Abstract
One of the core tenets of feedback control is that a system’s state contains all of the information necessary to predict a system’s future response given future inputs. If the state is not directly measured then it can be estimated using a suitably designed observer. This is a powerful idea with widespread consequences. This paper will present a critique of the use of observers in feedback control. Benefits and drawbacks will be highlighted including fundamental design limitations. The analysis will be illustrated by several real world examples including robots executing a repetitive task, relay autotuning in the presence of broadband disturbances, power line signalling in AC microgrid power systems, Type 1 diabetes management and harmonic suppression in power electronics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Utkin, V., Guldner, J., Shi, J.: Sliding Mode Control in Electromechanical Systems. Taylor and Francis Inc., Philadelphia (1999). ISBN 0-7484-0116-4
Drakunov, S.V.: An adaptive quasioptimal filter with discontinuous parameters. Autom. Remote Control 44(9), 1167–1175 (1983)
Drakunov, S.V.: Sliding-mode observers based on equivalent control method. In: Proceedings of the 31st IEEE Conference on Decision and Control (CDC), pp. 2368–2370 (1992). https://doi.org/10.1109/CDC.1992.371368, ISBN 0-7803-0872-7
Narendra, K.S.: A new approach to adaptive control using multiple models. Int. J. Adap. Control Signal Process. 26(8), 778–799 (2012)
Bernat, J., Stepien, S.: Multi modelling as new estimation schema for high gain observers. Int. J. Control 88(6), 1209–1222 (2015). https://doi.org/10.1080/179.2014.1000380
Krener, A.J., Isidori, A.: Linearization by output injection and nonlinear observers. Syst. Control Lett. 3, 47–52 (1983). https://doi.org/10.1016/0167-6911(83)90037-3
Hammouri, H., Kinnaert, M.: A new procedure for time-varying linearization up to output injection. Syst. Control Lett. 28(3), 151–157 (1996). https://doi.org/10.1016/0167-6911(96)00022-9
Ciccarella, G., Dalla Mora, M., Germani, A.: A Luenberger-like observer for nonlinear systems. Int. J. Control 57(3), 537–556 (1993). https://doi.org/10.1080/00207179308934406
Friedland, B.: The Control Handbook. CRC Press, IEEE Press (1999). Ch. Observers, pp. 607–618
Chen, C.-T.: Linear Systems Theory and Design (Oxford Series in Electrical and Computer Engineering), 3rd edn. Oxford University Press, Oxford (1998)
Ellis, G.: Observers in Control Systems: A Practical Guide. Academic Press, Boston (2002)
Kalman, R.E.: A new approach to linear filtering and prediction problems. Trans. ASME J. Basic Eng. 82(Series D), 35–45 (1960)
Joesph, I., Profeta, A., Vogt, W.G., Mickle, M.H.: Disturbance estimation and compensation in linear systems. IEEE Trans. Aerosp. Electron. Syst. 26(2), 225–231 (1990)
Wang, W., Gao, Z.: A comparison study of advanced state observer design techniques. In: American Control Conference (2003)
Luenberger, D.: Observers for multivariable systems. IEEE Trans. Autom. Control 11(2), 190–197 (1966)
Kalman, R.E., Bucy, R.S.: New results in linear filtering and prediction theory. Trans. ASME J. Basic Eng. 83, 93–107 (1961)
Sorenson, H. (ed.): Kalman Filtering Theory and Applications. IEEE Press, New York (1983)
Julier, S.J., Uhlmann, J.K., Durrant-Whyte, H.: A new approach for filtering nonlinear systems. In: American Control Conference, pp. 1628–1632 (1995)
Ahrens, J.H., Khalil, H.K.: Closed-loop behaviour of a class of nonlinear systems under EKF-based control. IEEE Trans. Autom. Control 52(9), 536–540 (2007)
Boutayeb, M., Aubry, D.: A strong tracking extended Kalman observer for nonlinear discrete-time systems. IEEE Trans. Autom. Control 44(8), 1550–1556 (1999)
Deza, F., Busvelle, E., Gauthier, J.P., Rakotopara, D.: High gain estimation for nonlinear systems. Syst. Control Lett. 18(4), 295–299 (1992)
Farza, M., M’Saad, M., Triki, M., Maatoug, T.: High gain observer for a class of non-triangular systems. Syst. Control Lett. 60(1), 27–35 (2011)
Freidovich, L.B., Khaili, H.K.: Lyapunov-based switching control of nonlinear systems using high-gain observers. Automatica 43(1), 150–157 (2007)
