Control Theory in Practice: Magnetic Levitation

A device that levitates a steel ball beneath an electromagnet is used for educational purposes at the United States Military Academy, West Point, New York. Students in the course “Mechatronics” engage in a set of laboratory exercises with the device to reinforce classroom learning. Mechatronics is a senior-level course that introduces the interdisciplinary design of smart systems. Students in the electrical engineering and mechanical engineering programs take the course together, and the material is taught by a team of instructors from both academic departments. The Magnetic Levitation experiments are the primary means of teaching the classical analog control portion of the course. Other aspects of the course involve interfacing microcontrollers with sensors and actuators, and digital control. The magnetic levitation device fits easily on a two-person workbench and requires a power supply and oscilloscope. An infra-red emitter / detector pair is used to sense ball position for a feedback compensator. Students first learn classical control theory in a co-requisite course, “Dynamic Modeling and Control.” Modeling principles are introduced in the context of the magnetic levitation system as an unstable plant to be controlled. The system can be simulated by models ranging from simply linear to more complex to teach the trade-off between model fidelity and model development effort. The students derive the nonlinear governing equations and then linearize the equations and develop the transfer function of the plant. Students design a compensator and simulate the resulting stabilized system with Matlab and Simulink software. Students build their compensator on a solderless project board to levitate the steel ball. A proven lead-type compensator using two resistors and a capacitor is readily provided to students that struggle with their own compensator design so that all teams may enjoy the fruit of a successful experiment. As a laboratory aid, the magnetic levitation system allows for basic and advanced approaches to both theoretical study and practical investigation of a nonlinear, unstable system control. The comparison of measured results to predicted behavior leads to insight about how the physical system is modeled by mathematics. Students write a case study describing the system in detail including characterization of the sensors and actuators. Instructors report that the hands-on nature motivates students to excel. Surveyed students cite the hands-on activities as relevant applications that help develop deeper understanding and greater appreciation for the concepts learned in the classroom. The students are motivated to learn by the fascination of defying gravity.