Improved Adaptive Controller Design Scheme to Attenuate the Noise Amplification Effect of Differentials*

Adaptive control is widely used in nonlinear systems, and is under active research. Although the conventional adaptive control guarantees the asymptotic stability, it may yield limited performance in real experiments due to many factors, such as noise and hardware limitations. In this paper, a proportional-integral adaptive controller with a proportional-integral-derivative update law is proposed to attenuate the effect of measurement noise and improve the performance of the closed-loop system. Two more improvements, dividing differential signals into two smoother signals and facilitating additional estimations to weight different components of the same signal, are used in addition to the proportional-integral-derivative-type update law. The stability is proved theoretically and the performance is verified by simulation tests.