SDRE and LQR Controls Comparison Applied in High-Performance Aircraft in a Longitudinal Flight

(1) Guilherme P. Dos Santos Mail (Federal University of Technology - Paraná (UTFPR), 84016-210, Ponta Grossa, PR, Brazil, Brazil)
(2) Adriano Kossoski Mail (São Paulo State University, School of Engineering, 17033-360, Bauru, SP, Brazil, Brazil)
(3) Jose M. Balthazar Mail (São Paulo State University, School of Engineering, 17033-360, Bauru, SP, Brazil, Brazil)
(4) * Angelo Marcelo Tusset Mail (Federal University of Technology-Paraná (UTFPR), Brazil)
*corresponding author


This paper presents the design of the LQR (Linear Quadratic Regulator) and SDRE (State-Dependent Riccati Equation) controllers for the flight control of the F-8 Crusader aircraft considering the nonlinear model of longitudinal movement of the aircraft.  Numerical results and analysis demonstrate that the designed controllers can lead to significant improvements in the aircraft's performance, ensuring stability in a large range of attack angle situations. When applied in flight conditions with an angle of attack above the stall situation and influenced by the gust model, it was demonstrated that the LQR and SDRE controllers were able to smooth the flight response maintaining conditions in balance for an angle of attack up to 56% above stall angle.  However, for even more difficult situations, with angles of attack up to 76% above the stall angle, only the SDRE controller proved to be efficient and reliable in recovering the aircraft to its stable flight configuration.


High-performance aircraft; LQR control; SDRE control



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[1] B. Etkin and L. D. Reid, Dynamics of flight: stability and control. New York: Wiley, 1996.

[2] M. F. V. Pereira, I. A. Prado, D. F. De Castro, J. M. Balthazar, R. G. A. Da Silva and A. Nabarrete, “On Nonlinear Dynamics and Flight Control at High Angles of Attack with Uncertain Aerodynamics,” In ASME 2016 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, 2016, V04BT05A029.

[3] A. J. Calise and R. T. Rysdyk, “Nonlinear adaptive flight control using neural networks,” IEEE control systems, vol. 18, n. 6, 1998, pp. 14-25.

[4] D. C. Pereira, J. M. Balthazar, F. R. Chavarette, and M. Rafikov, “On nonlinear dynamics and an optimal control design to a longitudinal flight,” Journal of Computational and Nonlinear Dynamics, vol. 3, no. 1, p. 011012, 2008. ttps://

[5] W. L. Garrard and J. M. Jordan, “Design of Nonlinear Automatic Flight Control Systems,” Automatica, Pergamon Press, vol. 13, no. 5, pp. 497–505, 1977.

[6] Q. Wang and R. F. Stengel, “Robust nonlinear flight control of a high-performance aircraft,” Control Systems Technology, IEEE, vol. 13, no. 1, pp. 15–26, 2005,

[7] H. J. Tol, C. C. Visser de, L. G. Sun, E. Kampen van and Q. P. Chu “Multivariate spline-based adaptive control of high-performance aircraft with aerodynamic uncertainties,” Journal of Guidance and Control, vol. 39, no. 4, pp. 781–800, 2016.

[8] F. Gavilan, R. Vazquez and J. A. Acosta, “Adaptive control for aircraft longitudinal dynamics with thrust saturation,” Journal of Guidance, Control, and Dynamics, vol. 38, no. 4, pp. 651–661, 2015.

[9] A. Mahmood, Y. Kim and J. Park, “Robust h∞ autopilot design for agile missile with time-varying parameters,” Transactions on Aerospace and Electronic Systems, IEEE, vol. 50, no. 4, pp. 3082–3089, 2014.

[10] G. P. Dos Santos, J. M. Balthazar, F. C. Janzen, R. T. Rocha, A. Nabarrete and A. M. Tusset, “Nonlinear dynamics and SDRE control applied to a high-performance aircraft in a longitudinal flight considering atmospheric turbulence in flight,” Journal of Sound and Vibration, vol. 436, pp. 273-285, 2018.

[11] P. Pounds, D. R. Bersak and A. M. Dollar, “Stability of small-scale UAV helicopters and quadrotors with added payload mass under PID control,” Aut Robots, vol. 33, pp. 129–142, 2012.

