This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: d dt ± X 1 X 2 ² = ± 1 1 0 1 ²± X 1 X 2 ² + ± 1 1 ² U Y = ³ 0 1 ´ ± X 1 X 2 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...
View
Full Document
 Spring '10
 Dr.SrinivasPalanki
 142857, Srinivas Palanki

Click to edit the document details