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(a) The BH curve of the ferromagnetic material cobalt steel Vacoflux 50. Magnetic flux density B(T) of the proposed designs with the parameters in Table 1 used at nominal air gap and current of (b) go=1.04 mm with i=5.75 A; (c) go=1.06 mm with i=5.75 A; (d) go=1.06 mm with i=5.75 A
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Abstract Recently, the reluctance actuator has attracted great attention to replace the Lorentz actuator in the next generation of wafer scanners in semi‐conductor lithography machines. The reluctance actuator has a non‐linear position‐force characteristic, which may cause high oscillations and unstable operation. This study presents a linearisatio...
Citations
... The critical voltage u cr is the voltage value where the reluctance actuator can generate an attractive magnetic force equal to the spring force. The critical voltage u cr can be determined by the steady state solution of the dynamic equation [23]. The step response of the RAMS is illustrated in Figure 7(a) for input voltage with amplitude of u = {3.5, 4, 4.5, 5, 5.5, 5.75, 6} V. ...
... Voice coil motors (VCM), however, are near their physical limit and cannot provide large enough thrust for the required high acceleration in the photolithography. Thus, a novel reluctance actuator is proposed in [7][8][9]. Compared with VCM, the reluctance motor has the advantages of high output density and According to the survey, one of the most general ways to suppress hysteresis is with flux feedback in a reluctance actuator. For example, in [10], the Hall element is used to measure the flux signal in the air gap, then the signal is used as a feedback variable. ...
To meet the ever-increasing demand for next-generation lithography machines, the actuator plays an important role in the achievement of high acceleration of the wafer stage. However, the voice coil motor, which is widely used in high-precision positioning systems, is reaching its physical limits. To tackle this problem, a novel way to design the actuator using the magnetoresistance effect is argued due to the high force densities. However, the strong nonlinearity limits its application in the nan-positioning system. In particular, the hysteresis is coupled with eddy effects and displacement, which lead to a rate-dependent and displacement-dependent hysteresis effect in the reluctance actuator. In this paper, a Hammerstein structure is used to model the rate-dependent reluctance actuator. At the same time, the displacement-dependent of the model is regarded as the interference with the system. Additionally, a control strategy combining inverse model compensation and the disturbance observer-based discrete sliding mode control was proposed, which can effectively suppress the hysteresis effect. It is worthy pointing out that the nonlinear system is transformed into a linear system with inversion bias and disturbance by the inverse model compensation. What is more, the sliding mode controller based on the disturbance observer is designed to deal with the unmodeled dynamics, displacement disturbances, and model identification errors in linear systems. Thus, the tracking performance and robustness to external disturbances of the system are improved. The simulation results show that it is superior to the PI controller combined with an inverse compensator and even to the discrete sliding mode controller connected with inverse compensator, confirming the effectiveness of the novel control method in alleviating hysteresis.
... Some examples include feedforward compensation with the inverse hysteresis model [7], [8], and observer-based on sheared-hysteresis model [4] and sensing coil voltage control circuitry with air gap observer [5]. Also, the dynamic behaviour of the reluctance actuator can be linearized by selecting the optimal design of the actuator to operate in the region away from the saturation point [9], [10]. Overall, little attention has been devoted to considering a control design that takes into account the nonlinearity of the reluctance actuator system. ...
... This system can be viewed as a cascade connection of two subsystems; the first is (7)-(8), with ξ as a virtual input, and the second is (9), with u as input. Now, the control objective is to design state feedback control to stabilize the system (7)- (9). Towards this goal, suppose there is a smooth state feedback control ξ = d ξ that can be designed to stabilize the origin of the system (7)- (8). ...
... 9 Reluctance actuators are being designed and proposed for use in the next generation of lithography machines. 3,[10][11][12] Reluctance actuators induce a magnetic field from a current and produce higher forces with a smaller actuator size. However, the reluctance actuator has a nonlinear force as a function of the input current and the air gap, negative stiffness, and nonlinearities such as hysteresis, fringing, and eddy currents. ...
... 13,14 Various methods exist to mitigate the nonlinear effects of reluctance actuators through a proportional-integral-differential (PID) controller, 15 observer design, 16 complex hysteresis modeling, 17 and optimal design parameters selection. 11,12 Although precise finite element analysis (FEA) modeling is used extensively in computing the dynamics of reluctance actuators 18 and hybrid reluctance actuators, 19 in contrast, an equivalent magnetic circuit (EMC)-based model is favored over the more accurate FEA due to lower computational requirements 20 and applicability in real-time measurements such as in Ref. 21. The mean path length (MPL) is introduced when considering the flux through the core in an EMC analytical model. ...
This paper investigates the effect of the flux’s mean path length (MPL) on the reluctance actuator’s analytical model. It determines the circumstances where the model neglecting the MPL is valid. The analysis is carried out for both C-Core and E-Core reluctance actuators; the analytical results are calculated by using MATrix LABoratory and then validated against a finite element model simulation by using COMputer SOLution Multiphysics. In addition, the experimental results of the magnetic force of C-Core and E-Core reluctance actuators are presented and compared with the analytical model. The comparison is obtained under different input currents and air gaps for two different ferromagnetic materials. It can be concluded that the analytical model is valid only for air gaps with a relatively high air gap displacement and for small air gaps, considering the MPL is necessary for accurate results. This means that whenever the reluctance actuator is proposed for high-precision motion system applications, it is essential that the analysis takes into account the effect of the MPL.
... However, the reluctance actuator has a nonlinear force as a function of the input current and the air gap, negative stiffness, and nonlinearities such as hysteresis, fringing, and eddy currents 13,14 . Various methods exist to mitigate the nonlinear effects of reluctance actuators, through PID control 15 , observer design 16 , complex hysteresis modelling 17 , and optimal design parameters selection 11,12 . ...
This paper investigates the effect of the flux's mean path length (MPL) on the reluctance actuator's analytical model. It determines the circumstances where the model neglecting the MPL is valid. The analysis is carried out for both C-Core and E-Core reluctance actuators; the analytical results are calculated using MATLAB, then validated against a finite element model simulation using COMSOL Multiphysics. Additionally, the experimental results of the magnetic force of C-Core and E-Core reluctance actuators are presented and compared with the analytical model. The comparison is obtained under different input currents and air gaps for two different ferromagnetic materials. It can be concluded that the analytical model is valid only for air gaps with a relatively high air gap displacement and for small air gaps, considering the MPL is necessary for accurate results. This means that whenever the reluctance actuator is proposed for high-precision motion system applications, it is essential that the analysis takes into account the effect of the MPL.
... Different from the Lorentz motor, the force of the reluctance motor is not linearly proportional but a square of the excitation current. So it could bring about larger force to current ratio and achieve significantly higher power densities and lower dissipations Ito et al., 2020;Moya-Lasheras et al., 2020;Burgstaller et al., 2021;Moya-Lasheras et al., 2021;Al Saaideh et al., 2022). As a promising new candidate, the reluctance motor also brings various intractable issues. ...
The performance of the actuator is becoming increasingly important in the ultra-precision stage. However, the traditional Lorentz motors with given mechanical parameters cannot provide enough force for the next-generation motion stage in the semiconductor industry since they achieve a physical limit of power factor. To tackle this problem, this study develops a novel-driven approach and its control strategy for high-dynamic stages. Explicitly, the proposed method utilizes a linear reluctance motor as an actuator, which could promote the continuous thrust significantly. A heuristic optimization-based Bouc–Wen model is established to describe the nonlinear behavior of the novel actuator. Also, a flux control algorithm based on the integral sliding mode is derived and adjusted for precision thrust generation. Comparative simulations on a specific linear reluctance motor confirm the effectiveness and superiority of the proposed method and show that it has the ability to conquer the force nonlinearity of the novel actuator.