[12] Z. M. Motea, H. Wahid, J. Zahid, S. H. Lwin and A. M. Hassan, “A Comparative Analysis of Intelligent and PID Controllers for an Aircraft Pitch Control System,” Applications of Modelling and Simulation, vol. 2, no. 1, pp. 17-25, 2018.

[13] R. V. K. Reddy, S. M. Sambasivam, S. Prem and C. Ramprasadh, “Design of a proportional-integral controller to track pitch angle in a mini aerial vehicle,” International Journal of Micro Air Vehicles, vol. 9, no. 1, pp. 15-24, 2017.

[14] Y. Kanokmedhakul, N. Pholdee, S. Bureerat and N. Panagan, “LQR aircraft pitch controller design forhandling disturbance using differential evolution,” Journal of Research and Applications in Mechanical Engineering, vol. 7, no. 2, pp. 145-153, 2019.

[15] B. S. Anjali, A. Vivek and J. L. Nandagopal, “Simulation and analysis of integral LQR controller for inner control loop design of a fixed wing micro aerial vehicle (MAV),” Procedia Technology, vol. 25, 2016, pp. 76-83.

[16] X. Chen, E. U. Haq and J. Lin, "Design, modeling and tuning of modified PID controller for autopilot in MAVs," 2016 17th IEEE/ACIS International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing (SNPD), 2016, pp. 475-480.

[17] R. Monica and R. Monica, “Optimized Controller Structured to Solve Aircraft Pitch Control Problem,” International Journal of Engineering and Technology, vol. 9, no. 2, pp. 1155-1162, 2017.

[18] C. Johny and B. R. Varghese, “Pitch control of an aircraft using lead compensator & fuzzy controller,” International Journal of Creative Research Thoughts, vol. 6, no. 2, pp. 594-594, 2018.

[19] G. Sudha and S. N. Deepa, “Opitimization for PID Control Parameters on Pitch Control of Aircraft Dynamics Based on Tuning Methods,” Optimization for PID Control Parameters on Pitch Control of Aircraft Dynamics Based on Tuning Methods, vol. 10, no. 1, pp. 343-350, 2016.

[20] K. P. Bharat and P. Sujatha, “QFT Robust Controller Design for Aircraft Pitch Control,” International Journal of Engineering and Management Research, vol. 7, no. 3, pp. 399-405, 2017.

[21] B. L. Stevens, F. L. Lewis and E. N. Johnson, Aircraft control and simulation: dynamics, controls design, and autonomous systems. John Wiley & Sons, 2015.

[22] F. Gavilan, J. A. Acosta and R. Vazquez, “Control of the longitudinal flight dynamics of an UAV using adaptive backstepping,” IFAC Proc, vol. 44, 2011, pp. 1892-1897.

[23] J. Guo, H. Zhang, X. Lu and J. Zhou, “Nonlinear disturbance observer-based adaptive sliding mode control for a generic hypersonic vehicle,” International Journal of Aerospace Engineering, vol. 2018, p. 6978170, 2018.

[24] Q. Shen, D. Wang, S. Zhu and E. K. Poh, “Integral-type sliding mode fault-tolerant control for attitude stabilization of spacecraft,” IEEE Transactions on Control Systems Technology, vol. 23, no. 3, pp. 1131–1138, 2015.

[25] S. Ijaz, C. Fuyang, M. T. Hamayun and H. Anwaar, “Adaptive integral-sliding-mode control strategy for maneuvering control of F16 aircraft subject to aerodynamic uncertainty,” Applied Mathematics and Computation,” vol. 402, 2021, p. 126053.

[26] K. D. Do, “Global inverse optimal control of vertical take-off and landing aircraft,” IFAC Journal of Systems and Control, vol. 15, 2021, p. 100132.

[27] D. Muniraj, M. C. Palframan, K. T.Guthrie and M. Farhood, “Path-following control of small fixed-wing H unmanned aircraft systems with type performance,” Control Engineering Practice, vol. 67, 2017, pp. 76-91.

[28] R. Lungu and M. Lungu, “Application of H2/H and dynamic inversion techniques to aircraft landing control,” Aerospace Science and Technology, vol. 46, 2015, pp. 146-158.

