Modeling and Decoupling Control of a Linear Permanent Magnet Actuator Considering Fringing Effect for Precision Engineering

In this article, accurate modeling and decoupling control of a linear ironless PM actuator are implemented for precision engineering. Given the fringing effect due to the finite length, the magnetic field of the PMs and the three-phase winding are both calculated by applying an improved Fourier series expansion. Subsequently, based on a distributed model, the associated flux linkage and winding inductances are obtained and validated. Compared with rotary motors of physical symmetry, the winding inductance matrix makes the electrical model of the finite-long linear actuator present a new non-uniform form, to which the classic decoupling technique is inapplicable directly. Therefore, improved decoupling strategies are established utilizing the zeroth-order approximation of the inductances based on the $dq0$ transformation, as well as a real-time updating scheme. Physical experiments show that high-order harmonics are eliminated by applying the non-uniform model, which makes it effective and applicable.