Motion Control Of Magnetic Levitation Stage Based On Model Predictive Control

The precision positioning stage is the core component of advanced manufacturing equipment,and its motion control effect decides the performance indicators of precision devices,such as machining accuracy and manufacturing efficiency.Benefiting from the non-contact characteristic,the magnetic levitation positioning technology has the advantages of zero friction,high accuracy,low inertia,and cleanliness,which makes the magnetic levitation stage can provide fast,precise,and multi-degree of freedom motion for manufacturing equipment,and has drawn increasing attention in the field of precision manufacturing.For motion control systems,the appropriate control scheme can further improve the motion performance,and thus it is of great practical significance to study the motion control technology of the magnetic levitation stage.As an advanced control technology,model predictive control can capture the future dynamics of the system based on the prediction model,and obtain the optimal control signal through constrained receding horizon optimization,which results in the significant improvement of dynamic performance for the motion control system.In this dissertation,focusing on the development of trajectory tracking performance,the theoretical and technical solutions for model predictive control in the motion control of the magnetic levitation stage are studied in detail.The magnetic levitation stage with a planar structure is first built,and a real-time control system including a sensing system,data acquisition,control unit,power amplifier,and other parts is constructed in a modular way.The electromagnetic model of the magnetic levitation stage is derived using the harmonic method,which together with the control system lay a foundation for the design and validation of the motion control schemes.A nonlinear model predictive control scheme based on the disturbance observer is designed for motion control of the magnetic levitation stage.The motivation lies in the improvement of dynamic performance for the magnetic levitation system under the input constraint and disturbance.The prediction model is established according to the nonlinear motion dynamics of the stage,and the disturbance estimation is introduced in the receding horizon optimization to improve the prediction accuracy.Based on the current saturation boundary,the input constraint is designed,and the objective function is formulated using the weight of the control input and tracking error to obtain the optimal control signal.The robust stability of the closed system is guaranteed by the decreasing property of the objective function,and the parallel Newton optimization algorithm is employed to ensure the real-time solution of the nonlinear optimization problem.The experimental results illustrate that the proposed control scheme can effectively improve the dynamic performance of the magnetic levitation stage.In order to further improve the response speed of the magnetic levitation stage,a fast model predictive control strategy is developed to facilitate the optimality of the control signal.The stage is dynamically decoupled as linear motion systems to perform the state prediction.The estimated disturbance compensates for the the prediction deviations,so the state prediction is able to accurately reflect the future system dynamics.By transforming the current saturation into a linear force constraint through spatial mapping,the problem is reduced to a convex optimization problem,which facilitates the computational efficiency of online optimization.According to the optimality theory and Lyapunov method,sufficient conditions related to the prediction horizon are derived to make the objective function converge along the time axis,while ensuring the robust stability of the system.In the experiments,the testing results demonstrate that the control signal obtained by the fast model predictive control is closer to the global optimal solution than the nonlinear one,which results in the further improvement of the dynamic performance for the magnetic levitation stage.The proposed fast model predictive control scheme also provides guidance for further expansion of model predictive control in the magnetic levitation stage.A robust model predictive control scheme is established for error-bounded tracking and offset-free positioning of the magnetic levitated stage.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,such that the obtained optimal control signals can suppress model mismatch and remove the positioning errors in steady state.Based on the augmented system,reference model,and error bound,the robust control invariant set is iteratively computed and it is used as the state constraint of the optimization to guarantee the recursive feasibility and robust stability of the control system.In the one-step prediction condition,the explicit expression of the optimal control signal is derived to promise the real-time calculation of online receding optimization.The experimental results show that the proposed control method can achieve offset-free positioning and restrict the upper bound of tracking error,while ensuring the dynamic performance for the magnetic levitation stage.A robust iterative learning model predictive control scheme is presented for trajectory tracking of the magnetic levitation stage.The motivation lies in the further development of disturbance rejection ability for the magnetic levitation system.Relying on the disturbance data in the last cycle,the error prediction model is constructed in a data-driven way,and the objective function that serves as the upper bound of tracking error is then derived based on the Lipschitz property of disturbances.A minimal robust positive invariant set is employed as the state constraint in optimization to restraint the tracking error of the system,and promises the recursive feasibility of optimization problem.In the invariant set framework,the time-domain stability and iterative convergence of the control system are proved theoretically.The computational efficiency of the constrained optimization problem with one horizon is enhanced by reducing the feasible region of the optimizer to a finite set.In the experiments,it is verified that the proposed control method can significantly reduce the tracking error of the magnetic levitation stage by effectively compensating the disturbance.This dissertation conducts a pioneering study of the application of model predictive control in the magnetic levitation stage,and some sufficient conditions for robust stability of the magnetic levitation system based on model predictive control are derived.On the basis of model predictive control,the error-bounded tracking method is proposed and its integration with iterative learning control is developed.Research findings indicate that model predictive control can significantly improve the dynamic property and the trajectory tracking performance of the magnetic levitation stage.