Improved UDE and LSO for a Class of Uncertain Second-Order Nonlinear Systems Without Velocity Measurements

Abstract

In recent years, the uncertainty and disturbance estimator (UDE) technique has been widely used for robustness improvement in state-feedback control systems. This article extends the design of the UDE to output feedback scenarios by considering the robust control problem of a class of Euler–Lagrange systems with a nonlinear velocity term but having no velocity measurements. We propose a simple feedback-control scheme that includes a modified Luenberger state observer (LSO) to estimate the velocity and a modified UDE to estimate exogenous disturbances. The novel feature of the scheme is that a mutual coupling between LSO and UDE is introduced to improve the estimation and control precision. To analyze the performance of the fifth-order nonlinear closed-loop system, we decompose it into a second-order tracking-error subsystem and a third-order estimation-error subsystem and propose a linear nonsingular state transformation and an ingenious parameter mapping for the estimation-error subsystem. Finally, by the singular perturbation theory, we derive a simple stability condition and a single-parameter tuning approach to reduce the steady-state estimation errors and tracking errors. The performance improvement resulting from the mutual coupling effect and the effectiveness of the tuning approach are demonstrated by numerical simulations and experimental verifications on a 3-DOF helicopter platform.