EIGENVALUE PROBLEMS ARISING IN THE CONTROL OF A DISTRIBUTED-PARAMETERBIOREACTOR

A distributed-parameter model of a continuous-flow fixed-bed reactor i s studied. The main emphasis lies on a structural property of the part ial differential equation (PDE) system model. This property, which in lumped parameter systems is called the nonminimum phase property, has certain implications in the controller design. The controller design f or the PDE model is constructed via semidiscretisation. The only space variable of the PDE model is discretised by using Galerkin's finite e lement method (FEM). For some parameter values of the PDE model the li nearising control of the semidiscretised model results in unstable beh aviour in the sense that the zero dynamics of the model is unstable. T his same unstable behaviour was also earlier observed in using the ort hogonal collocation for the semidiscretisation. Connections between th e location of the zeros of the original PDE model linearised around it s steady-state solution and the stability/instability properties of th e linearising control of the semidiscrete model are discussed in relat ion to the same issues in lumped-parameter differential system models.