The optimal closed-loop terminal propellant consumption control algorithm for liquid propulsion system of launch vehicle. Part I

In this paper we propose the algorithm of launch vehicle’s liquid propulsion system propellant consumption control problem solving, in which this problem is formulated as the optimal closed-loop terminal control problem for corresponding linear discrete-time dynamical system. To achieve this, initial nonlinear continuous model, which describes the plant dynamics, is linearized along given reference trajectory and then is discretized in accordance to control process requirements. As the result of this, we have formed approximating model represented as the vector-matrix system of recurrence equations. The constraints of state vector and control vector are also taken into account in this approximating system, and we assume that the constraints are convex, closed and limited polyhedra with finite number of vertices in corresponding vector spaces. The optimal open-loop and closed-loop terminal control problems are formulated for generated linear discrete-time dynamical system. For solving the problems the optimal closed-loop terminal control recurrence algorithm is developed, which consists in the solving of number of optimal open-loop terminal control problems for linear discrete-time dynamical system. Based on solution of finite sequence of optimal open-loop terminal control problem for linear approximate model we provide recurrence optimal closed-loop terminal control algorithm for initial nonlinear dynamical system. In the implementation of proposed optimal open-loop control algorithm we use the tool of reachable sets computation and analysis based on general algebraic recurrence approach for linear discrete-time dynamical systems and some modifications of this approach intended for reducing the computational complexity and consequently to increasing the operation speed. The performance of developed optimal closed-loop terminal control algorithm is presented on numerical model example of launch vehicle’s first stage liquid propulsion system propellant consumption closed-loop control optimization.