ps7a2 - Question#2 Show and label on this graph the gain...

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University of Maryland at College Park Dept. of Aerospace Engineering ENAE 432: Aerospace Control Systems Problem Set #7 Issued: 26 Mar. 2011 Due By: 1 Apr 2011 Question 1: Use Matlab to obtain Bode diagrams for the system G ( s ) below when K = 2 , 8 and 20. Use these to sketch by hand the corresponding polar plots for each case (three different plots). Accurately label the intersections with the unit circle and real axis. Hint: right click on the Bode diagrams to have Matlab show you the crossover frequencies and margins. Alternately, you can use the margin command to get the Bode diagrams with both margins displayed. G ( s ) = K ( s/ 10 + 1) 3 Question 2: Repeat Question #1 for the system G ( s ) = 1 + τs s ( s + 1) 2 when τ = 10 and τ = 0 . 1. Label also the point where the diagram crosses the imaginary axis in each case (if applicable). Question 3: Repeat Question #2 for the system G ( s ) = 1 + τs 50 s 2 ( s + 1) 2 Use the same values for τ .

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Question 4: Use the nichols command in Matlab to draw the Nichols chart for the two systems in
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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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