Active disturbance rejection control for rate-controlled input underactuated systems: Application to a reaction wheel pendulum

The paper deals with the application of Active Disturbance Rejection Control (ADRC) to underactuated systems with rate-controlled input dynamics, illustrated by a reaction wheel pendulum (RWP). In this class of plants, the derivative of the control signal appears in the input–output dynamics, which violates the standard integrator-chain assumption underlying classical ADRC and may degrade observer performance and closed-loop quality. To overcome this difficulty, two ADRC modifications that exploit partial model information are proposed. First, a reduced-order input–output model is derived, in which the derivative behavior of the input is analytically compensated, resulting in an affine input form compatible with the conventional ADRC structure. Second, a dual-output ADRC scheme is developed, combining an extended state observer with an inner-loop LQR-based state feedback, which enables simultaneous stabilization of the pendulum angle and the wheel speed despite a single actuator. For both variants, Lyapunov-based stability conditions are obtained. The proposed controllers are implemented and experimentally verified on a real reaction wheel pendulum setup. Swing-up-and-balance experiments around the lower and upper equilibrium positions show that the modified ADRC schemes reduce overshoot and oscillations, mitigate steady-state drift, and improve control performance with respect to a baseline model-free ADRC.