Decoupling through input–output blending

Abstract

The paper presents a novel decoupling method, based on blending the input and output signals of linear dynamical systems. For this purpose, blend vectors are introduced and calculated such that the minimum sensitivity of the controlled mode is maximised, while the worst case gain of the other subsystems is minimised from the blended input to the blended output. The problem is transformed to a standard optimisation program subject to Linear Matrix Inequality constraints. An arising rank constraint is resolved by an alternating projection scheme. The method is presented based on the decoupling of a single mode, but the extension to decouple multiple modes is also discussed. Numerical examples are given to validate the method and to illustrate how the proposed approach can be applied for control engineering problems.

Keywords:

• Decoupling
• minimum sensitivity
• linear matrix inequality
• mode control

Acknowledgements

The authors would like to thank for the valuable recommendations and discussions for Bálint Patartics and György Lipták. The research leading to these results is part of the FLEXOP project.

Disclosure statement

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

Notes

1 On the other hand, our aim is to avoid the use of additional frequency filters, due to their explicit appearance and effect in the computation of the blending vectors (see Section 4).

2 The D terms are retained in the equations only for completeness; however, their value is zero during the optimisation process.

Additional information

Funding

The research was supported by the ÚNKP-18-3, the ÚNKP-18-4 and the ÚNKP-19-4 New National Excellence Programs of the Ministry of Human Capacities. The research leading to these results is part of the FLEXOP project. This project has received funding from the European Unions Horizon 2020 research and innovation programme under grant agreement No 636307. This paper was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. The research reported in this paper was supported by the Higher Education Excellence Program of the Ministry of Human Capacities in the frame of Artificial Intelligence research area of Budapest University of Technology and Economics (BME FIKPMI/FM).