EXAMPLES ON LINEARIZATION

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Consider the electromagnetic suspension system shown in the figure. An electromagnet is
located at the upper part of the experimental system. Utilizing the electromagnetic force f,
we desire to suspend the iron ball. Note that this simple electromagnetic suspension
system is essentially unworkable. Hence feedback control is indispensable. As a gap
sensor, a standard induction probe of eddy current type is placed below the ball.


Assignment
Derive the equations of motion for the inverter pendulum problem and linearize the
equations about the equilibrium point. ( Do not assume small angle approximation.)