Khalil, H.K., Praly, L.: High-gain observers in nonlinear feedback control. Int. J. Robust Nonlinear Control (2013). https://doi.org/10.1002/rnc.3051
Krener, A.J.: The convergence of the extended Kalman filter. In: Rantzer, A., Byrnes, C.I. (eds.) Directions in Mathematical Systems Theory and Optimization. LNCIS, vol. 286, pp. 173–182. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36106-5_12
Memon, A.Y., Khalil, H.K.: Full-order high-gain observers for minimum phase nonlinear systems. In: Proceedings of the 48th IEEE Conference on Decision and Control, 2009 Held Jointly With the 2009 28th Chinese Control Conference, (CDC/CCC 2009), pp. 6538–6543. IEEE (2009)
Nazrulla, S., Khalil, H.K.: Robust stabilization of non-minimum phase nonlinear systems using extended high-gain observers. IEEE Trans. Autom. Control 56(4), 802–813 (2011)
Reif, K., Sonnemann, F., Unbehauen, R.: An EFK-based nonlinear observer with a prescribed degree of stability. Automatica 34(9), 1119–1123 (1998)
Song, Y., Grizzle, J.W.: The extended Kalman filter as a local asymptotic observer for discrete-time nonlinear systems. J. Math. Syst. Estim. Control 5(1), 59–78 (1995)
Arulampalam, M.S., Maskell, S., Gordon, N., Clapp, T.: A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans. Signal Process. 50(2), 174–188 (2002)
Doucet, A., Godsill, S., Andrieu, C.: On sequential Monte Carlo sampling methods for Bayesian filtering. Stat. Comput. 10, 197–208 (2000)
Rao, C.V., Rawlings, J.B., Mayne, D.Q.: Constrained state estimation for nonlinear discrete-time systems: stability and moving horizon approximations. IEEE Trans. Autom. Control 48(2), 246–258 (2003)
Smith, A.F.M., Gelfand, A.E.: Bayesian statistics without tears: a sampling-resampling perspective. Am. Stat. 46(2), 84–88 (1992)
Rawlings, J.B., Bakshi, B.R.: Particle filtering and moving horizon estimation. Comput. Chem. Eng. 30, 1529–1541 (2006)
Daum, F.: Nonlinear filters: beyond the Kalman filter. IEEE Aerosp. Electron. Syst. Mag. 20(8), 57–69 (2005). Part 2: Tutorials
Ho, Y.C., Lee, R.C.K.: A Bayesian approach to problem in stochastic estimation and control. IEEE Trans. Autom. Control 9(5), 333–339 (1964)
Handschin, J.E., Mayne, D.Q.: Monte Carlo techniques to estimate the conditional expectation in multistage nonlinear filtering. Int. J. Control 9(5), 547–559 (1969)
Gordon, N., Salmond, D., Smith, A.: Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEE Proc. F-Radar Signal Process. 140(2), 107–113 (1993)
Goodwin, G.C., De Dona, J.A., Seron, M.M., Zhuo, X.W.: Lagrangian duality between constrained estimation and control. Automatica 41, 935–944 (2005)
Seron, M.M., Braslavsky, J.H., Goodwin, G.C.: Fundamental Limitations in Filtering and Control. Springer, London (1997). https://doi.org/10.1007/978-1-4471-0965-5
Middleton, R.H., Goodwin, G.C.: Digital Control and Estimation: A Unified Approach. Prentice Hall, Englewood Cliffs (1990)
Luenberger, D.: Observing the state of a linear system. IEEE Trans. Mil. Electron. 8(2), 74–80 (1964)
Stein, G.: Respect the unstable. IEEE Control Syst. 23(4), 12–25 (2003)
Goodwin, G.C., Evans, R.J., Lozano-Leal, R., Feick, R.: Sinusoidal disturbance rejection with application to helicopter flight data estimation. IEEE Trans. Acoust. Speech Signal Process. 34(3), 479–484 (1986)
Edwards, W.J., Thomas, P., Goodwin, G.C.: Roll eccentricity control for strip rolling mills. IFAC World Congr. 20(5), 187–198 (1987)
Middleton, R.H., Goodwin, G.C., Longman, R.W.: A method for improving the dynamic accuracy of robot performing a repetitious task. Int. J. Robot. Res. 8(5), 67–74 (1989)
Goodwin, G.C., Seron, M.M., Townsend, C.: A modified relay autotuner for systems having large broadband disturbances. Automatica, March 2018. Accepted for publication
Lau, K., Goodwin, G.C., M’Closkey, R.T.: Properties of modulated and demodulated, systems with implications in feedback limitations. Automatica 41, 2123–2129 (2005)
Lau, K., Quevedo, D.E., Vautier, B.J.G., Goodwin, G.C., Moheimani, S.O.R.: Design of modulated and demodulated controllers for flexible structures. Control Eng. Pract. 15(3), 377–388 (2007)