[29] V. H. Nguyen and T. T. Tran, “A Novel Hybrid Robust Control Design Method for F-16 Aircraft Longitudinal Dynamics,” Mathematical Problems in Engineering, vol. 2020, 2020, p. 5281904.

[30] X. Yao and Y. Yang, “Adaptive Fault Compensation and Disturbance Suppression Design for Nonlinear Systems with an Aircraft Control Application,” International Journal of Aerospace Engineering, vol. 2020, 2020, p. 4531302.

[31] B. Andrievsky, Elena V. Kudryashova, Nikolay V. Kuznetsov and O. A. Kuznetsova, “Aircraft wing rock oscillations suppression by simple adaptive control,” Aerospace Science and Technology, vol. 105, 2020, p. 106049.

[32] R. Huang, J. Zhang and X. Zhang, “Adaptive tracking control of uncertain switched non-linear systems with application to aircraft wing rock,” IET Control Theory & Applications, vol. 10, no. 15, 2016, pp. 1755–1762.

[33] J. Huang, X. Fu and Z. Jing, “Singular dynamics for morphing aircraft switching on the velocity boundary,” Communications in Nonlinear Science and Numerical Simulation, vol. 95, p. 105625, 2021.

[34] Q. Zhu, S. V. Kumar, R. Raja and F. Rihan, “Extended dissipative analysis for aircraft flight control systems with random nonlinear actuator fault via non-fragile sampled-data control,” Journal of the Franklin Institute, vol. 356, no. 15, 2019, pp. 8610-8624.

[35] L. Sun, L. Shi, W. Tan and X. Liu, “Flying qualities evaluation based nonlinear flight control law design method for aircraft,” Aerospace Science and Technology, vol. 106, p. 106126, 2020.

[36] T. T. Tran and B. A. Newman, “Nonlinear flight control design for longitudinal dynamics,” in: AIAA Guidance, Navigation, and Control Conference, Kissimmee, Florida, 2015, AIAA, 2015, pp. 1–16.

[37] E. Safwat, W. Zhang, A. Kamel and M. Kassem, “Robustness Analysis of Modified Incremental Nonlinear Dynamic Inversion for Small UAVs,” Automatic Control and Computer Sciences, vol. 54, pp. 128–138, 2020.

[38] S. N. Deepa and G. Sudha, “Longitudinal control of aircraft dynamics based on optimization of PID parameters,” Thermophysics and Aeromechanics, vol. 23, pp. 185–194, 2016.

[39] M. M. Ferdaus, M. Pratama, S. G. Anavatti, M. A. Garratt, E. Lughofer “PAC: A novel self-adaptive neuro-fuzzy controller for micro aerial vehicles,” Information Sciences, vol. 512, pp. 481-505, 2020.

[40] K. Raj, V. Muthukumar, S. N. Singh, K. W. Lee, “Finite-time sliding mode and super-twisting control of fighter aircraft,” Aerospace Science and Technology, vol. 82-83, pp. 487-498, 2018.

[41] A. C. Alves, A. M. Tusset, J. M. Balthazar, J. J. Lima, F. C. Janzen, R. T. Rocha and A. Nabarrete, “SDRE Control Applied to the Wheel Speed of a Compressed Air Engine with Crank-Connecting-Rod Mechanism,” Shock and Vibration, vol. 2017, pp. 1-14, 2017.

[42] A. M. Tusset, V. Piccirillo, A. M. Bueno, J. M. Balthazar, D. Sado, J. L. P. Felix, R. M. L. R F Brasil, “Chaos control and sensitivity analysis of a double pendulum arm excited by an RLC circuit based nonlinear shaker,” Journal of Vibration and Control, vol. 22, 2016, pp. 3621-3637.

[43] J. J. Lima, A. M. Tusset, F. C. Janzen, V. Piccirillo, C. B. Nascimento, J. M. Balthazar, M. R. L. F. Brasil, “SDRE applied to position and vibration control of a robot manipulator with a flexible link,” Journal of Theoretical and Applied Mechanics, vol. 54, pp. 1067-1078, 2016.

[44] D. R. Santo, J. M. Balthazar, A. M, Tusset, V. Piccirilo, R. M. L. R. F. Brasil, M. Silveira, “On nonlinear horizontal dynamics and vibrations control for high-speed elevators,” Journal of Vibration and Control, vol. 24, pp. 825-838, 2018.


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