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HW8-Solution(2)

# HW8-Solution(2) - Flight Control Systems Homework#8...

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Flight Control Systems Homework #8 Solutions Dr. Bishop - Fall 2007 Reading Assignment: Modern Control Systems: Chapter 8 1-2. Exercises: E8.12, E8.14 3. Problems: P8.27 4. Design Problems: DP8.2 5 . Computer Problems: CP8.3 E8.12 (a) The transfer function is G ( s ) = C ( sI - A ) - 1 B + D = - 5 ( s - 1 ) s 2 + 3s + 2 . (b) The Bode plot is shown in Figure 1. -20 -10 0 10 Magnitude (dB) 10 -2 10 -1 10 0 10 1 10 2 90 180 270 Phase (deg) Bode Diagram Frequency (rad/sec) Figure 1: Bode Diagram for G ( s ) = - 5( s - 1) s 2 +3 s +2 . E8.14 The loop transfer function is L ( s ) = 20 ( s 2 + 1 . 4 s + 1)( s + 10) . The Bode plot of L ( s ) is shown in Figure 2. The frequency when 20log 10 | L ( ω ) | = 0 is ω = 1 . 32 rad/sec.

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-150 -100 -50 0 50 Magnitude (dB) 10 -2 10 -1 10 0 10 1 10 2 10 3 -270 -225 -180 -135 -90 -45 0 Phase (deg) Bode Diagram Frequency (rad/sec) Figure 2: Bode Diagram for L ( s ) = 20 ( s 2 +1 . 4 s +1)( s +10) . P8.27 The frequency response is shown in Figure 3. -60 -50 -40 -30 -20 -10 0 10 Magnitude (dB) 10 -1 10 0 10 1 10 2 10 3 -135 -90 -45 0 Phase (deg) Bode Diagram Frequency (rad/sec) K increases K decreases Phase plot remains unchanged as K varies Figure 3: Bode plot for K = 1
K 0.75 1 10 | L ( ) | =0 , dB 3.52 12.04 26.02 ω b , rad / s 8.3 14.0 33.4 ω c ,

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HW8-Solution(2) - Flight Control Systems Homework#8...

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