HW8 - -10-8-6-4-2 2-5-4-3-2-1 1 2 3 4 5 Root Locus Real...

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0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Problem 2 Step Response Time (sec) Amplitude (a) (b) (c)
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%Problem 3 >> G = tf([1 2],[1 1 0])*tf(1,[1 3])*tf(1,[1 7]) Transfer function: s + 2 ---------------------------- s^4 + 11 s^3 + 31 s^2 + 21 s >> rlocus(G) >> print -dpdf C:\HW8_fig1 >> print -dpdf C:\HW8_fig2 >> print -dpdf C:\HW8_fig3 >> print -dpdf C:\HW8_fig4 % From Figure 4, the expected overshoot is 8.92%. >> T = feedback(7.48*G,1) Transfer function: 7.48 s + 14.96 --------------------------------------- s^4 + 11 s^3 + 31 s^2 + 28.48 s + 14.96 >> step(T), grid >> print -dpdf C:\HW8_fig5 >> stepinfo(T) ans = RiseTime: 2.0726 SettlingTime: 6.8281 SettlingMin: 0.9232 SettlingMax: 1.0942 Overshoot: 9.4209 Undershoot: 0 Peak: 1.0942 PeakTime: 4.5580 % The actual overshoot is 9.4% (very close to the expected one).
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Unformatted text preview: -10-8-6-4-2 2-5-4-3-2-1 1 2 3 4 5 Root Locus Real Axis Imaginary Axis Root Locus Real Axis Imaginary Axis-10-8-6-4-2 2-5-4-3-2-1 1 2 3 4 5 System: G Gain: 112 Pole: 0.00546 + 3.47i Damping: -0.00157 Overshoot (%): 100 Frequency (rad/sec): 3.47 Root Locus Real Axis Imaginary Axis-10-8-6-4-2 2-5-4-3-2-1 1 2 3 4 5 System: G Gain: 2.71 Pole: -0.531 Damping: 1 Overshoot (%): 0 Frequency (rad/sec): 0.531 Root Locus Real Axis Imaginary Axis-10-8-6-4-2 2-5-4-3-2-1 1 2 3 4 5 System: G Gain: 7.48 Pole: -0.532 + 0.692i Damping: 0.61 Overshoot (%): 8.92 Frequency (rad/sec): 0.872 1 2 3 4 5 6 7 8 9 10 0.2 0.4 0.6 0.8 1 1.2 1.4 Step Response Time (sec) Amplitude...
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HW8 - -10-8-6-4-2 2-5-4-3-2-1 1 2 3 4 5 Root Locus Real...

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