# A#23_Revised - -4-2 2 4 6 8 Root Locus Real Axis...

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Assignment #23 (Revised) – p.1 ECSE-2410 Signals & Systems - Spring 2009 Due Fri 04/24/09 1(10). The root locus shown represents a system with the closed-loop transfer function G(s) K + 1 G(s) K = X(s) Y(s) . The breakaway point is = b σ -4.44. Note: All the poles of G ( s ) have real and imaginary parts that are integers (no complicated fractions or decimals!). (a) (5) Find the gain K so that one of the closed-loop poles is at . 2 1 = s (b) (2) Find the other two poles. c.) (3) Find the range of K that will make the closed-loop system overdamped. -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 -15 -10 -5 0 5 10 15 Root Locus Real Axis Imaginary Axis 2(10). The root locus below represents a system with the closed-loop transfer function G(s) K + 1 G(s) K = X(s) Y(s) . Find K as the root locus crosses the ω j axis. Note: All the poles of G ( s ) have real and imaginary parts that are integers (no complicated fractions or decimals!). 3(20). Text. 11.27 (a) & (c). -10 -8 -6 -4 - 2 0 2 -8 -6

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Unformatted text preview: -4-2 2 4 6 8 Root Locus Real Axis Assignment #23 (Revised) – p.2 ECSE-2410 Signals & Systems - Spring 2009 Due Fri 04/24/09 4(30). Using Nyquist and Bode plots and Bode approximations, find gain constant K at which the feedback systems shown are just on the verge of instability. Sketch the Nyquist and Bode (straight line magnitude and smooth phase) diagrams. (a) ( ) 3 1 1 ) ( + = s s G (b) ( ) 2 1 1 ) ( + = s s s G-+ ) ( s G X ( s ) (c) ( ) 1 ) ( 5 + = − s s e s G s Revised Problem 5: 5(30). Using the feedback block diagram in problem 4 above where ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = 100 1 10 1 1 1 400 ) ( s s s s G , (a) Sketch both the Bode straight line magnitude and the smooth phase diagrams. (b) Use Bode approximations to show that this system is unstable. (c) Sketch the Nyquist plot. Y ( s ) K...
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A#23_Revised - -4-2 2 4 6 8 Root Locus Real Axis...

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