topic8 - Topic #8 16.31 Feedback Control Systems...

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Topic #8 16.31 Feedback Control Systems State-Space Systems What are the basic properties of a state-space model, and how do we analyze these? SS to TF Cite as: Jonathan How, course materials for 16.31 Feedback Control Systems, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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Fall 2007 16.31 8–1 SS to TF In going from the state space model ˙ x ( t ) = A x ( t ) + Bu ( t ) y ( t ) = C x ( t ) + Du ( t ) to the transfer function G ( s ) = C ( sI A ) 1 B + D need to form inverse of matrix ( sI A ) A symbolic inverse – not very easy. For simple cases, we can use the following: a 1 a 2 a 3 a 4 ± 1 = 1 a 1 a 4 a 2 a 3 a 4 a 2 a 3 a 1 ± For larger problems, we can also use Cramer’s Rule Turns out that an equivalent method is to form: 1 G ( s ) = C ( sI A ) 1 B + D = det sI A B C D ± det( sI A ) Reason for this will become more apparent later when we talk
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topic8 - Topic #8 16.31 Feedback Control Systems...

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