On positive systems with multivariable positive control: Process stabilization

The process stabilization is tackled from the perspective of a family of positive systems with multivariable positive control. This framework is consistent because each of the n state variables and m control inputs in chemical processes is in R₊. The aim is to provide multivariable positive feedback control schemes which take values in the hyperbox U∈R₊^m; while sufficient conditions are satisfied to ensure the stabilization process. Two approaches are discussed: the first is a sliding mode control based on hyperplanes intersecting a (n−m)-dimensional segment of the state space which comprises the equilibrium point; such scheme guarantees robust stability. The second is a continuous feedback stabilizer based on Lyapunov functions, which enhances convergence rate while stabilization is ensured. The process stabilization is shown with two examples: a heat exchanger and an isothermal continuous stirred tank reactor. Both examples illustrate the usefulness of the proposed framework of multivariable positive control.