451hw7

451hw7 - and negative imaginary fields. e. 0.563 Julian...

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Julian Weathersby AME 451 HW7 18) -7 -6 -5 -4 -3 -2 -1 0 -15 -10 -5 0 5 10 15 The value of alpha was found to be 7 and the value of the gain, K, was found to be about 9997.
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Julian Weathersby AME 451 HW7 24) a. Root Locus Real Axis I m a g i n a r y A x i s -8 -7 -6 -5 -4 -3 -2 -1 0 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 System: g Gain: 9.41 Pole: -0.863 + 1.69i Damping: 0.455 Overshoot (%): 20.1 Frequency (rad/sec): 1.9 System: g Gain: 9.38 Pole: -4.27 Damping: 1 Overshoot (%): 0 Frequency (rad/sec): 4.27 System: g Gain: 59.7 Pole: -0.00227 - 3.31i Damping: 0.000686 Overshoot (%): 99.8 Frequency (rad/sec): 3.31 b. K = 9.41 for a 20% overshoot c. ts = 4.12 s; tp = 2.13 s d. -4.27 e. for 0 < K < 60 the system will be stable
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Julian Weathersby AME 451 HW7 26) Root Locus Real Axis I m a g i n a r y A x i s -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 System: g Gain: 0.296 Pole: -0.957 + 0.675i Damping: 0.817 Overshoot (%): 1.16 Frequency (rad/sec): 1.17 a. K = 0.296 at minimum damping ratio 0.817 b. 1.16 % c. Ts = 2.41 s; Tp = 2.69 s d. A second-order approximation is beneficial when observing a system that shows repetitive values for gain, damping, and frequency for instances in the positive
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Unformatted text preview: and negative imaginary fields. e. 0.563 Julian Weathersby AME 451 HW7 30) a. Root Locus Real Axis I m a g i n a r y A x i s-12-10-8-6-4-2 2 4 6-8-6-4-2 2 4 6 8 System: g Gain: 81.8 Pole: -0.798 + 1.09i Damping: 0.591 Overshoot (%): 10 Frequency (rad/sec): 1.35 System: g Gain: 81.7 Pole: -6.32 Damping: 1 Overshoot (%): 0 Frequency (rad/sec): 6.32 System: g Gain: 81.8 Pole: -7.08 Damping: 1 Overshoot (%): 0 Frequency (rad/sec): 7.08 System: g Gain: 396 Pole: 0.00386 - 2.53i Damping: -0.00153 Overshoot (%): 100 Frequency (rad/sec): 2.53 b. K = 81.8 yields a 10% overshoot c. -6.32 and -7.08; The second order approximation gave a value for K that is present at 3 other instances in the system which mean that four every second order system you can achieve the desired gain at 4 different instances, all which keep the system stable. d. 0 &lt; K &lt; 396...
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451hw7 - and negative imaginary fields. e. 0.563 Julian...

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