On optimal test signal design for identifying control-oriented dynamical empirical locally linear-affin multi-models

• Applicant: Professor Dr.-Ing. Andreas Kroll
• Subject Area: Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: from 2017 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 335920452

• Final Report Year: 2021

Final Report Abstract

The objective of the project was the development and examination of methods for designing test signals for nonlinear system identification with locally affine Takagi-Sugeno (TS) multi-models. At first, process model free test signal design methods were examined. These require little a-priori knowledge and permit gaining data for identifying an initial model. For this, in particular homogenization methods for multi- sine and multi-step signals were developed. These yield high quality models while permitting a systematic and transparent design. These initial models enable a subsequent model-based optimal test signal design. With respect to the process model-based test signal design, methods were examined that reduce the uncertainty of the parameter estimates. Additionally, methods were developed, which drive the system such that particularly informative regions are traversed. Process model-based methods design test signals that are optimal w.r.t. the model type and the assessment criterion. The multi-model structure of the TS models was exploited. The uncertainty reduction targeting test signal designs parametrize signal models such that a metric on the Fisher information matrix (FIM) is optimized. The recursive dependencies in partial derivatives due to a dynamic model occurring when evaluating the FIM make the optimization a hard task. Different assessment criteria, signal types, and simplifications were examined. One result was that local model parameters could be omitted in the test signal design without compromising the resulting model quality while reducing computational efforts. Furthermore, methods were developed to drive the system through informative regions in the scheduling space. These methods exploit knowledge about the system contained in the initial model. It was shown that parts of the transition regions between the local models are particularly informative. There, ‘way points’ are positioned. The sequence of these way points is defined by acknowledging the eigen dynamics of the autonomous system. In order to move from one way point to the next, a model-predictive controller is used which exploits the multi- model structure. This way, the entire experiment is assembled. Cases studies showed that the systematic error of the parameter estimates could be reduced with this design strategy. The methods were examined, characterized, demonstrated and statistically confirmed in two simulation studies and lab experiments on two actuators and on a 3-tank system. A Matlab(TM) toolbox for test signal design was developed, which is freely available from the applicant for non- commercial use.

Publications

• On optimal experiment design for identifying premise and conclusion parameters of Takagi-Sugeno models: nonlinear regression case, Applied Soft Computing, Nr. 60, S. 407-422, 2017
  Kroll, A., & Dürrbaum, A.
  (See online at https://doi.org/10.1016/j.asoc.2017.07.015)
• Optimal Experiment Design for Identifying Dynamical Takagi-Sugeno Models with Minimal Parameter Uncertainty, Proceedings of the 18th IFAC Symposium on System Identification (SysID), Stockholm, Schweden, Juli 2018
  Gringard, M. & Kroll, A.
  (See online at https://doi.org/10.1016/j.ifacol.2018.09.163)
• Zum optimalen Offline-Testsignalentwurf für die Identifikation dynamischer TS-Modelle: Steuerfunktionen zur optimalen Schätzung der Partitionsparameter, Proceedings of the 28th Workshop Computational Intelligence, Dortmund, November 2018
  Gringard, M. & Kroll, A.
  
• Zur Homogenisierung von Testsignalen für die nichtlineare Systemidentifikation, at – Automatisierungstechnik, Nr. 67 (10), S. 820-832, 2019
  Gringard, M. & Kroll, A.
  (See online at https://doi.org/10.1515/auto-2019-0041)
• On considering the output in space-filling test signal designs for the identification of dynamic Takagi-Sugeno models, Proceedings of the 21st IFAC World Congress, Berlin, Juli 2020
  Gringard, M. & Kroll, A.
  (See online at https://doi.org/10.1016/j.ifacol.2020.12.1336)
• Toolbox zum Testsignalentwurf für Standardtestsignale für die Identifikation von Eingrößensystemen: Prozessmodellfreie und -basierte Methoden, Proceedings of the 30th Workshop Computational Intelligence, Berlin, November 2020
  Himmelsbach, M. & Kroll, A.