Overshoot Suppression of Hydraulic Actuation Based on the Integrating Flow Compensation: Applied to Lift Tracking Control of an Engine Variable Valve Actuator

Overshoot is prevalent in hydraulic actuators due to the inertia of motion. Especially for high-speed position servo hydraulic actuators, overshooting is almost unavoidable in order to achieve high response position tracking. This paper addresses overshoot suppression in high-frequency electro-hydraulic systems (HESs). Traditional overshoot mitigation strategies—over-damping and reduced feedback coefficients—compromise dynamic performance, failing to meet high-frequency response requirements. And nonlinear factors, including friction, dead zones, and flow variations, are identified as critical contributors to overshoot. To suppress overshoot, a novel backstepping controller with integrated flow compensation is proposed and applied to hydraulic engine variable valve actuator. In the controller, the nonlinear friction force, system delay, dead zone, etc. are synthesized into the controller firstly. And the feedback gains are kept at a low level to reduce overshoot. Secondly, proportional valve response error is converted as flow error, and the integrating flow error is added to the controller. Finally, some comparative experiments are implemented on a hydraulic engine variable valve actuator (VVA). The experiment results show that the overshoot and tracking error of VVA are both reduced significantly with the guaranteed dynamic performance. When the desired maximum valve lift is 12mm and 10mm, the valve lift overshoot at opening stage is reduced from 1.2mm, 0.72mm to 0.03mm, 0.01mm respectively. And the overshoot at closing stage is reduced from 0.45mm, 0.11mm to 0.02mm, 0.02mm respectively. Note to Practitioners—High-frequency electro-hydraulic valve systems face critical overshoot-induced failures, including piston-valve collisions and valve seat damage, which increase maintenance costs by 18-25% in typical engine production lines. Traditional PID-based methods require trade-offs between overshoot suppression ( $\ge 5$ % residual) and response speed (+ 35% settling time). Our integrated backstepping controller resolves this dilemma through three field-ready steps: (1) Compensate nonlinearities (dead zones, asymmetric friction) via embedded LuGre modeling and inverse functions; (2) Convert valve displacement errors to hydraulic flow errors in real-time, preserving dynamics; (3) Implement delay compensation through automated lift retuning. Validated on VVA prototype, under the conditions of 12mm and 10mm maximum lift, the valve lift overshoot is restrained most significantly, and the overshoot is less than 0.05mm in both the opening and closing stages.