This paper focuses on boundary control of distributed parameter systems (also called infinite dimensional systems). More precisely, a passivity based approach for the stabilization of temperature profile inside a well-insulated bar with heat conduction in a one-dimensional system described by parabolic partial differential equations (PDEs) is developed. | Journal of Computer Science and Cybernetics, , (2016), 59–72 DOI: NONLINEAR CONTROL OF TEMPERATURE PROFILE OF UNSTABLE HEAT CONDUCTION SYSTEMS: A PORT HAMILTONIAN APPROACH HOANG NGOC HA1 , PHAN DINH TUAN2 1 Dept. of Control and Chemical Process Engineering, University of Technology, VNU–HCM; Email: 2 Hochiminh City University of Natural Resources and Environment; Abstract. This paper focuses on boundary control of distributed parameter systems (also called infinite dimensional systems). More precisely, a passivity based approach for the stabilization of temperature profile inside a well-insulated bar with heat conduction in a one-dimensional system described by parabolic partial differential equations (PDEs) is developed. This approach is motivated by an appropriate model reduction schema using the finite difference approximation method. On this basis, it allows to discretize and then, write the original parabolic PDEs into a Port Hamiltonian (PH) representation. From this, the boundary control input is therefore synthesized using passive tools to stabilize the temperature at a desired reference profile asymptotically. In particular, a simple proportional passive controller with a relaxing condition for the control gain matrix is adopted. The infinite dimensional nature of the original distributed parameter system in the PH framework is also discussed. Numerical simulations illustrate the application of the developments. Keywords. Port Hamiltonian framework, passivity, boundary control, model reduction. 1. INTRODUCTION In this paper, the authors deal with open systems in which (unstable) heat conduction processes take place. In general, such processes belong to irreversible thermodynamic systems and are distributed in space and time. As a matter of fact, their dynamics are described by parabolic partial differential equations (PDEs) [1–3]. The distributed parameter process systems are usually highly .
