Open AccessSampled-data integral control of multivariable linear infinite-dimensional systems with input nonlinearities
Author(s) -
Max E. Gilmore,
Chris Guiver,
Hartmut Logemann
Publication year - 2022
Publication title -
mathematical control and related fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.658
H-Index - 21
eISSN - 2156-8472
pISSN - 2156-8499
DOI - 10.3934/mcrf.2021001
Subject(s) - control theory (sociology) , mathematics , multivariable calculus , context (archaeology) , stability (learning theory) , controller (irrigation) , square (algebra) , linear system , exponential stability , nonlinear system , control (management) , mathematical analysis , computer science , physics , control engineering , artificial intelligence , machine learning , quantum mechanics , engineering , biology , paleontology , agronomy , geometry
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.