Open AccessStabilisation of unstable cascaded heat partial differential equation system subject to boundary disturbance
Author(s) -
Kang Wen,
Guo BaoZhu
Publication year - 2016
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2015.0953
Subject(s) - control theory (sociology) , cascade , disturbance (geology) , mathematics , partial differential equation , observer (physics) , boundary (topology) , backstepping , transformation (genetics) , stability (learning theory) , computer science , control (management) , engineering , mathematical analysis , adaptive control , physics , paleontology , artificial intelligence , biochemistry , chemistry , quantum mechanics , chemical engineering , machine learning , gene , biology
In this study, the authors consider boundary stabilisation for a cascade of unstable heat partial differential equation systems with interconnection at one end and general external disturbance at the control end. An unknown input type observer is first designed by sliding mode control method to estimate the state, and its Filippov type solution is determined. To design an output feedback, they need to know a state feedback which could be realised by the backstepping transformation. The transformation transforms the system into an equivalent target system where the governing equations are stable. To deal with the disturbance, they apply the active disturbance rejection control to estimate the disturbance by output. Based on observer and disturbance estimator, an output feedback control is then designed. The existence of solution to the closed‐loop system is proved and the stability is concluded. Finally, some numerical simulations are presented for illustration.