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Unformatted text preview: Flight Control Systems Homework #3 Solutions Dr. Bishop  Fall 2007 Reading Assignment: Modern Control Systems: Chapter 3 12. Exercises: E3.5, E3.20 34. Problems: P3.15, P3.29 5. Advanced Problems: AP3.7 6. Computer Problems: CP3.5 E3.5 From the block diagram we determine that the state equations are ˙ x 2 = ( fk + d ) x 2 + ax 1 + fu ˙ x 1 = kx 2 + u and the output equation is y = bx 2 . Therefore, ˙ x = Ax + Bu y = Cx + Du , where A = bracketleftbigg k a ( fk + d ) bracketrightbigg , B = bracketleftbigg 1 f bracketrightbigg , C = bracketleftbig b bracketrightbig and D = [ ] . E3.20 The linearized equation can be derived from the observation that sin θ ≈ θ when θ ≈ 0. In this case, the linearized equations are ¨ θ + g L θ + k m ˙ θ = 0 . Let x 1 = θ and x 2 = ˙ θ . Then in state variable form we have ˙ x = Ax y = Cx where A = bracketleftbigg 1 g/L k/m bracketrightbigg , C = bracketleftbig 1 bracketrightbig , and x ( ) = bracketleftbigg θ (0) ˙ θ (0) bracketrightbigg...
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This note was uploaded on 09/01/2010 for the course ASE 270L taught by Professor Dr.bishop during the Spring '10 term at University of Texas at Austin.
 Spring '10
 Dr.Bishop

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