Share:


Application of an optimal control algorithm for a gyroscope system of a homing air-to-air missile

    Izabela Krzysztofik Affiliation
    ; Zbigniew Koruba Affiliation

Abstract

Missile homing precision depends mainly on the correct determination of the current angle between the Gyroscope System Axis (GSA) and the target line-of-sight (LOS). A gyroscope automatic control system shall ensure spontaneous levelling of this angle, hence, constant homing of the gyroscope system axis in on the LOS, i.e. tracking the target by the head. The available literature on the subject lacks a description of how to use the controlled gyro system in the process of guiding the missile onto the target. In this paper, the authors present the original development of an optimal control algorithm for a gyro system with a square quality indicator in conditions of interference and kinematic influence of the missile deck. A comparative analysis of the LQR with the PD regulator was made. PD regulator parameters are also selected optimally, using the Golubencev method, so that the transition process of the homing system fades over a minimal time, while simultaneously ensuring the overlapping of the gyroscope axis with the target line-of-sight. The computer simulation results have been obtained in a Matlab-Simulink environment and are presented in a graphic form.

Keyword : non-linear dynamics, gyroscope system, optimal regulator, guidance, missile flight

How to Cite
[1]
Krzysztofik, I. and Koruba, Z. 2021. Application of an optimal control algorithm for a gyroscope system of a homing air-to-air missile. Aviation. 25, 1 (Apr. 2021), 41-49. DOI:https://doi.org/10.3846/aviation.2021.13899.
Published in Issue
Apr 13, 2021
Abstract Views
56
PDF Downloads
53
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

References

Awrejcewicz, J., & Koruba, Z. (2012). Classical mechanics: applied mechanics and mechatronics. Springer. https://doi.org/10.1007/978-1-4614-3978-3

Balakrishnan, S. N., Tsourdos, A., & White, B. A. (2013). Advances in missile guidance, control, and estimation. CRC Press.

Baranowski, L. (2013). Effect of the mathematical model and integration step on the accuracy of the results of computation of artillery projectile flight parameters. Bulletin of the Polish Academy of Sciences. Technical Sciences, 61(2), 475–484. https://doi.org/10.2478/bpasts-2013-0047

Chen, H.-K., & Ge, Z.-M. (2005). Bifurcations and chaos of a two-degree-of-freedom dissipative gyroscope. Chaos, Solitons and Fractals, 24(1), 125–136. https://doi.org/10.1016/j.chaos.2004.07.028

Chen, S.-C., Kuo, C.-L., Lin, C.-H., Hsu, C.-H., & Tsui, C.-K. (2013). Applications of fuzzy sliding mode control for a gyroscope system. Abstract and Applied Analysis, 2013, Article ID 931285. https://doi.org/10.1155/2013/931285

Gapinski, D., & Krzysztofik, I. (2014). The process of tracking an air target by the designed scanning and tracking seeker. In Proceedings of the 15th International Carpathian Control Conference, IEEE (pp. 129–134). Velke Karlovice, Czech Republic. https://doi.org/10.1109/CarpathianCC.2014.6843583

Gapiński, D., Krzysztofik, I., & Koruba, Z. (2018). Multi-channel, passive, short-range anti-aircraft defence system. Mechanical Systems and Signal Processing, 98, 802–815. https://doi.org/10.1016/j.ymssp.2017.05.032

Gapiński, D., & Stefański, K. (2014). A control of modified optical scanning and tracking head to detection and tracking air targets. Solid State Phenomena, 210, 145–155. https://doi.org/10.4028/www.scientific.net/SSP.210.145

Ge, Z.-M., & Lee, J.-K. (2005). Chaos synchronization and parameter identification for gyroscope system. Applied Mathematics and Computation, 163(2), 667–682. https://doi.org/10.1016/j.amc.2004.04.008

Grzyb, M., & Stefański, K. (2016). The use of special algorithm to control the flight of anti-aircraft missile. In Proceedings of the 22th International Conference Engineering Mechanics (pp. 174–177). Institute of Thermomechanics, Academy of Sciences of the Czech Republic, Svratka, Czech Republic.

Koruba, Z., & Krzysztofik, I. (2013). An algorithm for selecting optimal controls to determine the estimators of the coefficients of a mathematical model for the dynamics of a self-propelled anti-aircraft missile system. In Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 227(1), 12–16. https://doi.org/10.1177/1464419312455967

Krzysztofik, I., & Koruba, Z. (2014). Mathematical model of movement of the observation and tracking head of an unmanned aerial vehicle performing ground target search and tracking. Journal of Applied Mathematics, 2014, Article ID 934250. https://doi.org/10.1155/2014/934250

Krzysztofik, I., Takosoglu, J., & Koruba Z. (2017). Selected methods of control of the scanning and tracking gyroscope system mounted on a combat vehicle. Annual Reviews in Control, 44, 173–182. https://doi.org/10.1016/j.arcontrol.2016.10.003

Lei, Y., Xu, W., & Zheng, H. (2005). Synchronization of two chaotic nonlinear gyros using active control. Physics Letters A, 343(1–3), 153–158. https://doi.org/10.1016/j.physleta.2005.06.020

Lewis, F. L., Vrabie, D. L., & Syrmos, V. L. (2012). Optimal control (3rd ed.). John Wiley & Sons. https://doi.org/10.1002/9781118122631

Polo, M. P., Albertos, P., & Galiano, J. A. B. (2008). Tuning of a PID controlled gyro by using the bifurcation theory. Systems & Control Letters, 57(1), 10–17. https://doi.org/10.1016/j.sysconle.2007.06.007

Roopaei, M., Jahromi, M. Z., John, R., & Lin, T-C. (2010). Unknown nonlinear chaotic gyros synchronization using adaptive fuzzy sliding mode control with unknown dead-zone input. Communications in Nonlinear Science and Numerical Simulation, 15(9), 2536–2545. https://doi.org/10.1016/j.cnsns.2009.09.022

Sargolzaei, M., Yaghoobi, M., & Yazdi, R. (2013). Modeling and synchronization of chaotic gyroscopes using TS fuzzy approach. Advance in Electronic and Electric Engineering, 3(3), 339–346.

Tewari, A. (2002). Modern control design with MATLAB and SIMULINK. John Wiley & Sons.

Wang, C-C., & Yau, H-T. (2011). Nonlinear dynamic analysis and sliding mode control for a gyroscope system. Nonlinear Dynamics, 66, 53–65. https://doi.org/10.1007/s11071-010-9910-4

Yau, H-T. (2008). Chaos synchronization of two uncertain chaotic nonlinear gyros using fuzzy sliding mode control. Mechanical Systems and Signal Processing, 22(2), 408–418. https://doi.org/10.1016/j.ymssp.2007.08.007

Zarchan, P. (2012). Tactical and strategic missile guidance (6th ed.). AiAA Inc. https://doi.org/10.2514/4.868948