Damped Iterative Explicit Guidance for Multistage Rockets with Thrust Drop Faults

A damped iterative explicit guidance (DIEG) algorithm is proposed to address the problem of the insufficient convergence of classical explicit guidance methods in the event of thrust drop faults in multistage rockets. Based on the iterative guidance mode (IGM) and powered explicit guidance (PEG), this method is enhanced in three aspects: (1) an accurate transversality condition is derived and applied in the dimension-reduction framework instead of using a simplified assumption; (2) the Gauss-Legendre quadrature formula (GLQF) is adopted to increase the accuracy of the method by addressing the issue of excessive errors in calculating thrust integration using linearization methods based on a small quantity assumption under fault conditions; and (3) a damping factor for solving the time-to-go is introduced to avoid the chattering phenomenon and enhance convergence. A numerical simulation was conducted in single- and multistage mission scenarios by gradually reducing the engine thrust to compare the performance of DIEG and PEG. The results show that DIEG has a much larger convergence range than PEG and has fuel optimality similar to that of the optimization method in most fault scenarios. Finally, the robustness of DIEG under various deviations is verified through Monte Carlo simulation.