Optimal Reaching Method for Enhanced Higher-Order Sliding Mode Control of Electro-Hydraulic Servo Systems

To enhance the position tracking accuracy of heavy-duty asymmetric cylinder electro-hydraulic servo systems subject to unknown matched disturbances, a high-order sliding mode controller with optimal reaching method is proposed, which addresses the robust extension of the classic optimal control problem, which minimizes convergence time under bounded disturbances and system constraints. First, a state-space model of the asymmetric cylinder electro-hydraulic system is established to account for system uncertainties. Second, sliding mode control theory is employed to construct the auxiliary system (i.e., the sliding manifold), and a third-order sliding mode controller with optimal reaching is formulated. Third, Fatou’s Lemma and other theorems are applied to prove that the closed-loop system is globally asymptotically stable under the proposed third-order sliding mode controller with optimal reaching. Finally, a simulation model is built using MATLAB/Simulink. The results demonstrate that, compared with Levant’s third-order sliding mode controller and the quasi-continuous third-order sliding mode controller, the tracking accuracy of the proposed third-order sliding mode controller with optimal reaching is improved by 7 and 8 orders of magnitude, respectively; the convergence time is reduced by factors of 16.6 and 10.2, respectively, and chattering is significantly suppressed.