HW5-Solution(2)

# HW5-Solution(2) - Flight Control Systems Homework#5...

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Flight Control Systems Homework #5 Solutions Dr. Bishop - Fall 2007 Reading Assignment: Modern Control Systems: Chapter 5, Sections 5.1-5.6, 5.9-5.12. 1. Exercises: E5.10 2. Problems: P5.21 3. Advanced Problems: AP5.6 4. Design Problems: DP5.4 5 . Computer Problems: CP5.11 E5.10 The system is a type 1 . The error constants are K p = and K v = 1 . 0 . Therefore, the steady-state error to a step input is 0; the steady-state error to a ramp input is 1 . 0 A 0 , where A 0 is the magnitude (slope) of the ramp input. P5.21 The closed-loop transfer function is T ( s ) = 2(2 s + τ ) ( s + 0 . 2 K )(2 s + τ ) + 4 . (a) If R ( s ) = 1 /s , we have the unit step response Y ( s ) = 2(2 s + τ ) ( s + 0 . 2 K )(2 s + τ ) + 4 1 s . From the ±nal value theorem we obtain y ss = lim s 0 sY ( s ) = 2 τ 0 . 2 + 4 . Selecting K = 10 - 20 leads to y ss = 1 and a zero steady-state error due to a unit step input. (b) The characteristic equation is

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HW5-Solution(2) - Flight Control Systems Homework#5...

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