TV‐UDE: Time‐varying uncertainty and disturbance estimator

Abstract

The UDE (uncertainty and disturbance estimator)-based control approach has received increasing attention due to its simplicity and effectiveness in rejecting input disturbances. Despite this fact, the inherent transient performance issues associated with a high-gain UDE are rarely considered. We first design a classic UDE-based robust controller for a linear system subject to three types of model uncertainties: exogenous disturbance, state-dependent uncertainty, and input-dependent uncertainty. We prove by the singular-perturbation theory that arbitrarily small steady-state tracking errors can be achieved by choosing an enough-high gain for the UDE. We then design a novel time-varying UDE (TV-UDE) to improve the transient performance. The key of the improved design is to use a differential equation with a time-varying parameter, instead of a transfer function, to describe the underlying filtering relationship. The formula for the integration by parts is introduced to derive an explicit computable expression of the TV-UDE. Interestingly, the TV-UDE is reduced to a classic UDE if the design parameter is fixed. In addition, two types of smooth and bounded functions are proposed to guide the change of UDE parameter from a large value to a smaller value (i.e., from a small gain to a higher one), to ensure that the UDE generates a smooth high-accuracy estimate. The advantages of the TV-UDE are demonstrated by simulation and experimental comparisons on a 2-DOF AERO attitude control platform. The transient performance issues (such as the peaking phenomenon and obvious oscillation) of high-gain UDE are effectively avoided.