Adaptive fuzzy sliding mode algorithm-based decentralised control for a permanent magnet spherical actuator

Abstract

The dynamic model of multi-degree-of-freedom permanent magnet (PM) spherical actuators is multivariate and nonlinear due to strong inter-axis couplings, which affects the trajectory tracking performance of the system. In this paper, a decentralised control strategy based on adaptive fuzzy sliding mode (AFSM) algorithm is developed for a PM spherical actuator to enhance its trajectory tracking performance. In this algorithm, the coupling terms are separated as subsystems from the entire system. The AFSM algorithm is applied in such a way that the fuzzy logic systems are used to approximate the subsystem with uncertainties. A sliding mode term is introduced to compensate for the effect of coupling terms and fuzzy approximation error. The stability of the proposed method is guaranteed by choosing the appropriate Lyapunov function. Both simulation and experimental results show that the proposed control algorithm can effectively handle various uncertainties and inter-axis couplings, and improve the trajectory tracking precision of the spherical actuator.

Robust Adaptive Sliding-Mode Control of a Permanent Magnetic Spherical Actuator With Delay Compensation

“…Substitute (18) into (15) and obtain =̇c om −̇r (19) ̇=̈c om −̈r (20) ̇= (̈c om −̈r) = −̇c om −̈r − (̇c om ) (21)…”

“…By using (1), (15), (17), (21), (24), and (26), Equation 28 The function ̇( ) is negative semi-definite. Thus, the stability of the controller is proven according to Lasalle's invariant principle.…”

“…Thus, accuracy is not guaranteed. References [13][14][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 upper bound of the uncertain disturbance is reduced and the control performance is improved.…”

“…In this experiment, the rotor is controlled to move along the desired trajectory as (34), (35), and the experiment time is set to 6 sec. This desired trajectory is set to be identical with the experiment trajectory in reference [15]. Therefore, this experiment can also be viewed as a reference for comparison with the results of other pertinent works.…”

Adaptive Sliding‐Mode Control for Permanent Magnet Spherical Actuator Based on Trajectory Re‐Planning

“…Some references proposed to use sliding-mode control (SMC) to deal with modeling uncertainty and uncertain disturbances. Moreover, fuzzy logic [10,11] and adaptive term [12] are often combined with the SMC to improve the robustness and precision of the whole system. A neural network [13,14] capable of self-learning is also introduced in the control of PMSA, which shows great prospect in the simulation of case study.…”