Pintle-based rapid throttling of variable-thrust solid rocket motors (VTSRMs) can induce thrust overshoot, jeopardizing structural integrity and mission safety. This paper proposes a novel dual-objective co-optimization framework for energy-release control, termed a pressure–thrust co-regulation strategy. The main contributions are as follows: (1) A nonlinear dynamic model that couples chamber-pressure transients and internal ballistics is developed, and the mechanism of thrust overshoot is theoretically revealed: it stems from a mismatch between rapid throat-area variation and the comparatively slower pressure response. (2) A tracking-differentiator (TD)-based adaptive controller is designed, in which the TD module smooths step commands to reduce the rate of throat-area change, and the adaptive control law self-tunes online to accelerate pressure response, thereby suppressing overshoot without sacrificing response speed. (3) A dream optimization algorithm-backpropagation surrogate model is constructed to characterize the nonlinear mapping between controller parameters (speed factor γ and feedback gain k1) and performance metrics (thrust overshoot and settling time), achieving relative prediction errors below 6% against high-fidelity simulations. (4) The non-dominated sorting whale optimization algorithm, a multi-objective optimization algorithm combined with entropy-weighted TOPSIS, is used to obtain the Pareto-optimal solution set and select a compromise solution (γ = 4.2749 × 107, k1 = 219), yielding a peak thrust overshoot of 239.56 N and a response time of 0.57 s. The proposed framework provides an implementable control pathway for high-precision and high-safety thrust modulation in VTSRMs.
Wang et al. (2026) studied this question.