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Unformatted text preview: Question #2. Show and label on this graph the gain and phase margins of the system. Question 5: Suppose the denominator of the transfer function for a physical system T ( s ) can be written as 1 + L ( s ), where L ( s ) is a diﬀerent transfer function. Prove the following: if the polar diagram of L ( jω ) passes through the -1 point in the complex plane, then T ( s ) has a pole on the imaginary axis. Hint: the poles of T ( s ) here are the solutions of 1 + L ( s ) = 0. Question 6: Suppose that L ( s ) = 8 ( s/ 10 + 1) 3 Use the results from Question #5 and the Bode diagrams of L ( s ) to show that T ( s ) has a pole on the imaginary axis, and determine the speciﬁc location of this pole. Note: this can be easily done by explicit factorization, but to receive credit you must show how the results of Question #5 and the Bode diagrams lead to the desired information....
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- Spring '09
- Complex number, Bode diagrams