Abstract
Periodic cruise has the potential to improve the fuel-saving efficiency of hypersonic cruise vehicles but is difficult to optimize. In this paper, hypersonic periodic cruise trajectory is analyzed theoretically and optimized by an improved Particle Swarm Optimization algorithm. Firstly, through theoretical analysis, it is determined that the optimal throttle curve can be parameterized as a switching function. Considering the optimization direction of algorithm, a new penalty function for the constraints of periodic cruise is proposed. Then, PSO algorithm is improved and applied in periodic cruise trajectory optimization. Numerical results demonstrate that optimized periodic cruise trajectory costs less fuel compared with steady-state cruise trajectory, and without computing gradient information, the proposed method is also robust. Finally, the fuel-saving mechanism of periodic cruise is explored by comparing with steady-state cruise, which reveals that periodic cruise trajectory has higher impulse and lift-drag ratio, but lower mechanical energy loss rate.
Highlights
Hypersonic vehicle has a series of advantages and is attractive to researchers all over the world [1,2,3]
To confirm the effect of the proposed method and explore the performance of periodic cruise, take the initial altitude of 45 km and the initial Mach number of 14 as an example, numerical simulation is carried out based on the improve Particle Swarm Optimization (PSO) algorithm
It can be seen that the classic PSO, genetic algorithm (GA), and differential evolution algorithm (DE) all converge after approximately 80 iterations, while the improved PSO algorithm needs less than 40 iterations
Summary
Hypersonic vehicle has a series of advantages and is attractive to researchers all over the world [1,2,3]. A few theoretic analysis methods for trajectory design have been proposed [19, 20], but simplification and approximation methods were widely adopted in these analysis; otherwise, it was difficult to carry out because of the complexity of hypersonic flight. Kang et al [31] studied the optimal periodic cruise trajectory by combining genetic algorithm and direct shooting method; a method of two-level optimization was developed to deal with the parameters of initial state in the outer loop and the control variables in the inner loop, respectively. There are few researches about the direct application of evolutionary method in the optimization of periodic cruise trajectory without combined with gradient-based algorithm or pseudo-spectral method. This paper tries to directly apply evolutionary optimization method in periodic cruise trajectory design, which can optimize the trajectory robustly without initial guess or derivative information computed. The difference of trajectory between steady-state cruise and periodic cruise is discussed, and the fuel-saving mechanism of periodic cruise is explored by contrast with steady-state cruise
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