HW4-Solution(2) - Flight Control Systems Homework #4...

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Unformatted text preview: Flight Control Systems Homework #4 Solutions Dr. Bishop - Fall 2007 Reading Assignment: Modern Control Systems: Chapter 4 1-2. Exercises: E4.6, E4.10 3. Problems: P4.7 4. Advanced Problems: AP4.7 5. Design Problems: DP4.3 6. Computer Problems: CP4.10 E4.6 The closed-loop transfer function is T ( s ) = 5( s + 2) s 2 + 15 s + 10 . The step response is shown in Figure 1. Time (sec. ) Amplitude Step Response 1 2 3 4 5 6 7 8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 y(t)/A Figure 1: Step response. E4.10 (a) The closed-loop transfer function is T ( s ) = G c ( s ) G ( s ) 1 + G c ( s ) G ( s ) H ( s ) = 100 K 1 ( s + 5) s 2 + 105 s + (500 + 100 K 1 K 2 ) . 1 The steady-state tracking error is E ( s ) = R ( s )- Y ( s ) = bracketleftbigg 1- G c ( s ) G ( s )(1- H ( s )) 1 + G c ( s ) G ( s ) H ( s ) bracketrightbigg R ( s ) = s 2 + (105- 100 K 1 ) s + 500- 100 K 1 (5- K 2 ) s 2 + 105 s + 500 + 100 K 1 K 2 1 s and lim s sE ( s ) = 5- K 1 (5- K 2 ) 5 + K 1 K 2 ....
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HW4-Solution(2) - Flight Control Systems Homework #4...

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