hw6 - EML 4312 Fall 2009 State Space Homework 1. Consider...

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EML 4312 Fall 2009 State Space Homework 1. Consider the following block diagram K G p + Input Output Block diagram. where G p = s 2 +3 s 3 + s 2 +5 s +1 . Express the transfer function in terms of a state space realization. CHECK your Answer using methods from class. Sol: Using the Reachable cannonical form gives A = 010 001 1 5 1 B = 0 0 1 C = £ 301 ¤ check H = £ ¤ s 10 0 s 1 15 s 1 0 0 1 = s 2 s 3 + s 2 s 1
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2. Are the following state space systems controllable, observable, or both? a) A = 11 01 ¸ B = 1 0 ¸ C = £ ¤ Sol: C ( A, B )= £ BA B ¤ = 00 ¸ det ¸ =0 Not controllable O ( C, A £ CC A ¤ = ¸ det ¸ Not Observable b) A = a 0 0 b ¸ B = 0 1 ¸ C = £ ¤ C ( A, B £ B ¤ = 1 b ¸ det 1 b ¸ Not controllable. O ( C, A £ A ¤ = 0 b ¸ det 0 b ¸ Not Observable. c) A = a 1 0 b ¸ B = 0 1 ¸ C = £ ¤ C ( A, B £ B ¤ = 1 b ¸ det 1 b ¸ = 1 2
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Controllable.
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hw6 - EML 4312 Fall 2009 State Space Homework 1. Consider...

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