Robust controller design for uncertain nonlinear systems via adaptive fuzzy PID approach

The robust design problem of proportional-plus-integral-plus-derivative controller for uncertain nonlinear systems is studied in this paper. A novel adaptive fuzzy control scheme is developed to design an adaptive controller for the robust stabilization of uncertain nonlinear systems. A numerically tractable algorithm based on the technique of linear matrix inequalities is used to approximate the single input single output nonlinear systems. Adaptive control approaches claim to adapt system parameters against uncertainties. A robust control compensator is derived to offset the effect of uncertainties. It can be shown that the effect of the external disturbance on the tracking error can be attenuated to prescribed level and then the tracking control performance is achieved. Application of the proposed method to a second-order inverted pendulum system demonstrates the effectiveness of the proposed approach. Theory has proved that the algorithm of on-line self-adjusting by means of altering the fuzzy rules basis made the control system stable globally and then the tracking control has been achieved.