# zbMATH — the first resource for mathematics

Performance sensitivity of helicopter global and local optimal harmonic vibration controller. (English) Zbl 1165.93308
Summary: A comparison of local and global controllers is conducted for helicopter vibration reduction using actively controlled single/dual trailing-edge flaps. It is found that for high-speed flight conditions, both local and global controllers perform equally well. However, for low-speed flight, local controller gives a marginally better optimal solution compared to the global controller but at the cost of much greater computation time. An objective function containing the hub vibratory loads is minimized using the global controller. The control effort is weighted such that each flap is used to complete authority. A reduction of 73% and 75% in hub vibration is obtained at high-speed flight using single and dual flap configurations, respectively. At low-speed flight, single and dual flap configurations gave 52% and 63% reduction in vibration, respectively. Numerical studies using an aeroelastic simulation show that the vibration control system performs well up to $$\pm 5$$ degrees error in flap phasing from optimal phase. The control law is insensitive to small perturbations (up to $$\pm 0.3$$ deg) in the optimal flap harmonics and is fairly insensitive to stiffness and mass changes of the rotor blade as well as noise in the measured hub load data. Dual flap configuration was found to be more insensitive to errors in optimal flap control harmonics than single flap configuration.
##### MSC:
 93B35 Sensitivity (robustness) 74H45 Vibrations in dynamical problems in solid mechanics
Full Text:
##### References:
 [1] Jimenez, R.; Santos, L.; Kuhl, N.; Egana, J., The reconstruction of a specially structured Jacobi matrix with an application to damage detection in rods, Computers and mathematics with applications, 49, 11-12, 1815-1823, (2005) · Zbl 1082.74019 [2] Tiago, C.M.; Leitao, V.M.A., Application of radial basis functions to linear and nonlinear structural analysis problems, Computers and mathematics with applications, 51, 8, 1311-1334, (2006) · Zbl 1148.41031 [3] Barkai, S.M.; Rand, O., Implementation of the harmonic variables concept in the vibration analysis of a coupled rotor/fuselage system, Computers and mathematics with applications, 30, 9, 87-104, (1995) [4] Friedmann, P.P., The renaissance of aeroelasticity and its future, Journal of aircraft, 36, 1, 105-121, (1999) [5] Loewy, R.G., Helicopter vibrations: A technological perspective, Journal of American helicopter society, 29, 4, 4-30, (1984) [6] Peters, D.A.; Rossow, M.P.; Korn, A.; Ko, T., Design of helicopter rotor blades for optimum dynamic characteristics, Computers and mathematics with applications, 12, 1, 85-109, (1986) [7] Chattopadhyay, A.; McCarthy, T.R., A multidisciplinary optimization approach for vibration reduction in helicopter rotor blades, Computers and mathematics with applications, 25, 2, 59-72, (1993) [8] Chattopadhyay, A.; Pagaldipti, N., A multidisciplinary optimization using semi-analytical sensitivity analysis procedure and multilevel decomposition, Computers and mathematics with applications, 29, 7, 55-66, (1995) · Zbl 0835.76086 [9] Nguyen, K.; Chopra, I., Application of higher harmonic control to rotor operating at high speed and thrust, Journal of American helicopter society, 35, 3, 336-342, (1990) [10] Wood, E.R.; Powers, R.W.; Cline, C.H.; Hammond, C.E., On developing and flight testing a higher harmonic control system, Journal of American helicopter society, 30, 2, 1-20, (1985) [11] Friedmann, P.P.; Millott, T.A., Vibration reduction in rotorcraft using active control: A comparison of various approaches, Journal of guidance, control and dynamics, 18, 4, 664-673, (1995) [12] Kunze, O.; Arnold, U.T.P.; Waaske, S., Development and design of an individual blade control system for the sikorsky CH-53G helicopter, () [13] Wilbur, M.L.; Mirick, P.H.; Yeager, W.T.; Langston, C.W.; Cesnik, C.E.S.; Shin, S., Vibratory loads reduction testing of the NASA/army/MIT active twist rotor, Journal of the American helicopter society, 47, 2, 123-133, (2002) [14] Friedmann, P.P.; de Terlizzi, M.; Myrtle, T.F., New