Magnetic levitation - Prof. M. Maggiore

This research investigates the use of magnetic levitation to develop high-precision positioning systems. Our basic building block is a permanent magnet linear synchronous motor (PMLSM). Its schematic representation is shown below.

A PMLSM has two parts, a stator and a mover. The stator hosts a three-phase winding which generates a travelling magnetic field. The mover has a number of permanent magnets. A PMLSM is capable of generating two forces, longitudinal and normal, which can be more or less independently assigned by an appropriate choice of the three-phase currents. A M.A.Sc. student, Rafael Becerril, developed a detailed mathematical model of a PMLSM by extending the work of Nasar and Xiong. This was used to develop nonlinear controllers for an idealized device employing several PMLSMs to control three degrees-of-freedom (DOF). For more information on Rafael's work, see the references below.

R. Becerril, M.A.Sc. thesis, 2003. (download)
M. Maggiore, R. Becerril, "Modeling and Control Design for a Magnetic Levitation System", International Journal of Control, vol. 77, no. 10, pp.964.977, 2004. (download)

In collaboration with Jacob Apkarian at Quanser Inc., my student Brydon Owen began the experimental verification of the theory developed in the references above. At first Quanser Inc. constructed a two DOF device, shown to the left, which employs one PMLSM to actuate two DOF.

The mover is mounted on two linear guides that constrain its motion to lie on the vertical plane. The horizontal and vertical displacements of the mover are measured, by means of optical encoders, with a resolution of 10µm. Brydon used this device to validate our mathematical model and perform nonlinear setpoint stabilization and sinusoidal tracking. It turns out that our mathematical model is very accurate indeed and our nonlinear controllers perform well. See the movies below.

Low resolution movie (2.3Mb)
Medium resolution movie (11.9Mb)
High resolution movie (25.2Mb)

Next, it was necessary to find out whether our control methodology scales well when using multiple PMSLMs. Quanser Inc. built a second device which employs four PMLSMs to actuate three DOF, shown at the right.

The four PMLSMs are combined into 2 pairs by wiring together the 3 phases of each pair in parallel so that the system can be viewed as having two PMLSMs. The four movers are mounted on an aluminum comb platen. Its movement is constrained by linear guides to be purely translational. Brydon validated once again the mathematical model and verified that the nonlinear control design scales exceptionally well. The movies below show our three DOF device performing setpoint stabilization and sinusoidal tracking. The accuracy is 10µm (encoder resolution) for setpoint stabilization and about 0.1mm for sinusoidal tracking.

Low resolution movie (3Mb)
Medium resolution movie (14.2Mb)
High resolution movie (20.3Mb)

For more information on Brydon's work, see the references below:

B. Owen, M.A.Sc. thesis, 2005. (download)
B. Owen, M. Maggiore, "Implementation and Model Verification of a Magnetic Levitation System," American Control Conference, Portland, OR, USA, June 2005. (download)
B. Owen, M. Maggiore, J. Apkarian, "Nonlinear Control Design for a High-Precision Contactless Positioning System Using Magnetic Levitation," IEEE Conference on Control Applications, Toronto, ON, Canada, August 2005. (download)