Computational method for decentralized integral controllability of low dimensional processes

Abstract

Decentralized integral controllability (DIC) concerns the existence of stable decentralized controllers with integral action having stable independent detuning. The only information needed for DIC is the steady state process gain matrix. Hence it can be used to select control structures systematically at the early stage of control system design. The problem to check the necessary and sufficient condition of DIC is a type of robust stability problems for real parameter uncertainties and it is very hard to compute except for low dimensional processes. Available necessary and sufficient conditions which can be computed exactly are for processes of dimension up to 3 × 3. Here, an algebraic method which checks positivity of multivariable polynomials is applied to calculate DIC of processes. It provides a computable procedure for processes of dimension up to 5 × 5. It is a necessary condition for DIC of higher dimension processes and can be applied before a complex necessary and sufficient condition.