1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135

27

IMAGE Imgs/thesis.final.w628.gif

Figure 3.3 - Discrete System

x
iinitial state of the ith cycle/final state of the (i-1)th cycle

x
i+1final state of the uncontrolled ith cycle

x
i*
+1final state of the controlled ith cycle/initial state of the (i+1)th

cycle
U
nombasic cyclic control

DUi*computed control perturbation for ith cycle


We will furthermore choose to express the corrective control forces, DUi*, as the linear sum of

several "basis" corrective actions:

UnomN
+[!]kijDUj
j=1

Unom+Ki* DU

Ui


=


=

(3.4)

where [!]Ujare fixed control perturbations which are defined over a cycle and kijare linear scaling

factors applied to [!]Uj. Kiis the vector of perturbation scaling factors and [!]U is a vector whose

elements are the fixed control perturbations, [!]Uj, which remain the same from one cycle to the

next. Nis the dimensionality of our control system and is equal to the number of state variables

which we wish to observe (and control).


Rather than using the complete system state, we choose to work with a small number of regulation

variables(RVs).

Regulation variables are a projection of the system state and are the observed

[CONVERTED BY MYRMIDON]