Skip to main content
No AccessFull-Length Paper

Extended State Observer for Helicopter Mass and Center-of-Gravity Estimation

Published Online:

In flight estimations of helicopter mass and center of gravity are critical for health and lifecycle maintenance, flight control system feedback, and mission planning. This paper explores the use of an extended state observer for online estimation of helicopter mass and center-of-gravity location. The core algorithm is a nonlinear observer that offers provable stability properties. After describing the methodology, it is applied to a simulation of a commercial radio-controlled microcoaxial helicopter. Monte Carlo trade studies employing a comprehensive rotorcraft flight dynamics model are used to assess the algorithm’s estimation accuracy in the presence of model and measurement errors. Results show the helicopter mass, longitudinal center-of-gravity location, and lateral center-of-gravity location are estimated accurately in the presence of expected errors. The vertical center-of-gravity position is more difficult to estimate due to its limited observability during typical maneuvers.


  • [1] Bateman C., “Weight, Balance, and Tire Pressure Detection Systems,” U.S. Patent 4312042 A, Jan. 1982. Google Scholar

  • [2] Glover J., “Aircraft In-Flight Center of Gravity Measuring System,” U.S. Patent 4545019 A, Oct. 1985. Google Scholar

  • [3] Moffatt J., “Helicopter Gross Weight Determination from Monitored,” U.S. Army Aviation and Troop Command TR-96-D-5, Fort Eustis, VA, 1986. Google Scholar

  • [4] Morales M. and Haas D., “Feasiblity of Aircraft Gross Weight Estimation Using Artificial Neural Networks,” American Helicopter Society 57th Annual Forum, AHS International, Fairfax, VA, 2001, pp. 1872–1880. Google Scholar

  • [5] Bi N. B., Haas D. J. and McCool K., “Investigation of the In-Flight Gross Weight and CG Estimation of the V-22 Aircraft,” American Helicopter Society 60th Annual Forum, AHS International, Fairfax, VA, June 2004. Google Scholar

  • [6] Idan M., Iosilevskii G. and Nazarov S., “In-Flight Weight and Balance Identification Using Neural Networks,” Journal of Aircraft, Vol. 41, No. 1, 2004, pp. 137–143. doi: LinkGoogle Scholar

  • [7] Abraham M. and Costello M., “In-Flight Estimation of Helicopter Gross Weight and Mass Center Location,” Journal of Aircraft, Vol. 46, No. 3, 2009, pp. 1042–1049. doi: LinkGoogle Scholar

  • [8] Taylor B. and Rogers J., “Experimental Investigation of Real-Time Helicopter Weight Estimation,” Journal of Aircraft, Vol. 51, No. 3, May–June 2014, pp. 1047–1051. doi: LinkGoogle Scholar

  • [9] Apetre N., Sarkar S., Iyyer N. and Phan N., “Innovative Methods to Estimate Rotorcraft Gross Weight and Center of Gravity,” American Helicopter Society 67th Annual Fourm, AHS International, Fairfax, VA, 2011. Google Scholar

  • [10] Simon D., Optimal State Estimation: Kalman, H Inifinity, and Nonlinear Approaches, Wiley-Interscience, Hoboken, NJ, 2006, pp. 123–139, 336–337, 395–410. CrossrefGoogle Scholar

  • [11] Han J. Q., “A Class of Extended State Observers for Uncertain Systems,” Control and Decision, Vol. 10, No. 1, 1995, pp. 85–88 (in Chinese). Google Scholar

  • [12] Han J., “From PID to Active Disturbance Rejection Control,” IEEE Transactions on Industrial Electrionics, Vol. 56, No. 3, 2009, pp. 900–906. doi: CrossrefGoogle Scholar

  • [13] Hou Y., Gao Z., Jiang F. and Bolter B., “Active Disturbance Rejection Control for Web Tension Regulation,” Proceedings of the 40th IEEE Conference on Decision and Control, Vol. 5, IEEE Publ., Piscataway, NJ, 2001. doi: Google Scholar

