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.