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hw3-fa10

# hw3-fa10 - CALIFORNIA INSTITUTE OF TECHNOLOGY Control and...

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Unformatted text preview: CALIFORNIA INSTITUTE OF TECHNOLOGY Control and Dynamical Systems CDS 101 D. G. MacMynowski Fall 2010 Problem Set #3 Issued: 11 Oct 10 Due: 18 Oct 10 Note: In the upper left hand corner of the second page of your homework set, please put the number of hours that you spent on this homework set (including reading). 1. Choose one of the following linear systems, determine whether the origin is asymptotically stable and, if so, plot the step response and frequency response for the system. If there are multiple inputs or outputs, plot the response for each pair of inputs and outputs. (a) Bridged Tee Circuit. Consider the following electrical circuit, with input v i and output y = v o . 1 2 3 ~ v i v o R 1 R 2 C 1 C 2 The dynamics are given by d dt v c 1 v c 2 = - 1 C 1 parenleftBig 1 R 1 + 1 R 2 parenrightBig- 1 C 1 R 2- 1 C 2 R 2- 1 C 2 R 2 v c 1 v c 2 + 1 C 1 parenleftBig 1 R 1 + 1 R 2 parenrightBig 1 C 2 R 2 v i , y = 0 1 v c 1 v c 2 + v i , where v c 1 and v c 2 are the voltages across the two capacitors. Assume that R 1 = 100 Ω, R 2 = 100 Ω and C 1 = C 2 = 1 × 10- 6 F. NOTE: The sign of the C matrix is wrong, but this hasn’t been updated in solutions yet. (b) Coupled mass spring system. Consider the coupled mass spring system from Example 5.6 (Fig. 5.7) with m = 250, k = 50 and c = 10 (Note m 1 = m 2 = m ). The input u ( t ) is the force applied to the right-most spring....
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hw3-fa10 - CALIFORNIA INSTITUTE OF TECHNOLOGY Control and...

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