An adaptive backstepping robust control method of water hydraulic high-speed on/off valve considering nonlinear hydrodynamic force

Water hydraulic high-speed on/off valve (HSV) direct-driven by a voice coil motor (VCM) is extensively utilized in water hydraulic systems for underwater manipulators due to its simplistic structure, compact dimensions, rapid switching speed, and cost-effectiveness. In this paper, a model-based nonlinear adaptive backward robust control (ABRC) strategy is proposed to compensate for the nonlinear hydrodynamic forces and uncertain parameters of the HSV spool. A state-space equation using an equivalent model of HSV to perform ABRC design is developed, which considers valve spool disturbance and system parameter uncertainty. The dynamic response and displacement tracking accuracy of the valve spool under the ABRC algorithm through joint simulation analysis in AMESim/Simulink are investigated in comparison with Fuzzy-PID and sliding mode control (SMC) algorithms. The experimental results demonstrate that ABRC outperforms both the Fuzzy-PID and SMC algorithms in terms of dynamic response, with a spool opening time of approximately 5.2 ms and a closing time of around 6.0 ms. In addition, the RMSE values of ABRC under different operating conditions are 0.00064, 0.00247, and 0.00732, respectively. These results demonstrate significantly improved accuracy in tracking spool displacements compared to traditional control methods. Therefore, the BRAC strategy exhibits superior adaptability and robustness across varying operating conditions relative to conventional control methods. The findings of this study will provide valuable guidance for the design and engineering implementation of water-hydraulic HSV control systems in underwater manipulators.