputs to the FBBRC are configured on standard fuzzy sets on the basis Mamdani implications. The largest of maxima defuzzification method is used for two-level state output. The stability and optimality of the FBBRC can be established with the Lyapunov stability criterion and Pontrygin minimum principle, respectively. Non-linear bang–bang control action is inherently time-optimal and endows this property to the FBBRC. Because of its design simplicity and cost-effectiveness, the bang–bang control is desired for control applications such as spacecraft–satellite attitude, heating controls, and on/off valve controls. Comparison between the proposed FBBRC and the fuzzy bang–bang controller (FBBC) show that FBBRC gives a better response. Finally, we demonstrate a practical application of FBBRC by controlling the angular position of a single-axis pneumatic rotary actuator in real-time, using the Matlab-Simulink xPC target environment.