Research on adaptive backstepping control of electro-hydraulic force servo systems based on an extended state observer

Abstract

Electro-hydraulic force servo systems are subject to parameter uncertainties, unmodeled dynamics, nonlinear friction, and external disturbances, which seriously degrade force-tracking accuracy and robustness. To address these issues, this paper proposes an integrated control strategy that combines an extended state observer (ESO), adaptive backstepping control, and fuzzy online gain tuning. First, a nonlinear force-control model is established by considering pressure dynamics, leakage, and load elasticity, while friction, load disturbances, and unmodeled effects are uniformly represented as a compounded disturbance. Second, under the strict-feedback framework, adaptive virtual control laws and parameter update laws are derived via Lyapunov theory to achieve online estimation of uncertain parameters and guarantee bounded closed-loop signals. Third, a fourth-order ESO is designed to estimate the compounded disturbance in real time, and the estimated disturbance is injected into the control law as a feedforward compensation term to enhance disturbance rejection. In addition, a fuzzy inference mechanism is introduced to adjust the key backstepping gains online according to the tracking error and its rate of change, thereby improving adaptability under varying operating conditions. Simulation results under step and sinusoidal reference inputs show that, compared with conventional PID control, the proposed method reduces the step steady-state error by 43.2% and the sinusoidal tracking error by 70.5%, while also effectively suppressing amplitude attenuation and phase lag. These results demonstrate that the proposed ESO-based adaptive backstepping scheme provides a practical and effective solution for high-precision force tracking of electro-hydraulic servo systems under uncertainties.

Keywords

electro-hydraulic force servo system backstepping control extended state observer adaptive control fuzzy rules

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