## Transcribed Text

1 Objectives
To analyse and control position of a Magnetic Levitation (Maglev) system.
2 Tools Required
1. MATLAB
2. MATLAB Control Systems Toolbox
3. Simulink
3 Background
Figure 1: A typical attractive Maglev experimental setup.
source by http://zeltom.com/products/maglevplus
Magnetic Levitation (or Maglev in short) technology has been applied in various engineering
applications including Maglev train systems, magnetic bearings, active suspension system in au-
tomobiles and so on. The Magley technology is applied in wide applications due to its ability
in
generating nearly frictionless motions for ferromagnetic materials or permanent magnets. There
are two types of Maglev systems, namely attractive Maglev and repulsive Maglev. Figure
1
depicts typical experimental platform for attractive magnetic levitation and dise magnet is
levitated in mid-air. By varying the current through the coil of the electromagnet and thus the
generated magnetic field. the vertical displacement of levitating object is adjusted stably in a
range of few centimetres. Position feedback is generated using linear Hall effect sensor 4
which measures change of magnetic field due to change of vertical of position of the levitating
object. You can watch the operation of the system at this link.
The lynamic model of the magnetic levitation system is nonlinear system, due to the nonlinear
model of the generated magnetic force by the electromagnet. The model is linearised about the
desired equilibrium point at which the distance de between the levitating mass and the electro
magnet is around 2 cm. The transfer function G(s) of the magnetic levitation system is given
as.
AD(s)
2360.0
G(s)
(1)
/(s)
(s + 160.0)(s²-1960.0)
where AD(s) and /(s) are the Laplace Transforms of the displacement of the levitating object
about the equilibrium position de which is and the (negative current perturbation inputted
to the elect romagnet respectively. In other words. the output of the maglev system is the actual
position of the levitating object is d(t) de- Ad(t) and the input is the current i(t) =ive Di(t)
flow in the coil of the electromagnet. where in is the equilibrium current. Figure depicts the
block diagram of the feedback control system for position control of the object by magnetic
levitation. In this coursework. we will design compensator so that its output response satisfies
the given specifications.
Current to
Compensator
Plant
Displacement
Coil
AI(s)
C(s)
G(s)
AD(s)
Figure 2: Feedback Control of the Maglev system.
4 Procedures
1. Is the open loop system G(s) stable? Justify your answer. Simulate. with MATLAB OI
Simulink. the unit step response of the plant G(s) to support your claim.
10%
2. Plot the root locus of the system with C(s) = K. when 0 < K < too using MATLAB
function clocus. Find the exact location of the breakaway point of the root locus. [Hint:
use the MATLAB function roots to find the roots of polynomial.]
3. Find the value of K when the closed loop system has double poles.
4. Can the system be stablised by a simple proportional controller C(s) = K? Justify your
answer. Pick two values of K, say 50 and 500, and simulate the closed loop responses to
see if the system is stable.
20%
5. Suppose C(s) K(s 50). Find the range of K so that the closed loop system is stable
using the Routh-Hurwitz Stability Criterion.
6. Verify your result in Step (5) using root locus
7. By imposing the second order system approximation to the system, estimate the settling
time (=5% of the settling value of output, peak time and rise time (10%-90% of the final
value of response) of the closed loop system with 25% of overshoot
20%
8. We design compensator C(s) in position control of the Maglev system under the following
criteria:
Settling time less than seconds
Percentage of Overshoot (P. O.) less than 16%
Sketch the feasible region of dominant closed loop poles that satisfies the above design
criteria in the s-plane. Select pair of dominant closed loop poles from the feasible region
Determine the type of the compensator you need. phase-lead or phase-lag compensator
Perform the design using the graphical method discussed in lecture. Simulate the unit
step response of the compensated system using MATLAB or Simulink. Check if the sys-
tem response satisfies the design criteria. You may need to refine your design if is not
Remember to include your calculation and sketches in coursework submission.
9.
Generate the Bode plots of the compensated system in Step (8) and find its gain margin
and phase margin. [Hint: Check the MATLAB functions bode and margin).
40%
10. Produce a concise report detailing all your analysis, designs, investigations and results.
Where relevant provide Simulink models and MATLAB in files that have been used to
support your work.
10%

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