eletrical engineer UTFPR Dynamic Models – Description
1) The schematic of a magnetic suspension system is shown in the figure on the side. For small movements close to the reference position, the voltage e (in Volts) is related to the position of the ball x (in meters) by e = 30x. The upward force on the ball caused (in Newtons) by current i (in Amperes) can be approximated by f = 0.5i + 0.2x. The mass of the ball is 50g and the gravitational force is 9.8 N/kg. The output of the power amplifier is given by i = u + v0.
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a) Determine the dynamic model that relates the output e(t) to the input u(t).
b) Determine the value of Vo such that the ball is in equilibrium when x = 0, with u = 0.
c) Considering null initial conditions, determine the transfer function using Vo found in item b.
d) If the input u(t) is a step function, determine e(t).
2) Take the following system:
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a) Obtain the dynamic equation of the system.
b) Obtain the transfer function of the system.explained step by step
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