Abstract:

Objective Aiming at the poor performance of the traditional knitting needle drive system and the electromagnetic force nonlinearity of the reluctance force actuated maglev knitting needle drive system, a linear Lorentz force actuated maglev knitting needle drive system is proposed, and the adaptive robust sliding mode control is used to improve the system response speed, disturbance suppression ability, and robustness, realize the stable control of magnetic levitation knitting needles.
Method An electromagnetic force testing system was built to measure the linear characteristics of the driving force through a single-DOF force sensor. The robust and adaptive aspects were taking into account in the differential equation of the system, and an adaptive robust sliding mode controller was designed to improve the system response speed, disturbance suppression ability and adaptability to system uncertainty. A prototype of the Lorentz force actuated maglev knitting needle drive system was built, and the performance of the maglev knitting needle drive system was verified through experiments.
Results Twelve test points were evenly distributed within the effective stroke of the knitting needle to test the output characteristics of the electromagnetic force. Experiments showed that under the same current excitation condition, the output of electromagnetic force at each test point was consistent (Fig. 4). At different test positions, the electromagnetic force varied linearly with the continuously changing excitation current (Fig. 5). It showed that the driving force of the Lorentz force actuated knitting needle drive system had a linear relationship with the input current and had nothing to do with the output position. Under the action of adaptive robust sliding mode control, the step response of the system demonstrated that the knitting needle reached a steady state in 0.6 s without overshoot (Fig. 7(a)), and the steady-state error remained within ±15 μm (Fig. 7(b)). Compared with proportional, integral, and derivative (PID) control, adaptive robust sliding mode control had a faster response speed (Fig. 9), but its steady-state noise was about 1.5 times that of PID control (Fig. 10). It was found that the adaptive robust sliding mode control had a large static error due to the influence of chattering, while the PID control had a smaller static error of the knitting needle and better steady-state control performance. When the system was disturbed, the two control methods could restore the needle displacement to a steady state (Fig. 11), but the system would have a displacement deviation of about 0.7% under the PID control, causing 20 μm in a short time, while the displacement of the knitting needle did not change significantly under the adaptive robust sliding mode control. Compared with PID control, the disturbance suppression ability and robustness of the system was stronger under adaptive robust sliding mode control. The response of the 'three-position knitting' excitation trajectory showed that the system could reach the height of looping, tucking, and floating line and make a stable stop, and the actual displacement was consistent with the expected displacement. Under the action of the adaptive robust sliding mode controller, the designed system was able to drive the knitting needle to complete the 'three-position knitting' action.
Conclusion The experimental results show that the Lorentz force actuated maglev knitting needle drive system is a linear system with high linearity. The designed adaptive robust sliding mode control system has a good control effect, and compared with PID control it has obvious advantages in improving response speed, reducing overshoot and disturbance rejection ability. The designed knitting needle drive system can complete the 'three-position knitting' action.

Key words: knitting machinery, magnetic suspension technique, sliding mode control, Lorentz force, knitting needle actuator