Abstract-As direct-drive actuators, permanent magnet linear synchronous motors (PMLSMs) are widely used in high velocity and high precision applications. The detent force, however, can deteriorate the performance, even excite the mechanical resonance. This paper focuses on a novel detent force compensation scheme for PMLSM systems through a combination of structural design and control method. First, due to the bandwidth constraint of the control system, eliminating high frequency ripples is unfeasible; skewed permanent magnets (PM) considering an optimal skewing length are designed to suppress high order harmonic components. Second, based on the model of PMLSM with skewed PMs, a linearization observer is derived and applied independently to the velocity controller for further diminishing low order harmonic components. To facilitate implementation in the digital control system, a discretization method taking account of estimated errors is designed. Through the online calculation, the estimated detent force is injected to the control system in a feedforward way. To tune the proposed scheme properly, the convergence of the algorithm is analyzed by utilizing Lyapunov stability theory. Simulation studies are performed to prove the effectiveness of the proposed method, and experiments are provided to confirm the theoretical analysis and simulation results.Index Terms-Permanent magnet linear synchronous motors (PMLSMs), detent force, skewed permanent magnet, discretetime linearization observer, stability analysis.

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Ultra-low magnetic fields have drawn lots of attention due to their important role in scientific and technological research. The combination of a magnetic shield and an active compensation coil is adopted in most high performance magnetically shielded rooms. Special consideration needs to be taken in the coil design since the magnetic shield significantly affects the uniformity of the magnetic field that is generated by the coil. An analytical model for the magnetic field calculation of the coil inside a cubic magnetic shield is proposed based on the generalized image method, which is validated by finite element analysis. A novel design method of the coil used in a cubic magnetic shield with a large homogeneous volume is proposed. The coil parameters are optimized to obtain a large cubic uniform volume with desired total deviation rate by discretizing the central volume in the coil. In the desired total deviation rate, the normalized usable volume of the new coil increases by 70% when compared with the Merritt coil. A coil system is developed according to the parameters obtained based on this method. The magnetic flux density and practical deviation rate of the coil are measured to validate the accuracy of this model and the feasibility of the design method. The experimental magnetic flux density agrees well with the analytical value. The maximum practical deviation rate of uniform volume of 0.8 × 0.8 × 0.8 m is in good agreement with the theoretical design value, taking into account the experiment errors.