Lecture Notes on Modelling and Control of Mass Balance Systems

The aim of these lecture notes is to give a self content presentation of the modelling of engineering systems that are governed by a law of mass conservation and to briefly discuss some control problems regarding these systems. Modelling issues are first addressed in Sections 2 to 11. The general statespace model of mass balance systems is presented. The equations of the model are shown to satisfy physical constraints of positivity and mass conservation. These conditions have strong structural implications that lead to particular Hamiltonian and Compartmental representations. The modelling of mass balance systems is illustrated with two simple industrial examples : a biochemical process and a grinding process. Some open loop stability properties are briefly presented and illustrated with these examples. The control issue is then addressed in Sections 12 to 14. In general, mass balance systems have multiple equilibria, one of them being the operating point of interest which is locally asymptotically stable. However if big enough disturbances occur, the process may be lead by accident to a behaviour which may be undesirable or even catastrophic. The control challenge is then to design a feedback controller which is able to prevent the process from such undesirable behaviours. Two solutions of this problem are briefly described namely (i) robust output feedback control of minimum phase mass balance systems and (ii) robust state feedback stabilisation of the total mass.