Abstract Due to its high reliability, low cost, and simple structure, the permanent magnet linear synchronous motor (PMLSM) has been increasingly used in high-precision industrial servo applications. However, the lack of mechanical transmission in the structure makes it more susceptible to uncertainties such as parameter variations and load disturbance. Therefore, a fractional order boundary layer nonsingular fast terminal sliding mode control (FO-NFTSMC) strategy is proposed. Firstly, the dynamic model of PMLSM containing uncertainties is established. Then, the nonsingular fast terminal sliding mode control (NFTSMC) method is used to suppress the influence of uncertainties on the system, ensuring that the tracking error converges to zero in a finite time and avoiding the singularity problem. In addition, the Riemann-Liouville fractional order differential definition and the boundary layer technique are combined to realize a new fractional order differential boundary layer control. The fractional order boundary layer has the output characteristics of the integer boundary layer. It can also change the output value with the direction of change of the state trajectory, solving the contradiction between “Weak chattering” and “fast convergence” in the traditional integer order boundary layer control. The contrast experiments based on the FO-NFTSMC method and IO-NFTSMC method are carried out on a linear motor system. When tracking a given step command, the actual trajectory based on the FO-NFTSMC deviates less from the given tracking trajectory, and the steady-state error remains around 5 μm. In addition, the deviation value of the IO-NFTSMC strategy is larger, and the steady-state error remains around 10 μm. Therefore, the system based on the FO-NFTSMC has better tracking performance and weaker chattering. A linear motor mounted with a 2 kg payload can track a given sine signal to further study the effects of motor mass and friction on the PMLSM control system. The position tracking error of FO-NFTSMC has a smaller value than IO-NFTSMC, with a reduction of about 60 %. In addition, the IO-NFTSMC strategy responds slower at the beginning of the system response, reaching a steady state in about 0.1 s, while the FO-NFTSMC ensures the convergence time of the system. Also, the load disturbance of 5 N is suddenly added to the PMLSM system at the nominal condition to verify the anti-interference ability of the system. The experimental results show that the error curves of both control strategies fluctuate significantly, with the fluctuation amplitude of FO-NFTSMC being smaller and remaining within 10 μm. In contrast, the tracking error curve of IO-NFTSMC strategy has a larger fluctuation amplitude, with the maximum magnitude reaching about 30 μm. Finally, to verify the effect of the fractional-order boundary layer control on the system performance, an additional set of experiments were carried out to change only the fractional order. The experimental results show that the 0.2 order-based control system has good dynamic performance. The following conclusions can be drawn from the experimental analysis: (1) Compared with the IO-NFTSMC method, the FO-NFTSMC method improves the position tracking accuracy and robustness performance of the PMLSM system. (2) Using the fractional order boundary layer control, the sliding mode chattering is reduced, and the dynamic performance of PMLSM servo system is improved. (3) Fractional-order control systems have a wider range of parameter selection than integer-order control systems.
Zhao Xinyu,Wang Limei. Fractional Order Differential Boundary Layer Terminal Sliding Mode Control for Permanent Magnet Linear Synchronous Motor[J]. Transactions of China Electrotechnical Society, 2023, 38(10): 2709-2719.
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2023, Vol. 38 
