| Lithography is a key technology in the manufacture of integrated circuits and an indispensable process in the production of all devices that require high micro/nanometer precision.As a core equipment in the chip lithography process,a workpiece table in the lithography machine is responsible for high-precision motion control.The workpiece table should realize the planar motion of long stroke with high acceleration and high positioning accuracy.Air floating support devices can help achieve such motion control however they cannot work in the vacuum environment.Without the need of air floating,the maglev permanent magnet synchronous planar motor(PMSPM)featuring excellent motion performance is one better alternative that better fits the need of the recent popular ultraviolet lithography technology.The combination of linear motors can also realize the needed planar motion,however it is inferior to the planar motor due to low mechanical integration,which will cause undesirable effects for precise control.Moreover,the PMSPM also reduces the gravity center height of the movable part,which is beneficial for high acceleration speed.However,the PMSPM has more complex electromagnetic coupling characteristics,which makes the traditional motor control strategy not directly applicable to it.The PMSPM has six-degree-of-freedom,which requires more complex design of the control strategy.This paper aims to explore the key problems in the sixteen-phase concentric maglev PMSPM.In particular,the research focuses on its electromagnetic modeling,decoupling algorithm,closed-loop control strategy as well as motion control technology.An accurate maglev PMSPM electromagnetic model that meets real-time control requirements has been established in this work.The electromagnetic modeling of the proposed maglev PMSPM is the fundamental basis for realizing the six-degree-of-freedom motion control.The model is required to have high accuracy under the premise of fast computation to meet the requirements of real-time motion control.To this end,the coordinate system of the maglev PMSPM motion control is defined and the magnetic field analytical model of the Halbach permanent magnet array in the stator coordinate system is established.The magnetic field analytical model under the moving coordinate system is obtained by the coordinate transformation.The Lorentz force integral formula is used to solve the electromagnetic force and torque.Since the coil has a corner portion,it is usually simplified in previous works to facilitate the integral,which inevitably causes model error.In order to eliminate this error caused by the model simplification,the coil is decomposed into a straight part and a corner part.The linear part can be processed with direct integral method,while the corner part is dealt with separately through a more accurate method.An electromagnetic analytical model of the PMSPM can be achieved with the above considerations.Simulation and experiments are conducted to validate the accuracy of the proposed analytical model.The coupling characteristics and decoupling method of maglev PMSPM have been analyzed and explored in this work.The maglev PMSPM is a multi-input and multi-output system with strong-coupling characteristics.To achieve stable levitation control,it is necessary to decouple the electromagnetic force and torque in six degrees of freedom.In this paper,the application of the traditional dq transformation method in multi-degree of freedom is thoroughly analyzed,from which it has been found that although the dq transformation can effectively control the force,additional torque will be generated in other degrees of freedom.This implies that traditional dq transformation cannot be directly applied in the multi-degree-of-freedom motion control.To address this gap,a direct decoupling method using generalized inverse matrix is proposed,which can directly decouple the electromagnetic force and torque between six degrees of freedom and the sixteen phases winding current.The proposed approach has been validated through the electromagnetic force and torque decoupling control experiments.Moreover,the control precision mainly depends on the accuracy of the aforementioned electromagnetic model.In practical applications,the manufacturing deviation of the motor will reduce the decoupling performance of the system,and it can be dynamically compensated by the extended state observer.By applying a positional step signal on a single-degree-of-freedom,the response of other degrees of freedom can be observed to be influenced with a limited amount.Moreover,the proposed dynamic compensation is observed to be beneficial for the decoupling performance.A dynamic motion model has been established,based on which six-degree-of-freedom closed-loop strategy of maglev PMSPM is proposed.With the above decoupling,the motion control of each degree-of-freedom can be regarded as an independent subsystem.The electromagnetic force and torque of the maglev PMSPM decrease exponentially with the increase of the air gap height,and the levitation force is needed to cancel the gravity of the mover in normal operation.The gravity compensation model is established for the above characteristics.The control law of the maglev PMSPM system is analyzed,from which it can be noted that the magnetic levitation system has the characteristic of zero damping.This observance provides a fundamental basis for the controller design.Since the moving-coil type maglev PMSPM mover needs to connect accessories such as cables and cooling water pipes,additional force disturbance will be generated during the movement.In order to reduce such influence on the control performance of the system,the variable universe fuzzy control is used to adjust the PID parameters taking the platform hardware conditions into account.Experiments are conducted to validate the system robustness to external disturbance through comparing with various algorithms.The maglev PMSPM control platform has been built and its motion characteristics have been analyzed.The motion control platform is built with NI PXI-8110 controller as the core part.The six-degree-of-freedom position measurement scheme is designed and developed with the necessary filtering taken into account to realize the real-time solution of the maglev PMSPM mover position.The single-degree-of-freedom motion control is realized by the auxiliary and limit mechanism.The six-degree-of-freedom motion control of the maglev PMSPM is realized based on the single-degree-of-freedom motion control.The feedforward-feedback control structure effectively improves the dynamic performance of the system and reduces the position following error.In order to design a feedforward path with higher performance,the feedforward coefficient of the maglev PMSPM is analyzed and observed to feature smooth and continuous characteristics,based on which a dynamic compensation method is proposed with the covariance reset for least squares.The system position following error is explored under different test conditions: without feedforward,with fixed feedforward coefficient and proposed dynamic compensation method.The results show that the proposed dynamic compensation method has the best position following performance.In summary,this paper makes an in-depth exploration on the maglev PMSPM motion control and its related technologies.The proposed approach is validated through both simulation and experiments.This work has both theoretical and practical relevance for the application of the maglev PMSPM in high-precision control field. |
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