×

zbMATH — the first resource for mathematics

PID pitch attitude control for unstable flight vehicle in the presence of actuator delay: tuning and analysis. (English) Zbl 1393.93110
Summary: In the realm of flight control, proportional-integral-derivative (PID) control is still widely used in practice due to its simple structure and efficiency. The robustness and dynamic performance of PID controller can be evaluated by stability margins. Based on the empirical knowledge about the unstable flight dynamics, the analytical tuning formulas of the PID pitch attitude control with actuator delay are derived with the help of several proper approximations. These tuning formulas can meet the increasing Gain and Phase Margins (iGPM) requirement and avoid time-consuming trial-and-error tuning process. The feasible iGPM area is established in 2-D plane subject to several conditions, especially taking the decreasing gain margin into account, wherein the numerical polynomial solving approaches are employed. The relationship between an existing PD tuning scheme and the proposed PID tuning method is also revealed. The applicable area of the tuning rule is then investigated on the basis of a crucial assumption. Furthermore, the achievable decreasing gain and phase margins (dGPM) area is obtained when the decreasing gain margin is critical; and another tuning rule is derived according to the dGPM specifications. The effect of the actuator delay on the achievable GPM area is demonstrated in a straightforward manner such that the reasonable criteria can be specified. Finally two numerical paradigms are presented to validate the proposed method; and the robustness and dynamic performance of the PID control are also reexamined for unstable flight dynamics.

MSC:
93D99 Stability of control systems
93C95 Application models in control theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Kobayashi, O., Definition system and criteria related to the static stability of airplanes (1-3 report), Trans. Jpn. Soc. Aeronaut. Space Sci., 45, 148, 116-138, (2002)
[2] Sun, M.; Yang, R.; Wang, Z.; Chen, Z., Stability margin based PD attitude control tuning for unstable flight vehicle, Int. J. Syst. Sci., 44, 2, 240-251, (2013) · Zbl 1307.93364
[3] Hess, R. A.; Snell, S. A., Flight control system design with rate saturating actuators, AIAA J. Guid. Control Dyn., 20, 1, 90-96, (1997) · Zbl 0925.93268
[4] Snell, S. A.; Hess, R. A., Robust, decoupled, flight control design with rate saturating actuators, AIAA J. Guid. Control Dyn., 21, 3, 361-367, (1998)
[5] Klyde, D. H.; Mitchell, D. G., Investigating the role of rate limiting in pilot-induced oscillations, AIAA J. Guid. Control Dyn., 27, 5, 804-813, (2004)
[6] F.W. Nesline, P. Zarchan, Robust instrumentation configuration for homing missile flight control, in: Proceedings of AIAA Guidance and Control Conference, Reston, 1980, pp. 209-219.
[7] K.A. Wise, D.J. Broy, Agile missile dynamics and control, AIAA-96-3912, 1996.
[8] F.W. Nesline, M.L. Nesline, How autopilot requirements constrain the aerodynamic design of homing missiles, in: Proceedings of American Control Conference, San Diego, 1984, pp. 716-730.
[9] C.P. Mracek, D.B. Ridgely, Missile longitudinal autopilot: comparison of multiple three loop topologies, in: Proceedings of AIAA Guidance, Navigation, and Control Conference, San Francisco, AIAA-2005-6380, 2005.
[10] C.P. Mracek, D.B. Ridgely, Missile longitudinal autopilot: connections between optimal control and classical topologies, in: Proceedings of AIAA Guidance, Navigation, and Control Conference, San Francisco, AIAA-2005-6381, 2005.
[11] Liao, F.; Wang, J.; Yang, G., Reliable robust flight tracking control: an LMI approach, IEEE Trans. Control Syst. Technol., 10, 1, 76-89, (2002)
[12] Schierman, J. D.; Ward, D. G.; Hull, J. R.; Gandhi, N.; Oppenheimer, M. W.; Doman, D. B., Integrated adaptive guidance and control for re-entry vehicles with flight-test results, AIAA J. Guid. Control Dyn., 27, 6, 975-988, (2004)
[13] L. Fiorentini, A. Serrani, M.A. Bolender, D.B. Doman, Robust nonlinear sequential loop closure control design for an air-breathing hypersonic vehicle model, in: Proceedings of American Control Conference, Seattle, 2008, pp. 3458-3463.
[14] Tian, B.; Fan, W.; Zong, Q.; Wang, J.; Wang, F., Nonlinear robust control for reusable launch vehicles in reentry phase based on time-varying high order sliding mode, J. Franklin Inst., 380, 7, 1787-1807, (2013) · Zbl 1392.93007
[15] Mattei, M.; Scordamaglia, V., A full envelope small commercial aircraft flight control design using multivariable proportional-integral control, IEEE Trans. Control Syst. Technol., 16, 1, 169-176, (2008)
[16] Scott, J. E.; Shtessel, Y. B., Launch vehicle attitude control using sliding mode control and observation techniques, J. Frankl. Inst., 349, 2, 397-412, (2012) · Zbl 1254.93057
[17] Kato, A.; Inagaki, Y., Control law for automatic landing using fuzzy-logic control, Trans. Jpn. Soc. Aeronaut. Space Sci., 50, 170, 274-283, (2008)
[18] Stein, G., Respect the unstable, IEEE Control Syst. Mag., 23, 4, 12-25, (2003)
[19] Ridgely, D. B.; McFarland, M. B., Tailoring theory to practice in tactical missile control, IEEE Control Syst. Mag., 19, 6, 49-55, (1999)
[20] Wise, K. A., Singular value robustness tests for missile autopilot uncertainties, AIAA J. Guid. Control Dyn., 14, 3, 597-606, (1991)
[21] Wedell, E.; Chuang, C. H.; Wie, B., Stability robustness margin computation for structured real-parameter perturbations, AIAA J. Guid. Control Dyn., 14, 3, 607-614, (1991) · Zbl 0756.93066
[22] Aström, K. J.; Hägglund, T., Automatic tuning of simple regulators with specifications on phase and amplitude margins, Automatica, 20, 5, 645-651, (1984) · Zbl 0543.93039
[23] Ho, W. K.; Hang, C. C.; Cao, L. S., Tuning of PID controllers based on gain and phase margin specifications, Automatica, 31, 3, 497-502, (1995) · Zbl 0825.93598
[24] Ho, W. K.; Xu, W., PID tuning for unstable processes based on gain and phase margin specifications, IEE Proc. Control Theory Appl., 145, 5, 392-396, (1998)
[25] Wang, Q. G.; Fung, H. W.; Zhang, Y., PID tuning with exact gain and phase margins, ISA Trans., 38, 3, 243-249, (1999)
[26] Wang, Y. G.; Cai, W. J., Advanced proportional-integral-derivative tuning for integrating and unstable processes with gain and phase margin specifications, Ind. Eng. Chem. Res., 41, 12, 2910-2914, (2002)
[27] Paraskevopoulos, P. N.; Pasgianos, G. D.; Arvanitis, K. G., PID-type controller tuning for unstable first order plus dead time processes based on gain and phase margin specifications, IEEE Trans. Control Syst. Technol., 14, 5, 926-936, (2006)
[28] M. Sun, Z. Chen, Z. Yuan, A practical solution to some problems in flight control, in: Proceedings of the 48th IEEE Conference on Decision & Control, Shanghai, 2009, pp. 1482-1487.
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.