This article improves the transient response of a magnetically levitated (maglev) planar machine through the model predictive control (MPC) benefiting from explicitly incorporating the tightened constraints of the input vector. The maglev system is characterized as a second-order linear model via the inverse model method to facilitate the fast online receding horizon optimization. The estimated lumped disturbance compensates for the deviations of the prediction caused by the unmodeled errors, so the obtained control signals eventually eliminate the steady-state errors. The robust stability of the motion control system is guaranteed by a reasonable horizon length without requiring the state constraints, which reduces the computational burden for the real-time implementation. Experimental results demonstrate that the proposed controller outperforms the antiwindup PID controller, switching linear quadratic regulator, baseline MPC, and nonlinear MPC in terms of the trajectory tracking.

This article presents a robust model predictive control (MPC) scheme for error-bounded tracking of the magnetically levitated (maglev) planar motor. The motivation lies in bringing the machining error within the desired tolerance zone. An augmented system containing the dynamics of measured position, estimated state, and estimated disturbances is used as the prediction model of MPC, such that the obtained optimal control signals can remove the positioning errors in steady state caused by the disturbances. Based on the augmented system, reference dynamics and constraints, a robust control invariant (RCI) set is derived using an iterative procedure, which can be terminated in finite steps. The RCI set is explicitly incorporated into the MPC formulation for error-bounded tracking. The proposed method is successfully implemented on the maglev positioning system, and systematic experiments are given to illustrate that tracking errors are bounded in the defined region.

Multiaxis motion control over a large travel range is still difficult for magnetic levitation positioning systems because the accuracy of the magnetic force model deteriorates when both translation and rotation of the moving part take place. To overcome this issue, this article studies a dynamic force- and torque-regulating method based on the numerical wrench model and validates it with a 6-degree-of-freedom magnetically levitated (maglev) rotary table. In each sampling cycle, the current-wrench transformation matrix is determined by the numerical wrench model, and then it is employed to decide the exciting currents for each coil phase by solving the overdetermined equation. A field programmable gate array is used as the processor to meet the real-time requirement of the control system by taking advantage of the fine-grained parallelism in the numerical wrench model. A high-level synthesis tool, general intellectual property core, a very-high-speed integrated circuit hardware description language component, and a MicroBlaze processor are employed simultaneously to develop the controller. By utilizing the numerical regulator, the maglev rotary table realizes stable multiaxis motions. Comparative experiments with the existing analytical method illustrate that the numerical wrench model improves the static decoupling effect, decreases the positioning fluctuations, and enlarges the travel range.

This paper presents a robust iterative learning model predictive control (RILMPC) scheme for repetitive trajectory tracking of a magnetically levitated (maglev) planar motor. The motivation lies in the improvement of tracking performance and disturbance rejection ability for the maglev system. Relying on the past error in the repetitive motion, the model discrepancy is persistently compensated with iterations to improve the prediction accuracy. The cost function that serves as the upper bound of the tracking error is then derived from the past control trajectory based on the Lipschitz property of disturbances. In the proposed RILMPC scheme, a minimal robust positive invariant set is introduced into the MPC optimisation to cope with unmodeled dynamics and disturbances. Furthermore, it is theoretically shown that the perturbed closed‐loop system is stable, and the proposed RILMPC scheme is recursively feasible with perfect tracking performance under some conditions. Finally, comparative experiments carried out on a maglev planar motor demonstrate that the proposed control strategy possesses satisfactory transient/steady‐state tracking performance and robustness against disturbances.

The magnetic levitation system has been considered as a promising actuator in micromachining areas of study. In order to improve the tracking performance and disturbance rejection of the magnetically levitated rotary table, an iterative learning PID control strategy with disturbance compensation is proposed. The estimated disturbance compensates for the control signals to enhance the active disturbance rejection ability. The iterative learning control is used as a feed-forward unit to further reduce the trajectory tracking error. The convergence and stability of the iterative learning PID with disturbance compensation are analysed. A series of comparative experiments are carried out on the in-house, custom-made, magnetically levitated rotary table, and the experimental results highlight the superiority of the proposed control strategy. The iterative learning PID with disturbance compensation enables the magnetically levitated rotary table to realize good tracking performance with complex external disturbance. The proposed control strategy strengthens the applicability of magnetically levitated systems in the mechanism manufacturing area.