Stabilisation of unstable cascaded heat partial differential equation system subject to boundary disturbance

• Published in: IET control theory & applications Vol. 10; no. 9; pp. 1027 - 1039
• Main Authors: Kang, Wen, Guo, Bao-Zhu
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 05.06.2016
• Subjects: active disturbance rejection control; backstepping transformation; Boundaries; boundary disturbance; boundary stabilisation; closed loop system; control system synthesis; disturbance estimator; Disturbances; Estimates; Filippov type solution; interconnection; Mathematical analysis; Mathematical models; numerical analysis; numerical simulations; observers; Output feedback; output feedback control; Partial differential equations; sliding mode control method; stability; state feedback; Transformations; unknown input type observer; unstable cascaded heat partial differential equation systems; variable structure systems; numerical simulations; active disturbance rejection control; boundary stabilisation; interconnection; Filippov type solution; control system synthesis; boundary disturbance; unstable cascaded heat partial differential equation systems; disturbance estimator; output feedback control; numerical analysis; backstepping transformation; closed loop system; state feedback; partial differential equations; stability; observers; variable structure systems; unknown input type observer; sliding mode control method
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2015.0953

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.