A globally exponentially stable speed observer for a class of mechanical systems: experimental and simulation comparison with high-gain and sliding mode designs

ABSTRACT

It is shown in the paper that the problem of speed observation for mechanical systems that are partially linearisable via coordinate changes admits a very simple and robust (exponentially stable) solution with a Luenberger-like observer. This result should be contrasted with the very complicated observers based on immersion and invariance reported in the literature. A second contribution of the paper is to compare, via realistic simulations and highly detailed experiments, the performance of the proposed observer with well-known high-gain and sliding mode observers. In particular, to show that – due to their high sensitivity to noise, that is unavoidable in mechanical systems applications – the performance of the two latter designs is well below par.

KEYWORDS:

• Nonlinear systems
• observer theory
• mechanical systems
• high-gain and sliding mode observers

Acknowledgments

The authors are grateful to Frederic Mazenc for the help in the proof of Proposition 4.1 and Elena Panteley for some clarifications on PE and stability of the system (13) that significantly influenced the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Theorem 2 of Morgan and Narendra (1977) claims GAS in the simpler case when A(t) is a rank one matrix.

Additional information

Funding

This article is supported by Ministry of Education and Science of Russian Federation [GOSZADANIE 8.8885.2017/8.9, project number 14.Z50.31.0031].