# hw6 - 16.31 Handout#6 Prof J P How T.A TBD Due Nov 4 2007...

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Unformatted text preview: 16.31 Handout #6 Prof. J. P. How October 26, 2007 T.A. TBD Due: Nov 4, 2007 16.31 Homework Assignment #6 1. Consider the simple system G ( s ) = s − z o ( s + 3)( s + 4) (a) Confirm that one possible state-space model is given by: ⎡ ⎤ ⎡ ⎤ − 7 1 1 A = ⎣ ⎦ , B = ⎣ ⎦ , C = 1 , D = 0 − 12 − z o (b) Evaluate the controllability of this system as a function of the value of z o . (c) Use pole placement techniques to derive the full-state feedback gains ⎡ ⎤ x 1 u = − k 1 k 2 ⎣ ⎦ x 2 necessary to place the closed-loop poles at the roots of: s 2 + 2 ζω n s + ω n 2 = 0 (d) Use your analytic expressions for k 1 and k 2 to support the following two claims: • “The system has to work harder and harder to achieve control as the control- lability is reduced.” • “To move the poles a long way takes large gains.” 2. Given the MIMO system, ⎡ ⎤ 6 s + 5 7 ⎢ ⎥ ⎢ s 2 + 3 s + 2 s + 2 ⎥ G ( s ) = ⎢ ⎥ ⎣ 5 6 s + 17 ⎦ s + 2 s 2 + 5 s + 6 Develop a...
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• Fall '07
• jonathanhow
• Feedback Control Systems, Massachusetts Institute of Technology, state space model, dynamic output feedback

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hw6 - 16.31 Handout#6 Prof J P How T.A TBD Due Nov 4 2007...

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