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For the first, two independent 1D models are constructed then combined in the final simulation.

For the second, two variations are considered.

In the first, a 1D model is constructed in the

forward control dimension and inverted to obtain the required K^*
fwd^.

A second 1D model is then

constructed in the lateral control dimension making use of the known value of K^*
fwd^.

We refer to

this as forward-then-lateral (F-L) sampling.

Lateral-then-forward (L-F) sampling is similar but

performs 1D control in the lateral dimension first, then uses this result to construct a 1D model in

the forward dimension. We might expect that one or both of these approaches perform better than

superposition sampling since they both incorporate additional knowledge of the perturbations to

be applied. Somewhat surprisingly, this turns out not to be the case as we shall see in Chapter 4.

All three approaches give comparable results, with superposition slightly outperforming the other

two. The three sampling strategies investigated are illustrated in Figure 3.23.

(a)

interpolated points

(c)

sample points

final points

Figure 3.23 - 2D sampling strategies
(a) superposition (SP)
(b) forward then lateral (F-L)
(c) lateral then forward (L-F)

The final parameters to consider in constructing a good linear model of the discrete system are the

perturbation scaling factors used to sample h(K) (e.g. k¹and k²in Figure 3.22). Since the