Serial advanced-multi-step nonlinear model predictive control using an extended sensitivity method. (December 2020) - Kim, Yeonsoo; Thierry, David M.; Biegler, Lorenz T.
Abstract: Nonlinear model predictive control (NMPC) can directly handle multi-input multi-output nonlinear systems and explicitly consider input and state constraints. However, the computational load for nonlinear programming (NLP) of large-scale systems limits the range of possible applications and degrades NMPC performance. An NLP sensitivity based approach, advanced-step NMPC, has been developed to address the online computational load. In addition, for cases where the NLP solving time exceeds one sampling time, two types of advanced-multi-step NMPC (amsNMPC), parallel and serial, have been proposed. However, in previous studies, a serial amsNMPC could not be applied to large-scale problems because of the size of extended Karush–Kuhn–Tucker matrix and its Schur complement decomposition, and the robustness was analyzed under a conservative assumption for memory effects. In this paper, we propose a serial amsNMPC using an extended sensitivity method to increase the online computation speed further. We successfully apply it to a large-scale air separation unit using the sparse matrix handling packages of Python, Pyomo, and k_aug tools. Furthermore, an auxiliary NLP formulation is defined to analyze the robustness. Using this with the key properties of an extended sensitivity matrix, we can prove robustness while avoiding the memory effects term. Highlights: NMPC Advanced multi-step NMPC (amsNMPC) proposed when system requires ¿ 1 sampling time for NLP solution Robust stability proved through additional NLP & using its objective function as Lyapunov function Performance is demonstrated on large-scale air separation unit and CSTR Serial amsNMPC requires significantly less online computation time than ideal NMPC.