Microsoft Word - week9_elec691F

Consider a LTI plant described by: ν ω ν ω ω ν , , 1), () () () (, , 1), () () () () () () () (m m m m 1 K K & = + + = = + + = + + = ∑ = i t F t u D t x C t y i t F t u D t x C t y t E t u B t Ax t x where n R t x ∈) (is the state vector, i m i R t u ∈) (and i r i R t y ∈) (are the input and output to be regulated, respectively, of the th i local control station (ν , , 1 K = i); m) (m i r i R t y ∈ (ν , , 1 K = i) is an output which is available for measurement at the th i control station, and Ω ∈ R t) (ω is the disturbance. The matrices n n R A ν , , 1 K = i) are constant matrices. Let the reference input for the th i local control station be denoted by i r i R t y ∈) (ref (ν , , 1 K = i). Then the error in the th i local control station which is the difference between the output) (t y i and the specified reference input) (ref t y i (ν , , 1 K = i) is given by: ν , , 1), () () (ref K = − = i t y t y t e i i i. ⎣ ⎡ = ν ν ν ν F F F t e t e t e t u t u t u t y t y t y M M M M 1 1 1 ref ref 1 ref : ,) () (:) (,) () (:) (,) () (:) (.-The disturbance vector) (t ω is assumed to satisfy the following equation: