Multi-objective optimization of a magnetically levitated planar motor with multi-layer windings

In this paper, a novel magnetically levitated coreless planar motor with three-layer orthogonal overlapping windings is shown to have higher power density and higher space utilization compared to other coreless planar motors. In order to achieve maximum forces with minimum cost and minimum space, a multi-objective optimization of the novel planar motor is carried out. In order to reduce the computational resources required for finite element analyses, a fast but accurate analytical tool is developed, based on expressions of the flux density of the permanent magnet array, which are derived from the scalar magnetic potential method. The validity and accuracy is verified by 3D FE results. Based on the force formulas and the multi-objective function derived from the analytical models, a particle swarm optimization (PSO) algorithm is applied to optimize the dimensions of the planar motor. The design and optimization of the planar motor is validated with experimental results, measured on a built prototype, thus proving the validity of the analytical tools

Magnetically levitated planar actuator with moving magnets

Mechanical systems with multiple degrees of freedom typically consist of several one degree-of-freedom electromechanical actuators. Most of these electromechanical actuators have a standard, often integrated, commutation (i.e. linearization and decoupling) algorithm deriving the actuator inputs which result in convenient control properties and relatively simple actuator constraints. Instead of using several one degree-of-freedom actuators, it is sometimes advantageous to combine multiple degrees of freedom in one actuator to meet the ever more demanding performance specifications. Due to the integration of the degrees of freedom, the resulting commutation and control algorithms are more complex. Therefore, the involvement of control engineering during an early stage of the design phase of this class of actuators is of paramount importance. One of the main contributions of this thesis is a novel commutation algorithm for multiple degree-of-freedom actuators and the analysis of its design implications. A magnetically levitated planar actuator is an example of a multiple degree of freedom electromechanical actuator. This is an alternative to xy-drives, which are constructed of stacked linear motors, in high-precision industrial applications. The translator of these planar actuators is suspended above the stator with no support other than magnetic fields. Because of the active magnetic bearing the translator needs to be controlled in all six mechanical degrees of freedom. This thesis presents the dynamics, commutation and control design of a contactless, magnetically levitated, planar actuator with moving magnets. The planar actuator consists of a stationary coil array, above which a translator consisting of an array of permanent magnets is levitated. The main advantage of this actuator is that no cables from the stator to the translator are required. Only coils below the surface of the magnet array effectively contribute to its levitation and propulsion. Therefore, the set of active coils is switched depending on the position of the translator in the xy-plane. The switching in combination with the contactless translator, in principle, allows for infinite stroke in the xy-plane. A model-based commutation and control approach is used throughout this thesis using a real-time analytical model of the ironless planar actuator. The realtime model is based on the analytical solutions to the Lorentz force and torque integrals. Due to the integration of propulsion in the xy-plane with an active magnetic bearing, standard decoupling schemes for synchronous machines cannot be applied to the planar actuator to linearize and decouple the force and the torque components. Therefore, a novel commutation algorithm has been derived which inverts the fully analytical mapping of the force and torque exerted by the set of active coils as a function of the coil currents and the position and orientation of the translator. Additionally, the developed commutation algorithm presents an optimal solution in the sense that it guarantees minimal dissipation of energy. Another important contribution of this thesis is the introduction of smooth position dependent weighing functions in the commutation algorithm. These functions enable smooth switching between different active coil sets, enabling, in principle, an unlimited stroke in the xy-plane. The resulting current waveform through each individually excited active coil is non-sinusoidal. The model-based approach, in combination with the novel commutation algorithm, resulted in a method to evaluate/design controllable topologies. Using this method several stator coil topologies are discussed in this thesis. Due to the changing amount of active coils when switching between active coil sets, the actuator constraints (i.e. performance) depend on the xy-position of the translator. An analysis of the achievable acceleration as a function of the position of the translator and the current amplifier constraints is given. Moreover, the dynamical behavior of the decoupled system is analyzed for small errors and a stabilizing control structure has been derived. One of the derived coil topologies called the Herringbone Pattern Planar Actuator (HPPA) has been analyzed into more detail and it has been manufactured. The stator of the actuator consists of a total of 84 coils, of which between 15 and 24 coils are simultaneously used for the propulsion and levitation of the translator. The real-time model, the dynamic behavior and the commutation algorithm have been experimentally verified using this fully-operational actuator. The 6-DOF contactless, magnetically levitated, planar actuator with moving magnets (HPPA) has been designed and tested and is now operating successfully according to all initial design and performance specifications

