Robust Control Based on a Time-varying UDE for an Under-actuated 3-DOF Helicopter

Abstract

The UDE (uncertainty and disturbance estimator) based control approach has received increasing attention in recent years due to its simplicity and effectiveness to attenuate the influence of uncertainties and disturbances. Despite this fact, the trade-off issue of its steady-state performance and transient performance has not been addressed explicitly. A novel time-varying UDE (TV-UDE) is proposed to resolve the trade-off issue in this paper. The main idea behind the design is to use a differential equation with a time-varying parameter, rather than a transfer function, to represent the underlying filtering relationship. By changing the UDE gain smoothly, the performance limitations of a fixed-gain UDE are avoided. Moreover, the TV-UDE is reduced to a classic UDE when its parameter value is finally frozen. Two design specifications are provided to guide the design of the time-varying parameter. We then apply this design to the angular trajectory tracking problem of a 3-DOF helicopter model, and reveal the four time-scales property of the closed-loop dynamics. The advantages of the proposed approach are shown by simulation comparisons.