Magnetically levitated planar actuator with moving magnets: Dynamics, commutation and control design

Magnetically levitated planar actuator with moving magnets: Dynamics, commutation and control design 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 v vi Abstract 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.