Digital fuzzy sliding-mode control for a linear parameter-varying air–fuel ratio system

Abstract

Air–fuel ratio is a key factor for the minimization of the harmful pollutant emissions and maximization of fuel economy. However, a big challenge for air–fuel ratio control is a large time-varying delay existing in spark ignition engines. In this article, a digital fuzzy sliding-mode controller is proposed to control a linear parameter-varying sampled-data air–fuel ratio system. First, the Pade first-order technique is utilized to approximate the time-varying delay. The resultant system—a linear parameter-varying continuous-time air–fuel ratio system with unstable internal dynamics—is then discretized to a linear parameter-varying sampled-data air–fuel ratio system appropriate for a discrete-time control approach. Based on the linear parameter-varying sampled-data air–fuel ratio system, a stable sliding surface with a desired tracking error dynamics is presented. Two input scaling factors and one output scaling factor are determined for the proposed digital fuzzy sliding-mode controller. Then, the fuzzy inference is executed through a look-up table to stabilize the sliding surface into a convex set, and then make the tracking error possess uniformly ultimately bounded performance. The overall system stability is verified by Lyapunov’s stability criteria. Finally, the simulation results demonstrate the feasibility, effectiveness, and robustness of the proposed control scheme under different operating conditions and show the superiority of the proposed approach performance compared to the baseline controller.