In this study, a novel multiphase converged control structure with a switching mechanism is established based on the fundamentals of the fast-terminal sliding mode. This control structure achieves an excellent performance in a nonlinear dynamic system, and its primary objective is to control the piston trajectory in an innovative electrohydraulic, pneumatic, and mechanical hybrid system. This work focuses on abrupt gain-scheduled acceleration, which has been rarely studied in the literature but has increasingly diverse high-technology applications across various industries. The greatest challenge lies in the sensitivity and instability of the system during a sudden actuator acceleration. Moreover, the system parameter uncertainties and external disturbances strongly influence the degree of control of the system. By inheriting the robustness and fast convergence properties of sliding-mode algorithms, the proposed control law not only guarantees a finite-time convergence of tracking errors to their origin but also reduces the impact of composite disturbances in an extremely rapid experimental process. The effectiveness of the proposed structure is analyzed via numerical simulations and industrial implementation.