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Unformatted text preview: ME 132 Homework # 7 Issued: October 09, 2009 Due: October 17, 2009 1 Block diagrams Consider the block diagram shown below. Each block is a gain with the letter in the block denoting the numerical value of the gain. Find the matrix M (which is 1 3) such that y ( t ) = M u ( t ) d ( t ) n ( t ) + + + + + + + u y d n A D C B 2 Modeling Consider an inverted pendulum as shown be low. The pendulum has length L = 0 . 75 meters , and mass m 1 = 0 . 333 Kg . The cart has mass m 2 = 0 . 666 Kg . An actuator allows us to apply a thrust u to the cart, and a sensor measures the angle y . Take g = 10 m/sec 2 . y u (a) Find the inputoutput differential equation model for this system. (b) What are possible sources of modeling error that you may have neglected ? (c) What are possible disturbance sources ? (d) Is this model linear ? Timeinvariant ? (e) Can you suggest a sensing scheme to measure y ?...
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 Fall '08
 Tomizuka

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