Tracking Economic Optimum of a Continuous Fermenter using Adaptive Dual Nonlinear MPC

Controlling a system exhibiting input multiplicity at its optimum operating point is a difficult task as the steady state gain matrix can be singular at the optimum operating point. Moreover, the optimum operating point can shift due to changes in the process parameters. To operate such a system profitably, it is necessary to locate and track the shifting economic optimum in the face of changing process parameters. In this work, we propose a frequent real time optimization (RTO) scheme that employs a Wiener type model parameterized using orthonormal basis filters (OBF) for locating the shifting optimum. Parameters of the Wiener model are identified online using the recursive least squares and further used for carrying out RTO as well as control tasks. The optimum setpoints that correspond to the shifting economic optimum are communicated to a control layer for tracking. Recently proposed adaptive dual nonlinear MPC (ADNMPC) is used for tracking the optimum setpoints. The ADNMPC algorithm is capable of injecting probing input signals into the system as and when required to enhance the learning ability of the recursive parameter estimation scheme while simultaneously performing the control task. The efficacy of the proposed control scheme is demonstrated by conducting simulation studies on a benchmark continuous fermentation system.