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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.

The introduction of Ethernet makes the distributed network system more flexible and efficient, but it also makes nodes which are far apart from each other unable to work in the same time basis due to the long distance. This is not allowed for the high performance requirements of the system synchronization, such as high-precision multiaxis machining system. This paper presents a high-precision network clock synchronization algorithm, namely, optimal PI clock servo, which imposes a PI controller in order to compensate for the clock drift of each network node. Then a simulation platform established by the toolbox TrueTime is used to verify the stability of the algorithm and compare it with the clock synchronization algorithm of EtherCAT. The results show that the new synchronization algorithm has higher synchronization precision and faster convergence rate.

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