Control of Systems Exhibiting Input Multiplicities using Dual Nonlinear MPC. Issue 20 (2018) - Kumar, Kunal
Abstract: Control of a system exhibiting input multiplicity at an optimum (singular) operating point poses a challenging control problem due to loss of invertibility and change in the sign of the steady state gain in the neighbourhood of the optimum. In this work, for controlling systems exhibiting input multiplicities, we develop a novel adaptive dual NMPC (ADNMPC) formulation based on a Wiener model which is parameterized using orthonormal basis filters (OBF). The static nonlinear output map in the Wiener model is constructed using multidimensional quadratic polynomials. The OBF poles are chosen through an off-line identification exercise and the parameters of the static nonlinear map are updated on-line using recursive least squares algorithm. Similar to Kumar et al. (2017), by introducing concept of excitation horizon, the objective function in the NMPC formulation is modified to include terms that are sensitive to the parameter covariance. The proposed formulation provides su¢cient degrees of freedom to shape the probing signals. E¢cacy of the proposed approach is demonstrated by simulating problem of controlling a continuously operated fermenter system at its optimum operating point. Analysis of the simulation results shows that the proposed ADNMPC scheme judiciously injects perturbations into the process as and when required. The probing perturbations subside when the parameter estimates stabilize. In particular, it is observed that the intensity of the perturbation increase as the excitation horizon increases. The proposed on-line model adaptation also ensures better control performance with reference to a non-adaptive NMPC controller.