Mirzaeva, G., Goodwin, G.C.: Harmonic suppression and delay compensation for inverters via variable horizon nonlinear model predictive control. Int. J. Control 88(7), 1400–1409 (2015)
Townsend, C.D., Mirzaeva, G., Semenov, D., Goodwin, G.C.: Use of harmonic power line communication to enhance a decentralized control method of parallel inverters in an AC microgrid. In: Proceedings of the 3rd Annual Southern Power Electronics Conference (SPEC), pp. 1–6, December 2017
Goodwin, G.C., Middleton, R.H., Poor, V.H.: High speed digital signal processing and control. Proc. IEEE 80(2), 240–259 (1992)
Goodwin, G.C., Agüero, J.C., Cea, M.E., Salgado, M.E., Yuz, J.I.: Sampling and sampled-data models: the interface between the continuous world and digital algorithms. IEEE Control Syst. 33(5), 34–53 (2013)
Middleton, R.H., Goodwin, G.C.: Digital Estimation and Control: A Unified Approach. Prentice Hall, Englewood Cliffs (1990)
Åström, K.J., Hägglund, T.: Automatic tuning of simple regulators with specifications on phase and amplitude margins. Automatica 20(5), 645–651 (1984)
Berner, J., Hägglund, T., Åström, K.J.: Asymmetric relay autotuning - practical features for industrial use. Control Eng. Pract. 54, 231–245 (2016)
Atkinson, M.A., Eisenbarth, G.S., Michels, A.W.: Type 1 diabetes. Lancet 383(9911), 69–82 (2014)
Chee, F., Fernando, T.: Closed-Loop Control of Blood Glucose, vol. 368. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74031-5
Aronoff, S.L., Berkowitz, K., Shreiner, B., Want, L.: Glucose Metabolism and Regulation: beyond Insulin and glucagon. Diabetes Spectr. 17, 183–190 (2004)
Doyle III, F.J., Huyett, L.M., Lee, J.B., Zisser, H.C., Dassau, E.: Closed-loop artificial pancreas systems: engineering the algorithms. Diabetes Care 37(5), 1191–1197 (2014)
Kovatchev, B., Cobelli, C., Renard, E., Anderson, S., Breton, M., Patek, S., Clarke, W., Bruttomesso, D., Maran, A., Costa, S., et al.: Multinational study of subcutaneous model-predictive closed-loop control in type 1 diabetes mellitus: summary of the results. J. Diabetes Sci. Technol. 4(6), 1374–1381 (2010)
Gondhaledar, R., Dassau, E., Doyle III, F.J.: Periodic zone-MPC with asymmetric costs for outpatient-ready safety of an artificial pancreas to treat type 1 diabetes. Automatica 71, 237–246 (2016)
Kumareswaran, K.: Closed-loop insulin delivery in adults with type 1 diabetes. Ph.D. thesis, University of Cambridge (2012)
Bequette, B.: A critical assessment of algorithms and challenges in the development of the closed-loop artificial pancreas. Diabetes Technol. Ther. 7(1), 28–47 (2005)
Klonoff, D.C., Cobelli, C., Kovatchev, B., Zisser, H.C.: Progress in development of an artificial pancreas. J. Diabetes Sci. Technol. 3, 1002–1004 (2009)
Harvey, R.A., Wang, Y., Grosman, B., Percival, M.W., Bevier, W., Finan, D.A., Zisser, H., Seborg, D.S., Jovanovic, L., Doyle III, F.J., Dassau, E.: Quest for the artificial pancreas: combining technology with treatment. IEEE Eng. Med. Biol. Mag. 29(2), 53–62 (2010)
Bequette, B.W.: Challenges and recent progress in the development of a closed-loop artificial pancreas. Annu. Rev. Control 36(2), 255–266 (2012)
Cefalu, W.T., Tamborlane, M.V.: The artificial pancreas: are we there yet? Diabetes Care 37(5), 1182–1183 (2014)
Kovatchev, B., Tamborlane, W.V., Cefalu, W.T., Cobelli, C.: The artificial pancreas in 2016: a digital treatment ecosystem for diabetes. Diabetes Care 39(7), 1123–1126 (2016)
Weinzimer, S.A., Steil, G.M., Swan, K.L., Dziura, J., Kurtz, N., Tamborlane, W.V.: Fully automated closed-loop insulin delivery versus semiautomated hybrid control in paediatric patients with type 1 diabetes using an artificial pancreas. Diabetes Care 31(5), 934–939 (2008)
Bergman, R.N.: Minimal model: perspective from 2005. Horm. Res. 64(3), 8–15 (2005)
Kanderian, S.S., Weinzimer, S., Voskanyan, G., Steil, G.M.: Identification of intraday metabolic profiles during closed-loop glucose control in individuals with type 1 diabetes. J. Diabetes Sci. Technol. 3, 1047–1057 (2009)
