hw2 - G ( s ) = . 01 s 2 + . 02 s + . 01 . Using the matlab...

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MAE 171a Homework Problem Set 2 - Revised July 1st, 2:30PM Prof. Schwartz Due: Wednesday, July 7th 1. Sketch the output time response of a step input to the following transfer functions. Use partial fractions to decompose the response. (a) G ( s ) = 20 ( s +5)( s +10) (b) G ( s ) = 20( s +4 . 5) ( s +5)( s +10) (c) G ( s ) = - s +1 s 2 +4 s +1 2. The response of a system, y ( t ) to an input, u ( t ) , is given by ¨ y ( t ) + 5 ˙ y + 6 y ( t ) = u ( t ) . (a) Convert the system into a state space equivalent ˙ x = Ax + Bu y = Cx + Du (b) Find the transformation z = Tx such that T - 1 AT is diagonal. Rewrite the state space equations using z as the state. (c) Solve the di±erential equation using this form. Use u ( t ) = δ ( t ) . 3. On the grids provided on the ²nal page, use the asymptote method to sketch the frequency response of the following functions. Label important aspects of the plots. Check using matlab, and include your code. (a) 30 ( s +1)( s +20) (b) 100 s 2 +3 s +100 Hint: ²nd ω d 4. Use simulink to evaluate the step response of the system
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Unformatted text preview: G ( s ) = . 01 s 2 + . 02 s + . 01 . Using the matlab data, nd values for ,T s ,T p ,T r , and % overshoot and label the plot. Include code used to generate any plots. Hint: Use the workspace as a sink, and dont forget to use the block option to include time! 1 5. Determine the input/output transfer functions using the block diagrams below. G 1 R G 2 +- + + Y G 1 R G 2 +- + + Y + G 4 G 3 G 5-2 10-4 10-3 10-2 10-1 10 10 1 Frequency Response Magnitude 10-1 10 10 1 10 2 10 3-180-135-90-45 45 90 135 180 Frequency Response Phase 10-4 10-3 10-2 10-1 10 10 1 Frequency Response Magnitude 10-1 10 10 1 10 2 10 3-180-135-90-45 45 90 135 180 Frequency Response Phase 3...
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hw2 - G ( s ) = . 01 s 2 + . 02 s + . 01 . Using the matlab...

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