Fractional-Order Lyapunov-Based Backstepping-Like Feedback Control of N-DOF Mechanical Systems

This paper studies a fractional-order control and stability scheme for a class of n-DOF mechanical systems that are subject to actuator saturation and unknown disturbances. By the fractional-order Leibniz rule, a generalized fractional-order Lyapunov stability (FOLS) method is developed to support the design of a class of fractional-order robust controllers, which can guarantee the uniform ultimate boundedness and faster convergence. Based on this, a fractional-order backstepping-like feedback controller (FOBFC) is raised to realize an effective and stable control performance of mechanical systems, which can ameliorate the shortages of the traditional backstepping control effectively. Moreover, a set of fractional-order methods, including actuator compensation (FOAC) and disturbance observer (FODO), are proposed and involved in FOBFC to handle the actuator saturation and unknown time-varying disturbances, making it possible to achieve a more robust and stable control performance. Finally, numerical simulations and comparative experiments are carried out to demonstrate the effectiveness and superiority of the proposed fractional-order control scheme, in n-DOF mechanical systems. Note to Practitioners—A fractional-order control and stability scheme is developed to regulate a class of practical n-DOF mechanical systems, which is composed of FOBFC, FOAC and FODO. It can be applied to deal with the actuator saturation and time-varying disturbance of n-DOF mechanical systems, contributing to realizing a more robust and stable control performance. In the application, a Euler-Lagrange dynamics of mechanical systems is required for constructing the fractional-order tracking errors. Subsequently, FOBFC law can be raised based on the generalized FOLS, to guarantee the asymptotic convergence and stability of mechanical systems. To address the practical issues of mechanical systems, FOAC and FODO are necessary for the proposed control scheme to compensate for the actuator saturation adaptively, and handle the unknown and time-varying disturbances effectively.