Sliding Mode Fuzzy Control

Most Fuzzy Controlers (FCs) for nonlinear 2nd order systems are designed with a two-dimensional phase plane in mind. We show that the performance and the robustness of this kind of FCs stems from their property of driving the system into the so-called 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 controler (SMC) with a boundary layer (BL) near the switching line. This gives assured tracking quality even in the presence of high model uncertainties. Further improvement can be obtained by the introduction of a boundary layer at the FC. 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.