Control design for convection‐reaction systems with storage effects and positive relative degree

Abstract One‐dimensional distributed‐parameter systems consisting of several convection‐reaction equations, which are distributedly coupled with a reaction equation, are considered. To solve the open‐loop control problem for these kind of systems, an inversion‐based approach is proposed. Along the common characteristic projection, the system can be reduced to a single partial differential equation (PDE) whose boundary conditions (BCs) result from the particular choice of the output to be tracked. The solution of this latter equation constitutes the basis of the control design. The particular properties of the scalar boundary value problem (BVP) to be solved depend on the coupling structure of the originally given convection‐reaction system. While in most cases the output has a relative degree of zero, for practical applications a relative degree of one is of particular interest. In this case, the obtained scalar BVP which describes the internal dynamics, possesses the structure of an infinite‐dimensional differential‐algebraic equation (DAE). Within the paper, the properties of the solution of both problems are discussed from a system analytical point of view.