Active Disturbance Rejection Control of Second-Order Nonlinear Uncertain Systems with Guaranteed Transient and Steady State Tracking Error Bounds

This paper presents an active disturbance rejection control (ADRC) method for a class of second-order nonlinear uncertain systems with guaranteed transient and steady state tracking error bounds. To deal with the tracking error constraint, an output error transformation and sliding surface technique are introduced to transform the constrained second-order system into an equivalent unconstrained first-order one. Then, an ADRC method is developed to achieve output tracking of the transformed uncertain system. The author proves that the closed-loop system is semi-globally uniformly bounded and it is sufficient to guarantee the tracking error constraint for the original system. Simulation results of a system of two inverted pendulums connected by a spring and a damper demonstrate the effectiveness of the proposed control method.