Robust spline-line energy management guidance algorithm with multiple constraints and uncertainties for solid rocket ascending

For the solid rocket with depletion shutdown system,effective energy management is significant to meet terminal constraints by exhausting excess energy.Several traditional energy management algorithms cannot satisfy the altitude constraint and path constraints are not sufficiently considered.The velocity adjustment capability of these algorithms is limited and the uncertainties are not considered.Based on the on-line programming of velocity capability curve,Spline-Line Energy Management(SLEM)guidance algorithm is proposed.It introduces lateral maneuvers to further consume the available velocity on the basis of longitudinal energy management.After expressing the constraints as several algebraic equations,the closed-loop guidance problem is converted to solving a system of nonlinear equations about the curve parameters in real time.The advantage is that the altitude constraint can be satisfied theoretically.The overload and control variable change rate and amplitude constraints are also considered during the flight by constructing the feasible boundary of velocity capability curve.To improve the robustness,it is further extended by estimating the actual uncertainties.The effectiveness and advantages of SLEM are demonstrated by simulations and comparisons with other energy management algorithms.Simulation results show that the proposed approach can satisfy multiple constraints with high precision under the condition of uncertainties.