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560hw5 - x x k k k K ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ...

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12.5 , = 9 8 7 1 2 0 3 1 2 z A = 2 1 2 z B [ ] = = 437 40 2 40 0 1 142 11 2 2 z z z z z Mz B A B A B C , 3 ) ( rank = z Co , so controllable. Char. poly (from Matlab command ‘poly(Az)’) 3 27 13 ) ( 2 3 0 1 2 2 3 + + + = + + + = s s s a s a s a s A z Therefore, , = = 13 27 3 1 0 0 0 1 0 1 0 0 0 1 0 2 1 0 a a a A x = 1 0 0 x B [ ] = = 142 13 1 13 1 0 1 0 0 2 x x x x x Mx B A B A B C CL char. poly 1 0 2 1 2 3 2 3 ) ( ) ( ) ( x x x k a s k a s k a s x + + + + + + = Desired CL char. poly 1 3 3 ) 1 ( 2 3 3 + + + = + = s s s s Therefore [ ] [ ] 10 24 2 3 2 1 = = x x x x k k
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Unformatted text preview: x x k k k K . ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − − − = = − 2 14 29 1 13 13 2 15 53 1 Mx Mz C C P [ ] 1679 . 2 1578 . 2 7532 . 1 1 − − − = = − P K K x z Therefore, control law is 3 2 1 1679 . 2 1578 . 2 7532 . 1 z z z u + + = Check: eig ( ) . 1 , 1 , 1 − − − = − z z z K B A...
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