Design of Integral Controllers for Nonlinear Systems Governed by Scalar Hyperbolic Partial Differential Equations

The paper deals with the control and regulation by integral controllers for the nonlinear systems governed by scalar quasi-linear hyperbolic partial differential equations. Both the control input and the measured output are located on the boundary. The closed-loop stabilization of the linearized mod...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on automatic control 2017-09, Vol.62 (9), p.4527-4536
Main Authors: Ngoc-Tu Trinh, Andrieu, Vincent, Cheng-Zhong Xu
Format: Article
Language:English
Subjects:
Analysis of PDEs
Asymptotic stability
Automatic
Boundary control
Closed loop systems
Engineering Sciences
exponential stability
hyperbolic system
Iron
Lyapunov function
Mathematical model
Mathematics
Nonlinear systems
numerical simulation
Optimization and Control
Partial differential equations
proportional and integral (PI) controller
Topology
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The paper deals with the control and regulation by integral controllers for the nonlinear systems governed by scalar quasi-linear hyperbolic partial differential equations. Both the control input and the measured output are located on the boundary. The closed-loop stabilization of the linearized model with the designed integral controller is proved first by using the method of spectral analysis and then by the Lyapunov direct method. Based on the elaborated Lyapunov function, we prove local exponential stability of the nonlinear closed-loop system with the same controller. The output regulation to the set-point with zero static error by the integral controller is shown upon the nonlinear system. Numerical simulations by the Preissmann scheme are carried out to validate the robustness performance of the designed controller to face to unknown constant disturbances.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2017.2666040