Multi-Pivot Free-Jet Flexible Nozzle Dual-Loop Cooperative Active Disturbance Rejection Control

Free-jet altitude simulation requires coordinated regulation of the intake thermodynamic states and flexible-nozzle geometry under time-varying Mach number commands and possible actuator faults. This study proposes a cooperative dual-loop active disturbance rejection control (ADRC) framework for a multi-pivot semi-flexible nozzle and a dual-valve intake system. In the inner loop, a constrained cooperative allocation method determines the pivot forces required to match the reference nozzle profile, while a dual-valve allocation mechanism redistributes the control demand when a valve loses effectiveness. ADRC is employed for hydraulic-actuator position tracking, and an SMC-LADRC controller regulates the intake pressure and temperature. An outer Mach number feedback loop compensates for the residual error of the integrated system. The convergence of the projected-gradient allocation algorithm and the ultimate boundedness of the observer and tracking errors are established under bounded disturbance variations. Simulation results under Mach number transitions, external disturbances, and progressive valve failure show that the proposed method effectively maintains stable intake pressure and temperature, improves nozzle-profile tracking accuracy, suppresses Mach number fluctuations, and enhances the fault tolerance and overall control performance of the integrated free-jet system.