Universal Framework for Linear Motors and Multi-Axis Stages with Magnetic Levitation

This dissertation presents the electromagnetic design and experimental validation of a new framework for linear permanent-magnet (PM) machines with targeted applications in precision motion control. In this framework, a single forcer, which can generate two independent force components in two perpendicular directions, consists of a stationary Halbach magnet array and two Lorentz coils with a phase difference of 90° or 270°. Any number of coil pairs can be attached on the same moving frame to work with a common magnet array or matrix, forming a linear or planar PM motor. Key advantages of this framework are simple force calculation, a linear system model, and a reduced number of coils for force generation and allocation in multi-axis positioners. The proposed framework effectively allows for decoupled dynamics, simplifying the linear controller design and real-time implementation. To experimentally verify the theoretical framework proposed herein, a high-precision 6-axis magnetically levitated (maglev) stage is designed, constructed, and controlled. The development of this 6-axis positioning system is an integrated work, including magnetic-force calculation and analysis, mechanical design, fabrication, assembly, system modeling, system identification, and control system design. The mechanical components of the system include a stationary superimposed Halbach magnet matrix, which was previously built, and a moving platen with a plastic frame, four sets of 2-phase coils, and two precision mirrors. For position measurements, there are three laser interferometers for in-plane position measurements, three laser displacement sensors for out-of-plane position sensing, and two 2-channel Hall-effect sensors for the position feedback to initialize the position and expand the travel ranges of the platen in the XY plane. The positioning resolutions of 10 nm in the xy plane and in the vertical axis are demonstrated. In out-of-plane rotation about the two horizontal axes, experimental results show the unprecedented positioning resolution of 0.1 μrad. The maximum travel range in X and Y with nanoscale positioning resolution is 56 mm × 35 mm, limited by the lengths of the precision mirrors attached to the platen. With the trapezoidal-velocity input shaping, achieved performance specifications include the maximum acceleration and velocity of 0.6 m/s2 and 0.06 m/s, respectively, in translations in the horizontal plane. With the platen supported by the air bearings, the maximum acceleration and speed are 1.5 m/s2 and 0.15 m/s, respectively. A load test is performed with the platen carrying a load of 0.54 kg, which is 72% of its total mass, magnetically levitated in 6- axis closed-loop control. Experimental results show the reduced coupled dynamics between different axes in magnetic levitation. This framework of 2-phase Lorentz coils and linear Halbach arrays is highly applicable in precision-positioning linear motors and multi-axis stages, steppers, scanners, nano-scale manipulation and alignment systems, and vibration isolators

Design and Analysis of Long-Stroke Planar Switched Reluctance Motor for Positioning Applications

This paper presents the design, control, and experimental performance evaluation of a long-stroke planar switched reluctance motor (PSRM) for positioning applications. Based on comprehensive consideration of the electromagnetic and mechanical characteristics of the PSRM, a motor design is first developed to reduce the force ripple and deformation. A control scheme with LuGre friction compensation is then proposed to improve the positioning accuracy of the PSRM. Furthermore, this control scheme is proven to ensure the stable motion of the PSRM system. Additionally, the response speed and steady-state error of the PSRM system with this control scheme are theoretically analyzed. Finally, the experimental results are presented and analyzed. The effectiveness of the precision long-stroke motion of the PSRM and its promise for use in precision positioning applications are verified experimentally