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hw1sol

# hw1sol - (a The FBD for the system is which results in the...

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Problem 1: In many mechanical positioning systems there is flexibility between one part of the system and another. An example is shown in figure 2.7 (both edition 5 and 6 of the text) where there is flexibility of the solar panels. The figure shown below (2.36 5th or 2.42 6th ) depicts such a situation, where a force u is applied to the mass M and another mass m is connected to it. The coupling between the objects is often modeled by a spring constant k with a damping coefficient b, although the actual situation is usually more complicated than this. (a) Write the equations of motion governing this system. (b) Find the transfer function between the control input, u, and the output, y. Solution:

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Unformatted text preview: (a) The FBD for the system is which results in the set of equations: or (b) Take Laplace Transform of the equations of motion. This in matrix form is: Using Cramer's Rule to solve for Y now rearranging a bit and writing as a transfer function Solution: (a) equations of motion: Rotor: Load: Circuit: (b) The relation between the out torque and the armature current is: (This is the transducer linking the electric and the mechanical energy domains. Torque is an "effort" variable and current is a "flow" variable so this is a gyrator.) Now taking the Laplace Transform of the equations of motion using the gyrator to link the energy domains: rearranging and writing in the form of a transfer function:...
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hw1sol - (a The FBD for the system is which results in the...

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