UDE-PLC: Uncertainty and Disturbance Estimator with Phase-lead Compensation

It has been well understood that the estimation error of uncertainty and disturbance estimator (UDE) can be arbitrarily small provided the bandwidth of UDE is chosen to be sufficiently high. Unfortunately, due to many physical constraints, the allowed bandwidth of UDE is always practically limited, the UDE is not so ideal and its actual estimation performance may not be satisfactory. Motivated by this observation, we formulate a simple inequality constraint on the UDE bandwidth and propose an uncertainty and disturbance estimator with phase-lead compensation (UDE-PLC) to improve the estimation performance under such a constraint. The main idea behind the design is to use the cascade of a first-order phase lead compensator and a first-order Butterworth filter, instead of a single Butterworth filter, to build the estimation relationship. By choosing properly the involved three parameters, the obvious phase lag of the non-ideal Butterworth filter is well compensated and both the disturbance estimation error and trajectory tracking error are reduced by the proposed design. The design specifications and the guideline for parameter tuning are provided to make the philosophy behind the UDE-PLC easy to follow. The effectiveness of UDE-PLC is verified by simulation on a 2-DOF AERO attitude control platform.