  • [14] Su Y., Duan B. Y., Zheng C. H., Zhang Y. F., Chen G. D. and Mi J. W., “Disturbance-Rejection High-Precision Motion Control of a Stewart Platform,” IEEE Transactions on Control Systems Technology, Vol. 12, No. 3, 2004, pp. 364–374. doi: CrossrefGoogle Scholar

  • [15] Huang Y., Kekang X., Jingqing H. and Lam J., “Flight Control Design Using Extended State Observer and Non-Smooth Feedback,” Proceedings of the 40th IEEE Conference on Decision and Control, Vol. 1, IEEE Publ., Piscataway, NJ, 2001. doi: Google Scholar

  • [16] Martini A., Léonard F. and Abba G., “Dynamic Modelling and Stability Analysis of Model-Scale Helicopters Under Wind Gust,” Journal of Intelligent and Robotic Systems, Vol. 54, No. 4, 2009, pp. 647–686. doi: CrossrefGoogle Scholar

  • [17] Léonard F., Martini A. and Abba G., “Robust Nonlinear Controls of Model-Scale Helicopters Under Lateral and Vertical Wind Gusts,” IEEE Transactions on Control Systems Technology, Vol. 20, No. 1, 2012, pp. 154–163. doi: CrossrefGoogle Scholar

  • [18] Mehta A. and Pister K., “WARPWING: A Complete Open Source Control Platform for Miniature Robots,” 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2010), IEEE Publ., Piscataway, NJ, 2010. Google Scholar

  • [19] Johnson W., Helicopter Theory, Princeton Univ. Press, Princeton, NJ, 1980, pp. 184–193. Google Scholar

  • [20] Leishman J. G., Principles of Helicopter Aerodynamics, Cambridge Univ. Press, Cambridge, England, U.K., 2006, pp. 87, 388. Google Scholar

  • [21] Katz J. and Plotkin A., Low-Speed Aerodynamics: From Wing Theory to Panel Methods, McGraw–Hill, New York, 1991, pp. 156–158. Google Scholar

  • [22] Prouty R., Helicopter Performance, Stability, and Control, Krieger, Malabar, FL, 2005. Google Scholar

  • [23] Hoerner S., Fluid-Dynamic Drag: Practical Information on Aerodynamic Drag and Hydrodynamic Resistance, Hoerner Fluid Dynamics, Bakersfield, CA, 1985. Google Scholar

  • [24] Costello M. and Beyer E., “Performance of a Projectile/Rotor Kinetic Energy Reduction System,” AHS International Specialists’ Meeting—Unmanned Rotorcraft: Design, AHS International, Fairfax, VA, 2007. Google Scholar

  • [25] Klein V. and Morelli E., Aircraft System Identification: Theory and Practice, AIAA, Reston, VA, 2006, pp. 191–196. CrossrefGoogle Scholar

  • [26] Wheeler A. J. and Ganji A. R., Introduction to Engineering Experimentation, 2nd ed., Person Prentice–Hall, Upper Saddle River, NJ, 2004, pp. 142–144. Google Scholar

  • [27] Venables W. N. and Ripley B. D., Modern Applied Statistics with S, Springer Science+Business Media, New York, 2002, pp. 220–226. CrossrefGoogle Scholar

  • [28] Anon., “Operator’s Manual: Army Model UH-1H/V Helicopters,” Headquarters, U.S. Dept. of the Army Technical Manual TM-55-1520-210-10, Feb. 1988. Google Scholar

  • [29] Anon., “Operator’s Manual for Helicopter, Attack, AH-64A Apache,” Headquarters, U.S. Dept. of the Army Technical Manual TM-1-1520-238-10, Aug. 1994. Google Scholar

  • [30] Howlett J. J., “UH-60A Black Hawk Engineering Simulation Program, Volume 1: Mathematical Model,” NASA CR-166309, Dec. 1981. Google Scholar