Payload variations, friction, and external disturbances deteriorate the control performance of linear motor (LM) positioners. To provide high-speed and high-precision performance for the LM, an adaptive recursive terminal sliding mode (ARTSM) controller is proposed in this paper. For the controller, a fast nonsingular terminal sliding function and a recursive integral terminal sliding function are developed in a recursive structure such that the sliding surfaces are arrived successively and ultimately the tracking error can converge to zero in a finite time. Furthermore, by setting an appropriate initial value for the integral element of the ARTSM controller, the control system is enforced to start on the sliding surface at the initial time such that the reaching time is reduced. Stability analysis is presented to prove the finite-time convergence and zero tracking error of the closed-loop system under the proposed ARTSM controller. Experiment results also demonstrate the effectiveness of the controller in term of significantly reduced tracking errors and faster disturbance rejection in comparison with a recently reported fast nonsingular terminal sliding mode (FNTSM) controller for the LM positioner.

In light of ignoring the effect of backlash on mesh stiffness in existing gear dynamic theory, a precise profile equation was established based on the generating processing principle. An improved potential energy method was proposed to calculate the mesh stiffness. The calculation result showed that when compared with the case of ignoring backlash, the mesh stiffness with backlash had an obvious decrease in a mesh cycle and the rate of decline had a trend of decreasing first and then increasing, so a stiffness coefficient was introduced to observe the effect of backlash. The Fourier series expansion was employed to fit the mesh stiffness rather than time-varying mesh stiffness, and the stiffness coefficient was fitted with the same method. The time-varying mesh stiffness was presented in terms of the piecewise function. The single degree of freedom model was employed, and the fourth order Runge–Kutta method was utilized to investigate the effect of backlash on the nonlinear dynamic characteristics with reference to the time history chart, phase diagram, Poincare map, and Fast Fourier Transformation (FFT) spectrogram. The numerical results revealed that the gear system primarily performs a non-harmonic-single-periodic motion. The partially enlarged views indicate that the system also exhibits small-amplitude and low-frequency motion. For different cases of backlash, the low-frequency motion sometimes shows excellent periodicity and stability and sometimes shows chaos. It is of practical guiding significance to know the mechanisms of some unusual noises as well as the design and manufacture of gear backlash.

Water scarcity has been recognized as one of the major threats to human activity, and, therefore, water purification technologies are increasingly drawing attention worldwide. Nanofiltration (NF) membrane technology has been proven to be an efficient and cost-effective way in terms of the size and continuity of the nanostructure. Using a template based on hexagonal lyotropic liquid crystals (LLCs) and partitioning monomer units within this structure for subsequent photo-polymerisation presents a unique path for the fabrication of NF membranes, potentially producing pores of uniform size, ranging from 1 to 5 nm, and large surface areas. The subsequent orientation of this pore network in a direction normal to a flat polymer film that provides ideal transport properties associated with continuous pores running through the membrane has been achieved by the orientation of hexagonal LLCs through various strategies. This review presents the current progresses on the strategies for structure retention from a hexagonal LLCs template and the up-to-date techniques used for the reorientation of mesochanels for continuity through the whole membrane.