StateVector - STATE VECTOR MODEL An example of finding the...

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Tom Penick tomzap@eden.com www.teicontrols.com/notes 2/25/00 STATE VECTOR MODEL An example of finding the state vector model of a system given the transfer function in the s-domain. The Problem: Given the transfer function: ( 29 2 100 31 Gs ss = ++ find A , b , and D of the state vector model. State Vector Model: ( 29 ( 29 ( 29 X t A X t b ut =+ & X ( t ) = state vector, consisting of the output signal and its derivatives ( 29 Xt & = first derivative of the state vector A = a square matrix b = a vector u ( t ) = system input signal 1) Write the transfer function as a function of output divided by the input: ( 29 ( 29 ( 29 2 100 Cs U sss == 2) Cross multiply: ( 29 ( 29 ( 29 ( 29 2 3 100 sC s sC s C s Us + += 3) Convert to the time domain (inverse Laplace transform): ( 29 ( 29 ( 29 ( 29 3 100 c t c t c t + += & &&
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Tom Penick tomzap@eden.com www.teicontrols.com/notes 2/25/00 4) Pick a solution: Let ( 29 ( 29 1 x t ct = , ( 29 ( 29 2 x t = & The solution is not unique, but we just always use this one. Note that x 1 ( t ) and x 2 ( t ) are elements of the state vector X ( t ) and that there are two elements in this case because of the 2 nd
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This note was uploaded on 04/03/2012 for the course EE 366 taught by Professor Pore during the Spring '08 term at University of Texas at Austin.

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StateVector - STATE VECTOR MODEL An example of finding the...

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