Energy shaping plus damping injection control for a class of chemical reactors

Traditionally, stabilization of chemical reacting systems has been achieved with linear P or PD compensation schemes. Practical and numerical results have showed that classical linear compensation can yield acceptable performance. On the other hand, recent years have witnessed the emergence of systematic feedback control strategies based on energy and port-interconnected systems. These approaches exploit the physical structure of the chemical reactor to construct compensation schemes with physical appealing. The aim of this work is to show that traditional PD compensation for CSTRs can be interpreted in terms of mechanical system analogies. In the line of energy shaping plus damping injection for robotic systems, it is shown that proportional feedback is a type of potential energy shaping to accommodate a unique equilibrium point. On the other hand, derivative control acts as a damping injector for the energy balance within the chemical reactor. The stability proof uses a novel approach to convert the temperature dynamics into a second-order systems where the mechanical analogies become more evident. In this way, the stability analysis can be performed with singular perturbation methods with a Lyapunov function for the energy balance derived from a “potential plus kinetics” energy construction.