eesti teaduste
akadeemia kirjastus
SINCE 1952
Proceeding cover
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2020): 1.045

Disturbance decoupling by measurement feedback: sensor location; pp. 317–329

Full article in PDF format | doi: 10.3176/proc.2016.4.05

Arvo Kaldmäe, Ülle Kotta, Alexey Shumsky, Alexey Zhirabok



The paper addresses the problem on sensor location regarding the solvability of the disturbance decoupling probleem by the dynamic measurement feedback (DDDPM). Both, the discrete- and continuous-time nonlinear systems are considered. An exact formula is given to compute a controlled invariant vector function, necessary for the solvability of the DDDPM. Then, two methods are given to find a measured output, which guarantee the solution to the DDDPM. The results are illustrated by several examples.




1. Basseville, M., Benveniste, A., Moustakides, G. V., and Rougee, A. Optimal sensor location for detecting changes in dynamical behavior. IEEE T. Automat Contr., 1987, 32(12), 1067–1075.

2. Boukhobza, T. and Hamelin, F. Observability analysis and sensor location study for structured linear systems in descriptor form with unknown inputs. Automatica, 2011, 47, 2678–2683.

3. Chi, G. and Wang, D. Sensor placement for fault isolability based on bond graphs. IEEE T. Automat. Contr., 2015, 60(11), 3041–3046.

4. Commault, C. and Dion, J.-M. Sensor location for diagnosis in linear systems: a structural analysis. IEEE T. Automat. Contr., 2007, 52(2), 155–169.

5. Commault, C., Dion, J.-M., and Do, T. H. Sensor location and classification for disturbance rejection by measurement feedback. Automatica, 2011, 47, 2584–2594.

6. Dion, J.-M. and Commault, C. Structural analysis of sensor location for disturbance rejection by measurement feedback. Automatica, 2015, 52, 210–217.

7. Frisk, E., Krysander, M., and Aslund, J. Sensor placement for fault isolation in linear differential-algebraic systems. Automatica, 2009, 45(2), 364–371.

8. Huang, C. and Sira-Ramirez, A. A flatness based active disturbance rejection controller for the four tank benchmark problem. In Proceedings of the American Control Conference, Chicago, USA, 2015, 4628–4633.

9. Isidori, A. Nonlinear Control Systems. Springer, London, 1995.

10. Isidori, A., Krener, A. J., Gori-Giorgi, C., and Monaco, S. Nonlinear decoupling via feedback: a differential gemetric approach. IEEE T. Automat. Contr., 1981, 26, 331–345.

11. Kaldmäe, A., Kotta, Ü ., Jiang, B., Shumsky, A., and Zhirabok, A. Faulty plant reconfiguration based on disturbance decoupling methods. Asian Journal of Control, 2016, 18(3), 858–867.

12. Kaldmäe, A., Kotta, Ü ., Shumsky, A., and Zhirabok, A. Measurement feedback disturbance decoupling in discrete-time nonlinear systems. Automatica, 2013, 49(9), 2887–2891.

13. Kaldmäe, A., Kotta, Ü ., Shumsky, A., and Zhirabok, A. Disturbance decoupling for nonlinear systems: sensor location. In Proceedings of the 19th IFAC World Congress, 2014. Cape Town, South Africa, 7729–7734.

14. Kaldmäe, A., Kotta, Ü ., Shumsky, A., and Zhirabok, A. Faulty plant reconfiguration bymeasurement feedback: sensor location. In Proceedings of the 9th IFAC Symposium on Fault Detection, Supervision and Safety for Technical Processes. 2015, Paris, France, 1283–1288.

15. Kotta, Ü ., Tõnso, M., Shumsky, A. Ye., and Zhirabok, A. Feedback linearization and lattice theory. Syst. Control Lett., 2013, 62(3), 248–255.

16. Serpas, M., Hackebeil, G., Laird, C., and Hahn, J. Sensor location for nonlinear dynamic systems via observability analysis and max-det optimization. Comput. Chem. Eng., 2013, 48, 105–112.

17. Shumsky, A. Ye. Fault diagnosis of sensors in autonomous underwater vehicle: adaptive quasi-linear parity relations method. In Proceedings of the 6th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Process. 2006, Beijing, P.R. China, 415–420.

18. Singh, A. K. and Hahn, J. Determining optimal sensor locations for state and parameter estimation for stable nonlinear systems. Ind. Eng. Chem. Res., 2005, 44(15), 5645–5659.

19. Ucinski, D. Optimal sensor location for parameter estimation of distributed processes. Int. J. Control, 2000, 73(13), 1235–1248.

20. Zhirabok, A. N. and Shumsky, A. Ye. The Algebraic Methods for Analysis of Nonlinear Dynamic Systems. Dalnauka, Vladivostok, 2008 (in Russian).


Back to Issue