Solving the problem of minimax closed-loop control of liquid-propellant launch vehicle fuel consumption control

Abstract

The paper provides mathematical formalization and a method of solving the problem of minimax (guaranteed) closed-loop terminal control of fuel consumption of a liquid-propellant launch vehicle power plant. The initial discrete-continuous nonlinear model of the controlled object is linearized along the given reference phase path and is approximated by a linear discrete-time multistep dynamical system. The approximated system includes the state vector, the control vector and the disturbance vector that defines the error of formation of the approximated model. Taking into account the geometrical constrains of control and disturbance vectors in the approximated system, we formulate the main problem of minimax closed-loop terminal control of propellant consumption of the launch vehicles propulsion system. This problem consists in solving a number of auxiliary tasks of minimax open-loop terminal control. To solve each of these tasks we use an instrument of development and analysis of generalized attainability domains of the approximated linear discrete dynamical system. These techniques are implemented by modifying the general recurrent algebraic method. To solve the problems under consideration we propose an approach and an appropriate numerical algorithm that is reduced to the implementation of a finite sequence of only one-step algebraic and optimization operations. The efficiency of the proposed approach to solving the problem under consideration is demonstrated and verified by a computer simulation example. This simulation example consists in controlling the process of propellant consumption for Soyuz-2.1b launch vehicles third stage propulsion system.