Abstract
Mechanical systems with multiple degrees of freedom typically consist of several
one degreeoffreedom 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 degreeoffreedom 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 degreeoffreedom 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 xydrives, which are
constructed of stacked linear motors, in highprecision 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 xyplane.
The switching in combination with the contactless translator, in principle, allows
for infinite stroke in the xyplane.
A modelbased commutation and control approach is used throughout this
thesis using a realtime 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 xyplane 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 xyplane. The resulting current waveform through each individually
excited active coil is nonsinusoidal.
The modelbased 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 xyposition 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 realtime model, the dynamic behavior and the commutation algorithm have
been experimentally verified using this fullyoperational actuator. The 6DOF 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.
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  15 Jan 2008 
Place of Publication  Eindhoven 
Publisher  
Print ISBNs  9789038617046 
DOIs  
Publication status  Published  2008 
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Cite this
Lierop, van, C. M. M. (2008). Magnetically levitated planar actuator with moving magnets. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR631971