Stability analysis of nonlinear processes using empirical state affine models and LMIs

A novel methodology is proposed for the analysis of robust stability of a n onlinear process under PI (Proportional-Integral) control. The analysis is based on state-affine empirical models regressed from input-output data. Th e state model is represented by a set of polynomial matrices nonlinear with respect to the manipulated variables. This model in combination with a lin ear PI controller results in a closed loop model that can be shown to lie i n a polytope of matrices. This allows for the formulation of a Lyapunov sta bility test in terms of a simple set of LMIs (linear matrix inequalities). This set of inequalities can be also expanded to account for input saturati on. The stability analysis produces regions of stability, in terms of the P I controller parameters, that are significantly larger than the regions pre viously calculated by a singular value test. The issues of saturation and m odeling error are also incorporated into the analysis. The technique permit s also to test the stability of the closed loop system with a gain scheduli ng PI controller. The conservativeness of the analysis is assessed by compa rison to closed loop simulations of a highly nonlinear CSTR (continuous sti rred tank reactor) under PI control. (C) 2001 Elsevier Science Ltd. All rig hts reserved.