Robust control by fuzzy sliding mode

Abstrae1-Most fuzzy controllers (FCs) for nonlinear second order systems are designed with a two-dimensional phase plane in mind. We show that the performance and the robustness of this kind of FC stems from their property of driving the system into the sliding mode (SM), in which the controlled system is invariant to parameter fluctuations and disturbances. Additionally, the continuous distribution of the control values in the phase plane causes a behavior similar to that of a sliding mode controller (SMC) with a boundary layer (BL) near the switching line. This gives assured tracking quality even in the presence of high model uncertainties. Tracing the FC back to the principle of an SMC one obtains evidence about the stability of the closed-loop system. The choice of the scaling factors for the crisp inputs and outputs can be guided by the comparison of the FC with the SMC and with the modified SMC, respectively. At the end of the paper, an FC for a higher-order system is proposed. Simulation results show the practicability of the method.