Distributed Multipole Models for Design and Control of PM Actuators and Sensors

Closed-loop magnetic bearing and angular velocity control of a reaction sphere actuator

“…Depending on the practical case, the magnetic flux density model can be formulated with a variety of methods including the distributed multipoles (DMP) methods [33][34][35][36], which consists in modeling both the stator coils and the PMs as distributed multipoles, the charge and current models [27,[37][38][39], where PM are replaced by an equivalent spatial (volume or surface) distribution of ''magnetic charges'' that is in turn used as a source term in the magnetostatic field equations, the finite element analysis [40], which is widely adopted in the design optimization and model verification of spherical actuators, and the harmonic model [19,30,22,17,41], which is derived by solving Maxwell's equations under certain boundary conditions to express the solution as a series of space spherical harmonic function. A particular approach to the harmonic model method consists in employing boundary conditions measured on all the rotor surface to reconstruct the magnetic flux density model [42,43].…”

“…An alternative approach to characterize torque models, while reducing the computational time, consists in modeling both the stator coils and the permanent magnets as DMP. Unlike the Lorentz force or the Maxwell stress tensor methods that require integration, the dipole force computation is expressed in closed form [35,33,36]. Another category of approaches to derive expressions for the force and torque are the so-called hybrid methods, in which FEM or measured derived values are used in combination with an analytical model [51].…”

Magnetic field-based multi-DOF orientation sensor for PM-based spherical actuators

“…The computation of the magnetic flux density of the PM as measured by a sensor is achieved using the distributed multipole (DMP) model [9] [12]. The use of the DMP model is preferred because of its ability to characterize magnetic fields around PMs and EMs and are extendable to objects of other geometry.…”

“…More recently, Son and Lee used the distributed multipole (DMP) model to characterize the magnetic field of a single PM and design a magnetic field-based multi-DOF orientation sensor using methodically placed sensors [9]. One method discussed involved extraction of the PM orientation by expressing the measured magnetic field density as a polynomial function and solving the inverse problem.…”

Equivalent energized coil model for magnetic field of permanent-magnet spherical actuators

“…To simply the computation, the fundamental terms of spherical harmonics are usually utilized for the magnetic field formulation, which may compromise the modeling precision further. The DMP method is proposed by Lee and Son et al to solve the magnetic field of spherical wheel motors [29,30]. It can be used to formulate magnetic field of permanent magnet poles and helps to obtain analytical models in closed form.…”