Practical Fixed-Time Backstepping Control with an Extended Lumped Disturbance Observer for Electro-Hydraulic Servo Systems: Theory and Experiments

Practical fixed-time backstepping control of uncertain electro-hydraulic position servo systems must address derivative-related terms induced by low-order nonsmooth virtual controls while ensuring a settling-time bound independent of the initial conditions. This paper proposes a practical fixed-time backstepping control scheme with an extended lumped disturbance observer for systems driven by three-stage electro-hydraulic servo valves. Based on a third-order strict-feedback model, system uncertainties and these derivative-related terms are incorporated into extended lumped disturbances in the mechanical and hydraulic channels. Fixed-time disturbance observers estimate these terms online, and the backstepping controller compensates for them to achieve trajectory tracking. Lyapunov analysis shows practical fixed-time stability of the closed-loop error system: all error states converge to a small neighborhood of the origin within a settling-time bound independent of the initial conditions, while all closed-loop signals remain bounded. Simulations demonstrate improved sinusoidal tracking accuracy and illustrate the practical fixed-time convergence behavior under different initial conditions. Experiments under sinusoidal and random-wave references demonstrate improved tracking accuracy with smooth servo-valve driving voltages.