NONLINEAR MODEL PREDICTIVE CONTROL USING 2ND-ORDER MODEL APPROXIMATION

A model predictive control (MPC) algorithm using a nonlinear discrete perturbation model for lumped parameter systems has been proposed. The nonlinear ordinary differential equations (ODEs) representing the process are locally approximated using the terms up to second order in the Taylor expansion. Using regular perturbation technique and certain simplifying assumptions, the resulting equations are integrated over a sampling interval to obtain an approximate discrete model of the system. The Morse lemma is used to identify the conditions under which the proposed approximation will prove distinctly superior over the linear approximation. Under perfect model assumption, the performance of the proposed algorithm is demonstrated by simulating regulatory control of two continuously stirred tank reactors (CSTRs) characterized by zero steady-state gain with respect to one manipulated input at the optimum operating point and attendant change in the sign of the steady-state gain across the optimum. The MPC algorithm based on the proposed second-order model is shown to improve the closed loop performance when compared to other nonlinear MPC algorithms. Finally, it is shown that the proposed control algorithm is robust for moderate variations in plant parameters.