Maglevs work by levitating over the tracks and thus eliminating the need for moving parts. There...

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Maglevs work by levitating over the tracks and thus eliminating the need for moving parts. There are two sets of magnets in a Maglev system: one levitates the train above the track and the other pulls the train forward. In this project we focus on the control of levitation by focusing on a simplified model that describes the vertical position of an iron ball (abstracting the train) within a magnetic field created by a single electromagnet. The relevant equations are: 1 = X2 1 x2 = 2m = - -12-g R -(1-x1)+u, C (1) (2) (3) where x denotes the balls height, x2 the balls velocity, m is the balls mass, g is gravitys constant, is the magnetic flux linkage in the electromagnet, R is the resistance of the electromagnets coil, c is a positive constant modeling the electromagnets geometry and con- struction, and u is the voltage applied at the coils terminals constituting the input to this system. The values of the parameters are: m =30000, g = 9.8, R = 15, c = 5. 1. The objective is stabilize the ball's height at 0.01m. Find an equilibrium pair consistent with this objective. 2. Linearize the equations of motion around the desired equilibrium pair. 3. Compute the transfer function from the input du to 8x1. Maglevs work by levitating over the tracks and thus eliminating the need for moving parts. There are two sets of magnets in a Maglev system: one levitates the train above the track and the other pulls the train forward. In this project we focus on the control of levitation by focusing on a simplified model that describes the vertical position of an iron ball (abstracting the train) within a magnetic field created by a single electromagnet. The relevant equations are: 1 = X2 1 x2 = 2m = - -12-g R -(1-x1)+u, C (1) (2) (3) where x denotes the balls height, x2 the balls velocity, m is the balls mass, g is gravitys constant, is the magnetic flux linkage in the electromagnet, R is the resistance of the electromagnets coil, c is a positive constant modeling the electromagnets geometry and con- struction, and u is the voltage applied at the coils terminals constituting the input to this system. The values of the parameters are: m =30000, g = 9.8, R = 15, c = 5. 1. The objective is stabilize the ball's height at 0.01m. Find an equilibrium pair consistent with this objective. 2. Linearize the equations of motion around the desired equilibrium pair. 3. Compute the transfer function from the input du to 8x1.