Efficient Nonlinear Model Predictive Control: Exploiting the Volterra-Laguerre Model Structure

An analytical solution to the nonlinear model predictive control (NMPC) optimization problem is derived for single–input single–output (SISO) systems modeled by second–order Volterra–Laguerre models. All input moves except the current move (m > 1 in the NMPC framework) are approximated by solving an unconstrained linear MPC problem which utilizes a locally accurate linear model of the process. This linear MPC problem has an analytical solution; this is substituted into a nonlinear equation which is solved exactly for the current input move, ∆u(k|k). Results using this multi–m NMPC formulation are superior to a previously developed analytical NMPC controller that required m = 1 (Parker and Doyle III, 1998).