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In order to realize high-quality control for turboshaft engine with variable rotor speed, a cascade control method based on the acceleration estimator of gas turbine speed (Ngdot) through Complementary filtering – incremental nonlinear dynamic inversion (CF-INDI)with Newton's prediction is proposed. Firstly, an adaptive torsional suppression method based on the Recursive Least Square (RLS) algorithm and combined with the control index of power turbine speed is proposed and designed to solve the torsional instability of control system in turboshaft engine with variable rotor speed. Then, an online Ngdot estimated method based on CF-INDI with Newton's prediction is developed, and the complementary filtering method is applied to compensate for the inaccuracy of the state variable model available at a single working point, and Newton prediction is used to alleviate the problem of lagging acceleration estimate, which is accessible to realize the cascade control for turboshaft engine based on Ngdot. The simulation results show that the RLS adaptive torsional filter can effectively suppress the low-order torsional components with frequencies of 1.2 Hz and 2.0 Hz mixing in power turbine speed, and the torsional suppression effect is remarkable. In addition, under different flight conditions, CF-INDI with Newton prediction is faster and more accurate than INDI Ngdot estimate, and smoother than central difference method, which proves the feasibility of INDI Ngdot estimator. Meanwhile, after the application of CF-INDI with Newton prediction Ngdot estimator in cascade control, the anti-interference capacity of power turbine speed is stronger, and the dynamic control effect is superior, which has satisfactory robustness performance. [ABSTRACT FROM AUTHOR]

• A multidisciplinary simulation framework integrating the CCH and turboshaft engine is constructed. • A multi-objective optimization problem is designed to evaluate and quantify the flight performance and environmental impact of the CCH. • The NSGA-II multi-objective optimization method based on entropy weight evaluation is adopted. • The goal of low-emission for CCH is achieved through variable rotor speed and variable geometry adjustment. To address compatibility issues of the operational performance and environmental impact of Coaxial Compound Helicopters (CCH), a low-emission optimization control method for coaxial compound helicopter/engine based on variable geometry adjustment is proposed. Firstly, a multidisciplinary simulation framework for CCH and turboshaft engine is deployed by integrating the power characteristics of CCH, the performance of a variable geometry turbine engine, and the emission characteristics of nitrogen oxides (NO x). Subsequently, a multivariable and multi-objective optimization problem is formulated to assess and quantify the flight performance and environmental impact of CCH through a holistic optimization strategy. On this basis, a Non-dominated Sorting Genetic Algorithm II (NSGA-II) multi-objective optimization method based on entropy weight assessment is employed to obtain the optimal control plan for variable rotor speed and adjustable mechanisms within the operation envelope, by balancing the thermodynamic losses of the engine and the aerodynamic efficiency of the CCH. Finally, the optimization control method for CCH is validated based on flight missions. The simulation results demonstrate that the combination of variable rotor speed and variable geometry adjustment of engine effectively reduces the engine NO x emission index by more than 10.7 % within the full envelope, relative to the original rotor speed plan. In the actual flight mission profile, the total NO x emissions can be reduced by 11.78 %, improving the environmental impact of CCH. [ABSTRACT FROM AUTHOR]