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# HW8 - ME 132 Issued Homework 8 Due 1 Sensitivity Analysis...

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ME 132 Homework # 8 Issued: October 16, 2009 Due: October 23, 2009 1 Sensitivity Analysis Consider the block diagram shown below. Compute the sensitivity S a of the output y with respect to changes in the parameter A . Also find the sensitivity S c of the output y with respect to changes in the parameter C . + + + u - A C D y B 2 Model Properties Consider the following properties a model may have: M emoryless, L inear, T ime-invariant, C ausal. For each of the following models M , indicate which of the preceding properties the system possesses. (a) M { u ( t ) } = e u ( t ) (b) M { u ( t ) } = au ( t ) + b (c) M { u ( t ) } = u ( - t ) (d) M { u ( t ) } = integraltext t = -∞ u ( t ) dt 3 Homogeneous Solutions Analytically find the homogeneous solutions of each of the following differential equations. In each case plot (using matlab ) the solution for 0 t 10. (a) ˙ y ( t ) + y ( t ) = u ( t ), subject to the initial conditions y (0) = - 4. (b) ¨ y ( t ) + 1 . 2 ˙ y ( t ) + y ( t ) = u ( t ), subject to the initial conditions ˙ y (0) = 4 , y (0) = 2.

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