Oviedo, S., Vehi, J., Calm, R., Armengol, J.: A review of personalized blood glucose prediction strategies for T1DM patients. Int. J. Numer. Methods Biomed. Eng. 33(6) (2017)
Bondia, J., Dassau, E., Zisser, H., Calm, R., Vehi, J., Jovanovic, L., Doyle III, F.J.: Coordinated basal bolus infusion for tighter postprandial glucose control in insulin pump therapy. J. Diabetes Sci. Technol. 3(1), 89–97 (2009)
Goodwin, G.C., Graebe, S.F., Salgado, M.E.: Control System Design. Prentice Hall, Upper Saddle River (2001)
Cameron, F.M., et al.: Closed-loop control without meal announcement in Type 1 diabetes. Diabetes Technol. Ther. 19(9), 527–532 (2017)
Hovorka, R.: The future of continuous glucose monitoring closed loop. Curr. Diabetes Rev. 4(3), 269–279 (2008)
Ramkissoon, C.M., et al.: Unannounced meals in the artificial pancreas: detection using continuous glucose monitoring. Sensors 18, 884 (2008)
Messer, L.H., et al.: Optimizing hybrid closed-loop theory in adolescents and emerging adults using the MiniMed 670G system. Diabetes Care 41(4), 789–796 (2018)
Doyle, J.C., Stein, G.: Multivariable feedback design: concepts for a classical/modern synthesis. IEEE Trans. Autom. Control 26(1), 4–16 (1981)
Doyle, J.C., Glover, K., Khargonekar, P.P., Francis, B.A.: State space solutions to standard \(H_2\) and \(H_{\infty }\) control problems. IEEE Trans. Autom. Control 34(8), 831–847 (1989)
Limebeer, D.J., Green, M., Walker, D.: Discrete time \(H_{\infty }\) control. In: 28th CDC, pp. 392–396 (1989)
Stoorvogel, A.A., Saberi, A., Chen, B.M.: The discrete time \(H_{\infty }\) control with measurement feedback. Int. J. Robust Nonlinear Control 4, 457–479 (1994)
Zames, G.: Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms and approximate inverses. IEEE Trans. Autom. Control 26, 301–320 (1981)
Anderson, B.D.O., Moore, J.B.: Optimal Filtering. Dover, New York (2005)
Simon, D.: Optimal State Estimation Kalman, \(H_{\infty }\) and Nonlinear Approaches. Wiley, Hoboken (2006)
Jazwinski, A.H.: Stochastic Processes and Filtering. Dover, New York (2007)
Goodwin, G.C., Sin, K.S.: Adaptive Filtering Prediction and Control. Dover, New York (2009)
Söderström, T.: Errors-in-Variables Methods in System Identification. Springer, Heidelberg (2018). https://doi.org/10.1007/978-3-319-75001-9
Agüero, J.C., Goodwin, G.C.: Identifiability of errors-in-variables dynamic systems. Automatica 44, 371–382 (2008)
Stengel, R.F.: Optimal Control and Estimation. Dover, New York (1994)
Radke, A., Gao, Z.: A survey of state and disturbance observers for practitioners. In: Annual Control Conference, pp. 5183–5188 (2006)
Carrasco, D.S., Goodwin, G.C.: Connecting filtering and control sensitivity functions. Automatica 50(12), 3319–3322 (2014)
Goodwin, G.C., Seron, M.M.: A gold standard for optimal insulin infusion for Type 1 diabetes ingesting a meal with slow postprandial response (2018). Submitted for publication
Goodwin, G.C., Medioli, A.M., Carrasco, D.S., King, B.R., Fu, Y.: A fundamental control limitation for linear positive systems with application to Type 1 diabetes treatment. Automatica 55, 73–77 (2015)
Goodwin, G.C., Carrasco, D.S., Seron, M.M., Medioli, A.M.: A performance limit for a class of positive nonlinear systems. Automatica 95, 14–22 (2018)
Acknowledgements
The author gratefully acknowledges significant input into the development of this paper from Maria Seron. Input into specific sections has been provided by Diego Carrasco, Adrian Medioli, Richard Middleton, Mario Salgado, Bruce King, Carmel Smart, Tenele Smith, Galina Mirzaeva and Christopher Townsend.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Goodwin, G.C. (2018). A Critique of Observers Used in the Context of Feedback Control. In: Chen, Z., Mendes, A., Yan, Y., Chen, S. (eds) Intelligent Robotics and Applications. ICIRA 2018. Lecture Notes in Computer Science(), vol 10984. Springer, Cham. https://doi.org/10.1007/978-3-319-97586-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-97586-3_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-97585-6
Online ISBN: 978-3-319-97586-3
eBook Packages: Computer ScienceComputer Science (R0)