Abstract
This study proposes an adaptive robust sliding-mode control strategy with time delay compensation to address the issues of the inaccuracy of modeling, friction, uncertain disturbances, and time delay in a permanent magnet spherical actuator trajectory tracking control system. First, an improved linear predictor is designed to compensate for the time delay in position information. Second, a robust sliding mode controller is designed to suppress the influence of uncertain disturbance. Third, the constant parameters of the spherical actuator are estimated using the adaptive law and compensated at the control input. The stability of the adaptive robust sliding-mode controller is proved by the Lyapunov theorem. Simulation and experimental results show that the control strategy proposed in this research has good dynamic and static performance, which can provide reference for the further engineering application of multi-degree of freedom control system.
Highlights
A permanent magnet spherical actuator (PMSA) has the advantages of compact structure, relatively large range of motion and rapid dynamic response
This study proposes an adaptive sliding mode robust controller with modified linear predictor (LP), which combines the advantages of adaptive controller, sliding-mode control, and LP: (1) The adaptive controller can estimate the constant parameter of PMSA, which is needed to compensate for the centripetal and Coriolis forces
This study proposes an adaptive robust sliding-mode control system with delay compensation is proposed for the trajectory tracking control system of PMSA
Summary
A permanent magnet spherical actuator (PMSA) has the advantages of compact structure, relatively large range of motion and rapid dynamic response. The difficulties and challenges of PMSA control include inaccuracy of modeling, friction, uncertain disturbances, and time delay. References [13]–[15] combined, the robust sliding mode control with adaptive control and disturbance observer to compensate for the errors caused by modeling inaccuracy and friction in the control input. The preceding model-based delay compensation method is not applicable because of the difficulty in establishing an accurate dynamic model for the permanent magnet spherical actuator control system. The motivation of the current study is to develop a control strategy that can address the inaccuracy of modelling, friction, uncertain disturbances and time delay. DYNAMIC MODEL OF THE PMSA Considering friction and uncertain disturbance of PMSA, a Lagrange formulation of the PMSA control system in terms of the Cardan angles coordinates is established as follows:
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