Application of an optimal control algorithm for a gyroscope system of a homing air-to-air missile
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
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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