Magnetic Levitation System
The following figure shows the cross section of a magnetic levitation (MAGLEV) train.
The track is a T-shaped guideway. Electromagnets are distributed along the guideway in
matched pairs. The magnetic attraction of the vertically paired magnets balances the force
of gravity and levitates the vehicle above the guideway.
Fixed Reference Line
Train
z
h
Magnets
Track
d
Magnets with
magnetizing circuits
We want to control the gap distance d within a close tolerance in normal operation of the
train. (The gap distance between the track and the train is d = z - h, as shown in the
diagram above.) The gap is controlled by adjusting the current to the magnetizing circuits
on the magnets attached to the train. This produces a magnetic force on the fixed magnets
on the track. The force is approximately
f = −Gi + Hd
where G and H are positive constants. That force acts to accelerate the mass M of the
train in the vertical direction:
Md = −Gi + Hd
The magnetizing circuit satisfies the following differential equation:
L
di
LH ˙
+ Ri = v +
d
dt
G
The input is v ( t ) , voltage to the magnetizing circuit.
A block diagram of the system is given below.
H
v +
1/L
+
s+R/L
i
G
+
1
M
d
1
s
d
1
s
d
LH
G
The system parameters are
M = 100
G =5
H =1
L = 20
R=3
The objective of the control system is to accurately control the gap distance d.
Design a feedback controller that will move the train as close as possible to a desired
reference gap distance in the quickest time, with the least overshoot. You can use
MATLAB to perform all of the calculations. You may want to consider using the
following MATLAB commands/tools: sisotool, rlocus, ltiview, step. (With sisotool you
can adjust the controller and watch the step response change in real time.) Demonstrate
the system step response. Discuss your design steps and the reasons for your final
design. Your design process should involve several potential designs before reaching a
final design. (Consider at least proportional feedback and proportional-plus-derivative
feedback.)
You should turn in the following: 1) a complete discussion of all of your design steps,
describing what potential designs were tested, and a justification for your final design, 2)
root locus plots illustrating the final design and other potential designs, 3) step response
plots for the final design and other potential designs. This project should be considered
an individual project. Although you may discuss general strategies with other students,
you should perform your design and implementation individually. There is no single
correct design. Each design should be different.