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HW 7 solutions

# HW 7 solutions - EML 4312 HW 7 Solutions 1a The equation to...

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EML 4312 HW 7 Solutions 1a. The equation to find a transfer function from a state space representation: ( ) ( ) [ ] [ ] [ ] [ ] [ ] [ ] ( ) Or since the given A matrix is not in the controllable canonical form we must find a transformation matrix, P, to bring the given A, B, C matrices into that form. [ ] [ ] Where a 1 comes from the characteristic equation: s 2 + a 1 s + a 2 . The characteristic equation is: s 2 5s + 3. Then we can calculate the transformation matrix P. [ ] Now we can obtain the controllable canonical form of our system. [ ] [ ] [ ] So using the controllable canonical form we can get the transfer function, H(s) ( ) 1b. The given A matrix is in controllable canonical form so we don’t need to find a transformation matrix and we can find the transfer function from the state space representation without any calculations.

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( ) 1c. . The equation to find a transfer function from a state space representation: ( ) ( ) [ ] [ ] [ ] [ ] [ ] [ ] ( ) Or since the given A matrix is not in the controllable canonical form we must find a transformation matrix, P, to

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