Control optimization for a dual-mode single-stage nuclear shuttle

The performance of a single-stage surface-to-orbit shuttle-whether chemical-propellant or nuclear--can be considerably improved by 'mixed-mode" propulsion. A mixed-mode shuttle would be fitted with engines designed to use two different propellant combinations--a highthrust (mode 1) propellant, such as ammonia, and a high-specific-impulse (mode 2) propellant, such as hydrogen.

The first step in the evaluation of the mixed-mode nuclear shuttle is a preliminary trajectory optimization study. This study, using a simple mission and a simple shuttle model, would be the basis for more complex trajectory optimization studies. The problem considered in this thesis is that of minimizing the propellant expenditure of a mixed-mode nuclear shuttle for a given orbit. The starting point for any optimization problem is a mathematical model of the system, in state variable form.

Application of the methods of optimal control theory results in a two-point boundary-value problem and an associated algebraic problem. Three numerical methods are briefly described which could be used to solve these problems. However a more flexible method, that of finite differences, is proposed in this study to handle the more restricted problem. Replacement of the derivatives with finite-difference approximations results in a set of nonlinear algebraic equations. These equations are solved by the Newton-Raphson technique; central-difference approximations are used for the Jacobian matrix, and the linearized algebraic equations are solved by the Gauss elimination method. −A procedure is presented for obtaining good starting values for the

Newton-Raphson iteration. This is done by neglecting the effects of atmosphere; as a result, the optimality conditions are greatly simplified. As it turned out, this procedure proved sufficient for an evaluation of mixed-mode propulsion. Consequently, the finite difference method was not used to obtain numerical results, although the correctness of the program was verified.

The analysis of the problem is given in detail, along with numerical results for various combinations of the input variables, and the finite-difference computer program, properly documented.

In conclusion, suggestions for extensions of this work are presented and methods of approach are outlined.