Sampled-data integral control of multivariable linear infinite-dimensional systems with input nonlinearities

Gilmore, Max E.; Guiver, Chris; Logemann, Hartmut

Abstract

A low-gain integral controller with anti-windup component is presented for exponentially stable, linear, discrete-time, infinite-dimensional control systems subject to input nonlinearities and external disturbances. We derive a disturbance-to-state stability result which, in particular, guarantees that the tracking error converges to zero in the absence of disturbances. The discrete-time result is then used in the context of sampled-data low-gain integral control of stable well-posed linear infinite-dimensional systems with input nonlinearities. The sampled-date control scheme is applied to two examples (including sampled-data control of a heat equation on a square) which are discussed in some detail.

Citation

Gilmore, M. E., Guiver, C., & Logemann, H. (2022). Sampled-data integral control of multivariable linear infinite-dimensional systems with input nonlinearities. Mathematical Control and Related Fields, 12(1), 17-47. https://doi.org/10.3934/mcrf.2021001

• Journal Article Type: Article
• Acceptance Date: Dec 1, 2020
• Publication Date: 2022-03
• Deposit Date: Dec 11, 2020
• Publicly Available Date: Feb 1, 2022
• Print ISSN: 2156-8472
• Publisher: American Institute of Mathematical Sciences
• Peer Reviewed: Peer Reviewed
• Volume: 12
• Issue: 1
• Pages: 17-47
• DOI: https://doi.org/10.3934/mcrf.2021001
• Keywords: Anti-windup methods, discrete-time, input-to-state stability, integral control, quantization, sampled-data control, saturation, well-posed infinite-dimensional systems
• Public URL: http://researchrepository.napier.ac.uk/Output/2710376