Stabilization of distributed systems using irreversible thermodynamics

Abstract

We connect thermodynamics and the passivity theory of nonlinear control. The storage function is derived from the convexity of the entropy and is closely related to the thermodynamic availability. We relate dissipation to positivity of the entropy production. In this form the supply function is a product of force and flow variables in deviation form. Feedback signals originate from intensive variables like temperature, pressure and composition. We show that the physical dimension of the system matters: The larger the distributed system is, the more difficult the stationary state may be to stabilize. Any chemical process can be stabilized by distributed PID control provided that the sensor and actuator locations are suitable. We apply the results to heat conduction and reaction diffusion equations.