43

Foreach

particular RV at the end of a single step for a range of applied perturbation scalings.

curve, a different initial state is used. The initial state for step nwas generated by first simulating

n-1 steps with the open-loop base PCG. By the fourth step, the figure is falling noticeably.

(a)

(b)

The graphs illustrate that hip pitch varies nearly linearly with Q_fwdfor all three choices of RV.

Similarly, hip roll is nearly linear with respect to Q_lat. These relationships provide evidence which

supports our assumption that the discrete system can be modelled using a linear model. Despite the

fact that the perturbations themselves are mutually independent, their effect on the RVs is not

cleanly decoupled. Thus, they do not provide truly independent control over each RV dimension

as desired.

In general, however, the magnitudes of the undesired variations are not excessively

large relative to the accessible range of RV values in the desired control dimensions.

Completely

independent control of the RVs would imply a diagonal discrete system Jacobian.

The relatively

small effects of each perturbation on other's control dimension mean that the off-diagonal elements

of the discrete system Jacobian will be small compared to the diagonal elements.