OPTIMUM DESIGN AND LINEAR GUIDANCE LAW FORMULATION OF ENTRY VEHICLES FOR GUIDANCE PARAMETERS AND TEMPERATURE ACCUMULATION ALONG OPTIMUM ENTRY TRAJECTORIES

摘要

The objective of this report is to construct a method to simultan-eously derive an optimal approximate closed form passive controller (no energy expenditure) and to optimally design a vehicle capable of earth entry. The approximate feature of the controller is desirable to facilitate relatively simple calculations in an on-board computer so that steering commands are computable in the short intervals between control points. The simultaneous design of the vehicle controller and the configuration is handled by defining a lumped parameter control which contains all param¬eters of possible passive control and the constants describing the vehicle configuration. The optimal lumped parameter control is found by the "neighboring optimal" method from the set of controls which satisfy the entry nonlinear differential equations, the set of initial and final state conditions (two point boundary value problem) and a practical bounded control restraint. A technique is described to further partition this dis¬crete point set (in time) of lumped optimal controls into the configuration constants and an optimal approximate closed form polynomial controller using Tchebycheff approximation theory. The criterion for optimization contains, in addition to the integrated deceleration and the temperature accumulation terms, a new class of functions which are formed from the sensitivity or influence coefficients at each point of control along a nomi¬nal entry trajectory. The nominal trajectory thus selected is least sus¬ceptible to disturbance, initial condition and guidance errors along the optimal entry path. Finally, a closed loop linear guidance law is derived, using this approximate controller, for a typical entry mission. A new independent monotonic variable is substituted (for the most often used variable, time) into this guidance law to reduce guidance errors due to the differences in time interval between the optimal nominal and the neigh¬boring optimal trajectories.