≤ ≤ max
Goddard
AOE 5244
D V, h V h
T t T
Matlab’s constr.m IMSL’s DNCONF
apollo.aoe.vt.edu
Mid-Term Examination
Take-Home Portion
8 November 1996
The problem is to maximize the altitude that the rocket can achieve
This is a open-book examination but do not discuss it with anyone until it
has been submitted to me. Please turn in all your work and this question sheet.
The problem is due in-class on Monday, 11 November 1996.
1. (50) The problem deals with vertical ascent (one-dimensional
motion) of a rocket. The forces include thrust, weight and aerodynamic drag
modelled as a prescribed function ( ) ( is the velocity and is the al-
titude). The control is the thrust magnitude and is subject to the bounds
0 ( ) . The dynamics are similar to Prob 3. on HW. Set 5 (the
differences being that the thrust direction is always vertical, the thrust magni-
tude can be controlled and there is a drag force.) Set up the control problem
for numerical solution as a Nonlinear Programming Problem by assuming the
thrust-level is piecewise constant.
No numerical calculations are needed (nor are they possible since no data is
furnished). Provide the necessary analysis and a recipe for the numerical solu-
tion by some standard package ( , , the SQP
from Prof. Schittkowski on , or ??). You do not have to
write any specific code (FORTRAN or MATLAB), but should provide sufficient
details so that a knowlegeable programmer could provide the implementation.
If you do provide the code then be sure to include sufficient commentary - define
symbols and describe what you are doing.
1