Consider the magnetic levitation system shown in Figure 1. An electromagnet is located at the upper part of the experimental system. Using the electromagnetic force f, you want to suspend the iron ball. Assume that the state variables are x₁ = x, x2 = x, and x3 =i. The electromagnet has an inductance L = 0.508H and a resistance R = 23.2. Use a Taylor series approximation for the electromagnetic force. The current is i₁ = 10 + i, where I = 1.06A is the operating point and i is the variable. The mass m is equal to 1.75kg. The gap is x = x + x, where x = 4.36mm is the operating point and x is the variable. The electromagnetic force is f = k(₁₁/xg)², where k = 2.9 × 10-4 Nm²/A². a) Determine the state matrix differential equation. b) Find the equivalent transfer function X(s)/V(s). Note: v(t) (+ Electromagnet i₁(t) Iron ball Force f(t) x(t) mg Gap sensor Figure 1 The magnetic levitation system is essentially unworkable. Hence, feedback control is crucial. A standard induction probe of the eddy current type is placed below the ball as a gap sensor. Also, state any reasonable assumptions you make during the derivation.

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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Consider the magnetic levitation system shown in Figure 1. An electromagnet is located at the upper part
of the experimental system. Using the electromagnetic force f, you want to suspend the iron ball. Assume
that the state variables are x₁ = x, x2 = x, and x3 =i. The electromagnet has an inductance L =
0.508H and a resistance R = 23.2. Use a Taylor series approximation for the electromagnetic force.
The current is i₁ = 10 + i, where I = 1.06A is the operating point and i is the variable. The mass m is
equal to 1.75kg. The gap is x = x + x, where x = 4.36mm is the operating point and x is the
variable. The electromagnetic force is f = k(₁₁/xg)², where k = 2.9 × 10-4 Nm²/A².
a) Determine the state matrix differential equation.
b) Find the equivalent transfer function X(s)/V(s).
Note:
v(t) (+
Electromagnet
i₁(t)
Iron ball
Force f(t)
x(t)
mg
Gap sensor
Figure 1
The magnetic levitation system is essentially unworkable. Hence, feedback control is crucial. A standard
induction probe of the eddy current type is placed below the ball as a gap sensor. Also, state any
reasonable assumptions you make during the derivation.
Transcribed Image Text:Consider the magnetic levitation system shown in Figure 1. An electromagnet is located at the upper part of the experimental system. Using the electromagnetic force f, you want to suspend the iron ball. Assume that the state variables are x₁ = x, x2 = x, and x3 =i. The electromagnet has an inductance L = 0.508H and a resistance R = 23.2. Use a Taylor series approximation for the electromagnetic force. The current is i₁ = 10 + i, where I = 1.06A is the operating point and i is the variable. The mass m is equal to 1.75kg. The gap is x = x + x, where x = 4.36mm is the operating point and x is the variable. The electromagnetic force is f = k(₁₁/xg)², where k = 2.9 × 10-4 Nm²/A². a) Determine the state matrix differential equation. b) Find the equivalent transfer function X(s)/V(s). Note: v(t) (+ Electromagnet i₁(t) Iron ball Force f(t) x(t) mg Gap sensor Figure 1 The magnetic levitation system is essentially unworkable. Hence, feedback control is crucial. A standard induction probe of the eddy current type is placed below the ball as a gap sensor. Also, state any reasonable assumptions you make during the derivation.
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