Design of prescribed time control method for pressure of solid ducted rockets

This paper addresses the pressure control problem in Solid Ducted Rockets (SDRs), characterized by significant time-varying dynamics, non-minimum phase behavior, and model uncertainties. A prescribed time (PT) theorem is developed, leading to the design of a single-parameter controller that guarantees pressure tracking error convergence within a user-defined time, independent of initial conditions. Numerical simulations employ a 4 s period, 50 % duty cycle square-wave pressure command across four operating conditions, spanning low and high pressure regimes. Results demonstrate zero pressure overshoot under the proposed PT controller across all conditions. The proposed PT controller achieves pressure error convergence within 0.05–0.09 s, approximately 55.6–73.7 % faster than a tuned PID controller and 25–44.4 % faster than the prior PT controller. Compared to the prior PT controller, the maximum negative mass flow overshoot is reduced by up to 51.5 %; relative to the PID controller, the reduction reaches up to 86.6 %, and up to 86.6 % compared to the MPC controller. A rigorous Lyapunov-based analysis proves global convergence within the prescribed time and robustness under bounded disturbances. The controller’s robustness is further substantiated through Monte Carlo simulations, demonstrating resilience against external disturbances, and parameter mismatch simulations, verifying reliable performance despite model uncertainties. Featuring a single, physically interpretable design parameter, the controller facilitates intuitive tuning and continuous regulation, delivering rapid, robust, and precise pressure control for complex, time-sensitive systems.