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Unformatted text preview: d dt X 1 X 2 = 1 1 0 1 X 1 X 2 + 1 1 U Y = 0 1 X 1 X 2 + 0 . U (7) Srinivas Palanki (USA) Process Outputs 5 / 7 Process Outputs Dynamics of a Linear System with Process Outputs A linear dynamical system in deviation form is represented as dX dt = AX + BU Y = CX + DU X (0) = X (8) where X = xx s U = uu s Y = yy s (9) Srinivas Palanki (USA) Process Outputs 6 / 7 Process Outputs We saw in the previously that the dynamics of the states, X ( t ), is given by X ( t ) = e At . X (0) + e At . Z t eAt BU ( t ) dt (10) The dynamics of the outputs is given by Y ( t ) = C . e At . X (0) + C . e At . Z t eAt BU ( t ) dt + D . U (11) Unforced Dynamics: Y ( t ) = C . e At . X (0) (12) Forced Dynamics: Y ( t ) = C . e At . Z t eAt BU ( t ) dt + D . U (13) Srinivas Palanki (USA) Process Outputs 7 / 7...
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This note was uploaded on 01/07/2011 for the course CHE 452 taught by Professor Dr.srinivaspalanki during the Spring '10 term at S. Alabama.
 Spring '10
 Dr.SrinivasPalanki

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