Unknown input observer design for linear time-invariant multivariable systems based on a new observer normal form

Abstract

In various applications in the field of control engineering, the estimation of the state variables of dynamic systems in the presence of unknown inputs plays an important role. Existing methods require the so-called observer matching condition to be satisfied, rely on the boundedness e variables or exhibit an increased observer order of at least twice the plant order. In this article, a novel observer normal form for strongly observable linear time-invariant multivariable systems is proposed. In contrast to classical normal forms, the proposed approach also takes the unknown inputs into account. The proposed observer normal form allows for the straightforward construction of a higher-order sliding mode observer, which ensures global convergence of the estimation error within finite time even in the presence of unknown bounded inputs. Its application is not restricted to systems which satisfy the aforementioned limitations of already existing unknown input observers. The proposed approach can be exploited for the reconstruction of unknown inputs with bounded derivative and robust state-feedback control, which is shown by means of a tutorial example. Numerical simulations confirm the effectiveness of the presented work.

Keywords:

• Multivariable systems
• normal forms
• robust state estimation
• sliding mode observation
• unknown input observer

Acknowledgments

The authors would like to thank Roland Falkensteiner for the constructive discussions and the important input during the coffee breaks.

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant agreement 734832. The financial support by the Christian Doppler Research Association, Austria, the Austrian Federal Ministry for Digital and Economic Affairs and the National Foundation for Research, Technology and Development, Austria is gratefully acknowledged. This work was partially supported by the Graz University of Technology LEAD project ‘Dependable Internet of Things in Adverse Environments’.

Notes on contributors

Helmut Niederwieser

Helmut Niederwieser received his MSc degree in Information and Computer Engineering from Graz University of Technology in 2019. He is a PhD student at the Institute of Automation and Control, Graz University of Technology. He currently holds a Junior Researcher position at BEST - Bioenergy and Sustainable Technologies GmbH, Graz, Austria. His research interests include robust state and parameter estimation in thermochemical and thermotechnical processes.

Markus Tranninger

Markus Tranninger received his MSc degree in Electrical Engineering from Graz University of Technology in 2015, and he completed his PhD at the Institute of Automation and Control, Graz University of Technology in 2020. He currently holds a Postdoc position at the Institute of Automation and Control at Graz University of Technology, Austria. He is part of the Graz University of Technology research center on Dependable Internet of Things. His research interests include state estimation and fault detection for complex dynamical systems.

Richard Seeber

Richard Seeber received his MSc degree in Electrical Engineering from Graz University of Technology in 2012, and he completed his PhD at the Institute of Automation and Control, Graz University of Technology in 2017. He currently holds a Postdoc position at the Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems. His research interests include theory of sliding mode control systems, control of automotive test beds, and control of systems with actuator constraints.

Markus Reichhartinger

Markus Reichhartinger received his MSc degree in Information and Computer Engineering from Graz University of Technology, Austria in 2006, and he completed his PhD at the Control and Mechatronic Systems Group, Klagenfurt University, Austria in 2011. He currently holds a Associate Professor position at the Institute of Automation and Control at Graz University of Technology. His research interests include the theory and applications of sliding mode control as well as automatic control applications in the automotive industry, biomedicine and biotechnology.