Time-varying uncertainty and disturbance estimator without velocity measurements: Design and application

Abstract

The uncertainty and disturbance estimator (UDE) technique has been proven to be simple but effective in reconstructing unknown disturbances. However, classic UDE with a constant gain cannot deal with more complicated issues, such as the trade-off between steady-state and transient performance of the estimator, simultaneous attenuation of input disturbances and measurement noises, etc. Motivated by this observation, the design of UDE technique is extended to the time-varying situation and an implementable form of time-varying UDE (TV-UDE) is proposed. In particular, velocity measurements are assumed to be unavailable in the design. A time-varying ordinary differential equation is constructed to build the estimation relationship. A formula for the integration by parts is thereafter introduced to derive an implementable form of the TV-UDE. The classic UDE is shown to be a special case of the TV-UDE. The UDE is combined with a nominal dynamic output-feedback controller to yield a robust control solution to a class of uncertain second-order attitude control systems without velocity measurements. The design of a TV-UDE is discussed with a low initial gain and a higher final gain to avoid transient performance issues. Finally, numerical simulations and physical experiments are carried out on a 2-DOF AERO attitude helicopter platform to demonstrate the control performance of the solution. It is illustrated that the proposed design can effectively reduce the steady-state errors in both the trajectory tracking and target pointing tasks. Meanwhile, the input saturation and peaking phenomena associated with a high-gain estimation are avoided by applying the TV-UDE.