Estimation of Derivatives and Reconstruction of Discontinuities
In many technical processes better results are achieved when not only the measurements but also their derivatives are used in process control. Additionally, the identification of fast process variations may be favorable in order to react suitably.
In practice, measurement noise makes the estimation of derivatives and the identification of fast process changes difficult. Recent algebraic methods for these tasks provide good noise attenuation and allow for efficient real-time implementation.
Here, the key challenge is the parameterization in practical applications, since the wrong parameterization causes poor estimation results. Therefore, methods for the systematic selection of estimation parameters are developed at the Chair of Systems Theory and Control Engineering.
A. Othmane, L. Kiltz, and J. Rudolph, Survey on algebraic numerical differentiation: historical developments, parametrization, examples, and applications, International Journal of Systems Science, 2022. DOI
A. Othmane, J. Rudolph, Data and computation efficient model-based fault detection for rolling element bearings using numerical differentiation, 2021 5th International Conference on Control and Fault-Tolerant Systems (SysTol), 2021, Pages 163-168. DOI
A. Othmane, J. Rudolph, H. Mounier, Systematic comparison of numerical differentiators and an application to model-free control, presented at ECC 2021, selected for 2021 European Control Conference Special Issue. DOI
A. Othmane, J. Rudolph, H. Mounier, Systematic comparison of numerical differentiators and an application to model-free control, European Journal of Control, Vol. 62, 2021 European Control Conference Special Issue, Nov. 2021, Pages 113-119. DOI
A. Othmane, H. Mounier, J. Rudolph, Parametrization of algebraic differentiators for disturbance annihilation with an application to the differentiation of quantized signals, in: 24th International Symposium on Mathematical Theory of Networks and Systems MTNS 2020, IFAC-PapersOnLine, Volume 54, Issue 9, 2021, Pages 335-340. DOI
A. Othmane, J. Rudolph, H. Mounier, Analysis of the parameter estimate error when algebraic differentiators are used in the presence of disturbances, in: 21th IFAC World Congress, IFAC-PapersOnLine, Volume 53, Issue 2, 2020, Pages 572-577. DOI
L. Kiltz, C. Join, M. Mboup, and J. Rudolph, Fault-tolerant control based on algebraic derivative estimation applied on a magnetically supported plate, Contr. Eng. Pract., 26, 107-115, 2014.
L. Kiltz and J. Rudolph, Parametrization of algebraic numerical diﬀerentiators to achieve desired filter characteristics, in: Proc. 52nd IEEE Conference on Decision & Control, Florence, Italy, December 10–13, 2013, pp. 7010–7015, 2013.
L. Kiltz, M. Janocha and J. Rudolph, Algebraic estimation of impact times: juggling a ball with a magnetically levitated plate, in: Proc. 2nd Int. Conf. on Systems and Computer Science, Villeneuve d'Ascq, France, August 26-27, 2013, pp. 145-149, 2013.
L. Kiltz, M. Mboup, and J. Rudolph, Fault diagnosis on a magnetically supported plate, in: Proc. 1st Int. Conf. on Systems and
Computer Science, Villeneuve d'Ascq, France, August 29-30, 2012.
Interpretation und Anwendung algebraischer Ableitungsschätzer
Video: Juggling a table tennis ball with a plate floating in a magnetic field
The floating plate is automatically controlled in such a way that a table tennis ball bounces continuously. Ball position is not measured. Instead, collisions between the 2.7 g table tennis ball and the 4.7 kg tabletop are detected using a simple mathematical process model and algebraic estimation methods. The estimation results are used to move the plate appropriately.
Beiträge zur Steuerung der Flughöhe eines auf einer elektromagnetisch gelagerten Platte springenden Balls (Bachelor-Arbeit 2012)