Magnetic Levitation Experiment NYU Tandon （磁悬浮实验纽约大学经脉）.pdf

Magnetic Levitation Experiment Magnetic Levitation Experiment Quanser Consulting Inc. 1 Description The “maglev” experiment consists of an electromagnet encased in a rectangular enclosure. One electromagnet pole faces a black post upon which a 2.54 cm steel ball rests. The ball elevation from the post is measured using a sensor embedded in the post. The post is designed such that with the ball at rest on its surface it is 14mm from the face of the electromagnet. The purpose of the experiment is to design a controller that levitates the ball from the post and the ball position tracks a desired trajectory. 2 Mathematical Model 2.1 Electrical system The coil used in the electromagnet has an inductance and a resistance. The voltage applied to the coil results in a current governed by the differential equation: di V i R % L l dt The actual system is equipped with resistor Rs in series with the coil whose voltage Vs can be measured using the A/D. The measured voltage can be used to compute the current in the coil. The sense resistor in the circuit results in the equation : di V i (R %R ) % L l s dt The state space equations for the current is given by: R %R 1 l s 0 i 0 i L % L V 0 .i 1 0 . 0 Maglev 1 0 we have introduced an integrator for the current ( . i )for reasons which shall become i clearer in the control system design section. Note that the sense resistor is only 1 S compared to