Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

Chapter 7 / Missile Trajectory Optimisation
_ _
direction using a Fibonacci search to determine step length (α) resulting in a
control update,
Ξ
k
U : = U − α ⋅ Ξ
k+
1
⎛
⎜
⎜
7-19
k
∂ H
k
Equation 7.10-2
T
⎛ H ⎞ ∂ U ⎜
k U ⎟
k
: ⎜ ⎝
∂
⎜ ∂
= ⎟ −
⎠ ⎟ ⋅ Ξ
⎜
T k − 1
∂ U ⎟ ⎜
⎟
k
⎝
⎠
⎜
⎜
⎝
∂ H
∂ U
k − 1
⎛
⋅ ⎜
∂ H
⎛
⎜ ∂ H
⋅
⎜
⎝
∂ U
⎞
⎟
k − 1
T
⎞
⎟
⎠
⎞
⎟
⎟
⎟
⎟
⎠
Equation 7.10-3
OP_LIMITS limits the control change allowed between iterations improving
the stability of the optimisation process. Gradient scaling is crucial for good
performance since for this application the parameters involved used have a
large dynamic range. To accelerate line searches experience indicates that
the number of cost evaluations in any direction should be ≤ 5, Moody [M.12] .
Post launch no stopping conditions are required since the controls are used
by the autopilot. If the optimisation is terminated without completion the
previous controls and gradients are re-instating.
7.11 Trajectory Optimisation Simulator
The optimisation simulator shown in Figure 7-3 is embedded in the missile
simulator. The modules performing the optimisation functions in this figure
are highlighted in bold and placed in parentheses. The numbers identifying
certain blocks represent the order in which the functions are performed.
Setting GU_DM_TP to zero activates the missile trajectory optimisation
bypassing the conventional guidance laws. The optimiser defaults and
initialisation are performed by D_OPTIMER and I_OPTIMISER, even if the
facility is not subsequently activated. The TPBVP can be formulated using
either reference or missile state observer data. Counting numerical
operations to establish the processor load is inaccurate and fails to account
for overheads associated with data communication, storage and algorithm
control etc. Instead, the simulation increments a process timer latched to the
hosts Central Processing Unit clock. Scaling the process timer controls the
amount of processing power available to the optimiser. As the scale factor
increases more processing time is allowed until eventually a near-optimal
result is obtained that is very-nearly equivalent to static re-optimisation.