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Dynamics and Control of Mechanical Systems: Exercises on Mass-Spring-Damper and Electromagnets

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lyneth
8 diapositives · 238 Views · Jul 28, 2014

This document covers a series of exercises focused on dynamic systems in mechanical engineering. It includes problems related to a mass rolling on a frictionless cart connected by a spring and damper, exploring inputs and outputs, and analyzing forces in an electromagnet-driven loudspeaker. Additionally, the document explores Keynesian Economics, deriving a state-space model from GNP, consumption, investment, and government expenditures. Tools such as Nyquist, Bode, and Root locus methods are reviewed in preparation for the final exam.

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Dynamics and Control of Mechanical Systems: Exercises on Mass-Spring-Damper and Electromagnets
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  1. Problem Session 5a Professor Walter W. Olson Department of Mechanical, Industrial and Manufacturing Engineering University of Toledo

  2. Exercise 1 u x A mass m (kgm) rolls frictionless on a massless cart. The mass is connected to the cart by a spring with a spring rate of k (N/m) and damper with a rate of b (n-s/m). The input is u(t) and the desired output is x(t). k m massless cart b

  3. Exercise 1 Solution u x k m massless cart b

  4. Exercise 2 Electromagnet A loudspeaker works on the law of motors: where F is the force, i is the current, and l is the length of the coil wires. Assume that the cone can be represented by a mass, m, which is resisted by viscous damping with rate b and is driven by the force, F, produced by the current above. Cone Bobbin Coil

  5. Exercise 2 Electromagnet Cone Bobbin Coil

  6. Exercise 3 (From text, Problem 2.4, page 62) Keynesian Economics: Keynes' simple model is given by where Y is the Gross National Product (GNP), C is consumption, I is investment and G is government expenditures for year k. Consumption and investment are modeled with Derive the state space model with the GNP as the output.

  7. Exercise 3

  8. Summary • Robustness • Unmodeled dynamics • Tools: • Nyquist • Bode • Root locus • Course Review Next: Final Exam