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

Ngoc-Tu Trinh (1) , Vincent Andrieu (1) , Cheng-Zhong Xu (1)

1 LAGEP - Laboratoire d'automatique et de génie des procédés

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.

Mots clés: hyperbolic; PI controller; nential stability; numerical simulation; system; expo-; Lyapunov function; partial differential equations; Index Terms—Boundary control

Domaines: Automatique / Robotique; Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Ngoc-Tu Trinh, Vincent Andrieu, Cheng-Zhong Xu. Design of Integral Controllers for Nonlinear Systems Governed by Scalar Hyperbolic Partial Differential Equations. IEEE Transactions on Automatic Control, 2017, 62 (9), pp.4527 - 4536. ⟨10.1109/TAC.2017.2666040⟩. ⟨hal-01643291⟩