HW10-Solution(2) - Flight Control Systems Homework#10...

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Flight Control Systems Homework #10 Solutions Dr. Bishop - Fall 2007 Reading Assignment: Chapter 11, Sections 11.1-11.6, 11.9-11.12 1. Exercises: E11.9 2. Problems: P11.26 3. Advanced Problems: AP11.14 4. Design Problems: DP11.7 5 . Computer Problems: CP11.11 E11.9 The controllability matrix is P c = bracketleftbig B AB bracketrightbig = bracketleftbigg k 1 k 1 k 2 k 2 k 1 + k 2 bracketrightbigg , and det P c = k 2 1 + k 2 2 . So, the condition for complete controllability is k 2 1 negationslash = k 2 2 . P11.26 The observability matrix is P o = C CA CA 2 = 2 4 0 0 2 4 4 8 14 . The det P o = 184 negationslash = 0, hence the system is observable. The gain matrix L = 5 . 45 0 . 48 1 . 24 results in the observer poles at s 1 , 2 = 1 ± 2 j and s 3 = 10, as desired. AP11.14 The controllability matrix is P c = 0 0 4 0 4 24 4 24 124 and the observability matrix is P o = 2 9 2 8 8 21 84 97 118 . Computing the determinants yields det P c = 64 negationslash = 0 and det P 0 = 9358 negationslash = 0 , hence the system is controllable and observable. The controller gain matrix
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  • Spring '10
  • Dr.Bishop
  • controllability matrix, Flight Control Systems, gain matrix, observer gain matrix, controller gain matrix

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