Mathematical Modeling and Optimization of Aircraft Autopilot Systems using Linear Programming
Laxman S. Sawant, Sadhana R. Salunkhe
Abstract
This paper explores the mathematical modeling and optimization of aircraft autopilot systems focusing on enhancing control performance, stability, and efficiency. The study integrates advanced optimization methods such as PID optimization, Linear Quadratic Regulator (LQR), Genetic Algorithms, and Linear Programming (LPP), to optimize fuel consumption and minimize control deviations under varying flight conditions. The mathematical models are used to simulate autopilot system responses, incorporating constraints such as control limits, speed, and altitude. Further, sensitivity analysis and the dual problem are employed to evaluate system robustness under different conditions. The findings are intended to contribute to the design of more efficient and reliable autopilot systems for modern aircraft.
References
1. A. Forrester and A. Keane; Recent Advances in Surrogate-Based Optimization. Progress in Aerospace Sciences, 45(1), 50-79 (2009).
2. A. Kumar and H. Singh; Sensitivity Analysis in Linear Programming: An Application to Flight Control Optimization. International Journal of Optimization and Control, 10(2), 87-98 (2020).
3. D. Sun and Y. Wu; Mathematical Modeling and Control of Aircraft Dynamics. Journal of Aerospace Engineering, 32(5), 1-14 (2019).
4. J.D. Anderson; Introduction to Flight. McGraw-Hill (2011).
5. K. Deb; Optimization for Engineering Design: Algorithms and Examples. Prentice Hall (2000).
6. K. Glover and D. Lewis; Design of Optimal Control Systems. Springer (2014).
7. N.S. Nise; Control Systems Engineering. Wiley (2015).
8. P. Varaiya and J. Lee; Autopilot System Design using Linear Quadratic Control. IEEE Transactions on
Aerospace and Electronic Systems, 35(2), 50-58 (1999).
9. S. Boyd and L. Vandenberghe; Convex Optimization. Cambridge University Press (2004).
10. S.K. Mohapatra and B.K. Patel; Robust PID Optimization for Aircraft Autopilot Systems using Genetic
Algorithms. International Journal of Control Systems and Robotics, 14(3), 45-57 (2022).
11.X. Wang and Z. Luo; Numerical Simulation of Aircraft Autopilot Systems: A State-Space Perspective.
Computational Mechanics in Aerospace Engineering, 28(4), 567-580 (2018).
12.Y. Shao; J. Wang and Y. Li; Optimization of Aircraft Trajectory using Linear Programming. Aerospace
Science and Technology, 45, 125-133 (2015).
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