Power-shaping control of reaction systems: The CSTR case

Power-shaping control is a recent approach for the control of nonlinear systems based on the physics of the dynamical system. It rests on the formulation of the dynamics in the Brayton–Moser form. One of the main obstacles for using the power-shaping approach is to write the dynamics in the required form, since a partial differential equation system submitted to sign constraints has to be solved. This work comes within the framework of control design approaches that could possibly generate a closer link between the notions of energy that are specific to reaction systems as derived from thermodynamics concepts, and the dynamic system stability theory. The objective of this paper is to address the design of power-shaping control to reaction systems, and more particularly the step of solving the partial differential equation system. In order to illustrate the approach, we have selected the classical yet complex continuous stirred tank reactor (CSTR) as a case study. We show how using the power-shaping approach leads to a global Lyapunov function for the unforced exothermic CSTR. This Lyapunov function is then reshaped by means of a controller in order to stabilize the process at a desired temperature.