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A sliding mode control (SMC) strategy is proposed for a second-order non-linear system using fractional calculus and adaptive fuzzy compensator, named fuzzy fractional-order SMC (FFOSMC). The major contribution of this research includes the formulation of a robust fractional-order controller based on a novel non-integer sliding manifold. The proposed controller utilizes reduced discontinuous switching gain using a fuzzy logic system. A fractional-order adaptation law is derived to update the fuzzy logic system, which has more degrees of freedom to achieve the desired performance. The stability of the closed-loop system is guaranteed using fractional-order Lyapunov theory. The parameters of the proposed control method are optimized using Simulink response optimization. Finally, the performance of the FFOSMC is fully investigated and compared with a conventional SMC controller and an integral SMC controller. From simulation results, it is concluded that the proposed algorithm is effective and more robust.

An electro-hydraulic load simulator (EHLS) is a typical case of torque systems with strong external disturbances from hydraulic motion systems. A new velocity synchronizing compensation strategy is proposed in this paper to eliminate motion disturbances, based on theoretical and experimental analysis of a structure invariance method and traditional velocity synchronizing compensation controller (TVSM). This strategy only uses the servo-valve's control signal of motion system and torque feedback of torque system, which could avoid the requirement on the velocity and acceleration signal in the structure invariance method, and effectively achieve a more accurate velocity synchronizing compensation in large loading conditions than a TVSM. In order to facilitate the implementation of this strategy in engineering cases, the selection rules for compensation parameters are proposed. It does not rely on any accurate information of structure parameters. This paper presents the comparison data of an EHLS with various typical operating conditions using three controllers, i.e., closed loop proportional integral derivative (PID) controller, TVSM, and the proposed improved velocity synchronizing controller. Experiments are conducted to confirm that the new strategy performs well against motion disturbances. It is more effective to improve the tracking accuracy and is a more appropriate choice for engineering applications.

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