developments in vibration reduction with actively controlled trailing edge flaps, Mathematical and computer modelling, 33, 10-11, 1055-1083, (2001) · Zbl 1197.74052 [15] Dawson, S.; Marcolini, M.; Booth, E.; Straub, F.; Hassan, A.; Tadghighi, H.; Kelly, H., Wind tunnel test of an active flap rotor: BVI noise and vibration reduction, () [16] Milgram, J.; Chopra, I., A parametric design study for actively controlled trailing edge flaps, Journal of the American helicopter society, 43, 2, 110-119, (1998) [17] Milgram, J.; Chopra, I.; Straub, F., Rotors with trailing edge flaps: analysis and comparison with experimental data, Journal of the American helicopter society, 43, 4, 319-332, (1998) [18] Myrtle, T.F.; Friedmann, P.P., Application of a new compressible time domain aerodynamic model to vibration reduction in helicopters using an actively controlled flap, Journal of the American helicopter society, 46, 1, 32-43, (2001) [19] Abdel-Hameed, M.S.; Nakhi, Y.A., Optimal control of a finite dam with diffusion input and state dependent release rates, Computers and mathematics with applications, 51, 2, 317-324, (2006) · Zbl 1161.93329 [20] Galperin, E.A., Reflections on optimality and dynamic programming, Computers and mathematics with applications, 52, 1-2, 235-257, (2006) · Zbl 1159.49034 [21] Pontryagin, L.S., The mathematical theory of optimal processes, (1962), Wiley-Interscience New York · Zbl 0112.05502 [22] Keys, P., The solution and sensitivity of a general optimal control problem, Applied mathematical modelling, 4, 4, 287-294, (1980) · Zbl 0466.49019 [23] Dorato, P., On sensitivity in optimal control systems, IEEE transactions on automatic control, AC-8, 256-257, (1963) [24] Pagurek, B., Sensitivity of the performance of optimal control systems to plant parameter variation, IEEE transactions on automatic control, AC-10, 178-180, (1965) · Zbl 0201.47701 [25] Witsenhausen, H., On the sensitivity of optimal control systems, IEEE transactions on automatic control, AC-10, 495-496, (1965) [26] Weng, P., Existence and global stability of positive periodic solution of periodic integrodifferential systems with feedback controls, Computers and mathematics with applications, 40, 6-7, 747-759, (2000) · Zbl 0962.45003 [27] Liu, G.; Yan, J., Positive periodic solutions for a neutral differential system with feedback control, Computers and mathematics with applications, 52, 3-4, 401-410, (2006) · Zbl 1141.34344 [28] Viswamurthy, S.R.; Ganguli, R., An optimization approach to vibration reduction in helicopter rotors with multiple active trailing edge flaps, Aerospace science and technology, 8, 3, 185-194, (2004) · Zbl 1062.74588 [29] D.H. Hodges, E.H. Dowell, Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades, NASA TN D-7818, 1974 [30] Bagai, A.; Leishman, J.G., Rotor free-wake modeling using a pseudo-implicit technique including comparisons with experiment, Journal of the American helicopter society, 40, 3, 29-41, (1995) [31] G. Bir, et al. University of Maryland Advanced Rotorcraft Code (UMARC) Theory Manual, UM-AERO report 92-02, 1992 [32] Borri, M., Helicopter rotor dynamics by finite element time approximation, Computers and mathematics with applications, 12, 1, 149-160, (1986) [33] Ganguli, R.; Chopra, I.; Weller, W.H., Comparison of calculated vibratory rotor hub loads with experimental data, Journal of the American helicopter society, 43, 4, 312-318, (1998) [34] Torok, M.S.; Chopra, I., Rotor loads prediction utilizing a coupled aeroelastic analysis with refined aerodynamic modeling, Journal of the American helicopter society, 36, 1, 58-67, (1991) [35] Hariharan, N.; Leishman, J.G., Unsteady aerodynamics of a flapped airfoil in subsonic flow by indicial concepts, Journal of aircraft, 33, 5, 855-868, (1996) [36] Cribbs, R.C.; Friedmann, P.P., Actuator saturation and its influence on vibration reduction by actively controlled flaps, () [37] Belegundu, A.D.; Chandrupatla, T.R., Optimization concepts and applications in engineering, (1999), Pearson Education Singapore · Zbl 0941.90074 [38] W. Johnson, Self-tuning regulators for multicyclic control of helicopter vibration, NASA TP 1996, 1982
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.