Reaction invariants and their importance in the analysis of eigenvectors, state observability and controllability of the continuous stirred tank reactor

Abstract

Two different projection operators are found, projecting the state space of a continuous stirred tank reactor (C.S.T.R.) dynamic model on the space of asymptotically invariant states (or on the space of true invariant states for a batch reactor). The first projection gives an explicit expression for the invariants, but it requires a certain partitioning of the stoichiometric matrix. The other projection avoids this difficulty, but gives a description of the invariants by a set of equations which do not have full rank. Concerning the observability of the dynamical modes, it turns our that the invariants put certain restrictions on the observation matrix for the system to be observable. The corresponding conditions for the system to be controllable by feed composition control are briefly outlined. Certain properties of the solution of the linearized system are also analyzed.