A dynamic operability analysis approach for nonlinear processes

Current process operability indicators are mostly restricted to linear approximations of the process dynamics. Other operability analysis approaches that have the capability to include full nonlinear process models rely on mixed integer dynamic optimisation techniques which, in general, require large amount of computations. In this paper we propose a dynamic operability analysis approach for stable nonlinear processes that can be readily applied during process design and can be solved efficiently using a limited amount of computations. The process nonlinear dynamics are approximated by a series interconnection of static nonlinearities and linear dynamics, represented by the so-called Hammerstein–Wiener models. These type of models can often be obtained during process design where detailed steady-state nonlinear models are available, combined with some (usually limited) information on the process dynamics. Using an extended internal model control (IMC) framework, we investigate the interaction between the static nonlinearities and linear dynamics on the operability of the process. The framework extends the well-known equivalence between operability and invertibility of linear processes to nonlinear systems. In particular, by exploiting some results from the theory of passive systems we provide conditions that guarantee the existence of the inverse of the static nonlinearities. We show that the inverse can be attained inside a specific input/output region. This region imposes a constraint on the maximum magnitude of the signals that appear in the closed-loop and represents the effect of the static nonlinearities on the operability of the overall process. Dynamic operability is then quantified using a linear matrix inequality (LMI) optimisation approach that minimises a given performance criterion subject to the constraint imposed by the static nonlinearities.