zbMATH — the first resource for mathematics

Stability margin-based PD attitude control tuning for unstable flight vehicle. (English) Zbl 1307.93364
Summary: Proportional-derivative (PD) attitude control is widely used for the flight vehicles, especially in boost phase. Some of the flight dynamics are open-loop unstable, which often limits the achievable closed-loop performance. Based on the intrinsic characteristics of the linear model obtained from the small perturbation theory, simple numerical analytical tuning formulae of PD attitude control are derived to meet the gain and phase margin specifications. According to Routh stability criterion, the decreasing gain margin is obtained by using the approximation of delay amid low frequency with the established tuning rule. Some numerical polynomial solving approaches are employed to seek the feasible stability margin region, which is explicitly plotted in the 2-D plane. Taking engineering practice into account, the maximum gain constraint is also imposed. Finally, several numerical examples are presented to validate the analysis result.

93D99 Stability of control systems
93C95 Application models in control theory
Full Text: DOI
[1] DOI: 10.1080/00207720903470114 · Zbl 1198.93199 · doi:10.1080/00207720903470114
[2] DOI: 10.2514/3.25351 · Zbl 0705.93032 · doi:10.2514/3.25351
[3] Han J, IEEE Transactions on Industrial Electronics 56 pp 1– (2009) · doi:10.1109/TED.2008.2010311
[4] DOI: 10.1016/0005-1098(94)00130-B · Zbl 0825.93598 · doi:10.1016/0005-1098(94)00130-B
[5] Ho WK, IEEE Transactions on Control Systems Technology 59 pp 446– (1997)
[6] DOI: 10.1016/S0005-1098(02)00201-7 · Zbl 1018.93011 · doi:10.1016/S0005-1098(02)00201-7
[7] DOI: 10.1016/S0005-1098(99)00055-2 · Zbl 0935.93034 · doi:10.1016/S0005-1098(99)00055-2
[8] DOI: 10.1049/ip-cta:19982243 · doi:10.1049/ip-cta:19982243
[9] DOI: 10.1109/TAC.2008.925810 · Zbl 1367.93232 · doi:10.1109/TAC.2008.925810
[10] H.A. Kiam, Chong, G., and Li, Y. (2005), PID Control System Analysis, Design, and Technology,IEEE Transactions on Control System Technology, 13, 559–576
[11] Lee CH, International Journal of Computational Cognition 2 pp 63– (2004)
[12] Mracek , CP . and Ridgely, D.B. (2005), ’Missile Longitudinal Autopilots: Comparison of Multiple Three Loop Topologies’, inProceedings of the AIAA Guidance, Navigation and Control Conference, San Francisco, CA,AIAA Paper2005-6380
[13] DOI: 10.1109/TCST.2004.824334 · doi:10.1109/TCST.2004.824334
[14] DOI: 10.1109/TCST.2006.876913 · doi:10.1109/TCST.2006.876913
[15] DOI: 10.1080/00207729508929056 · Zbl 0825.93361 · doi:10.1080/00207729508929056
[16] DOI: 10.1109/37.806916 · doi:10.1109/37.806916
[17] Sun , MW . Chen, Z.Q., and Yuan, Z.Z. (2009), ’A Practical Solution to Some Problems in Flight Control’, inProceedings of the Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, China, December, pp. 1482–1487
[18] DOI: 10.1080/00207720600783785 · Zbl 1101.93034 · doi:10.1080/00207720600783785
[19] DOI: 10.1021/ie000739h · doi:10.1021/ie000739h
[20] DOI: 10.2514/3.20681 · Zbl 0756.93066 · doi:10.2514/3.20681
[21] DOI: 10.2514/3.20680 · doi:10.2514/3.20680
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.