EECS 419/ ISD 599-889
Winter 2021

Your mission, should you choose to accept it (note: you have to accept it), is to create a Simulink
model of an actuator consisting of a coil of wire and a cylinder of soft magnetic material, a cross-
section of which is shown below.

The inductance L of the coil changes with the position x of the cylinder, and can be represented
as follows:

( )
2
0 ,d
x
xL x L L e
 
− 
 = +

where 150 ,L Hµ=

0 2 ,L mH= and 4 .dx cm= The coil has a resistance 3 .R m= Ω The soft
magnetic cylinder has a mass 0.1m kg= and can freely move in the x-direction. Assume the
actuator is in space (i.e., zero gravity).
The Simulink model should model the electrical dynamics of the coil, the electromechanical
force exerted on the cylinder, and the resulting mechanical dynamics of the cylinder. It should
have as an input the coil voltage v and outputs coil current i, electromechanical force fem, cylinder
velocity u, and cylinder position x.
Once the model is complete, simulate and plot the outputs of the actuator due to the following
voltage excitations:
a. A unit step. Plot all outputs from t=-0.5s to t=3s.
b. The voltage waveform below (note that the coordinates of the waveform are provided).
Plot all outputs from t=0 to t=0.3s.

For each simulation the mover is initially at rest (i.e., zero velocity) at a displacement x=-3cm.
Choose an appropriate tolerance or time step to ensure accurate results. Also, for each simulation
describe qualitatively what the cylinder is doing. Submit your Simulink files, plots, and any
Matlab m-files used.  