Development of adaptive dual predictive control schemes based on Wiener–Hammerstein models

Abstract

Adaptive MPC schemes often employ local linear approximation of the system dynamics, which may not be adequate to capture the dynamic behavior of systems exhibiting strongly nonlinear dynamics. In particular, it is challenging to control a system exhibiting input multiplicity behavior at its optimum operating point as the steady-state gain matrix can smoothly become singular at the optimum operating point. In this work, with the aim of controlling systems with fading memory that exhibit such strongly nonlinear dynamics, a novel adaptive dual nonlinear MPC (ADNMPC) formulation is developed based on discrete-time block-oriented models. The block-oriented models are parameterized using the generalized orthonormal basis filters (GOBF). The nonlinear black-box model is further used to formulate a stochastic optimal control problem. A deterministic approximation to the stochastic optimal control problem is then systematically derived. Subsequently, an ADNMPC scheme is developed using the deterministic approximation as a basis. The efficacy of the proposed approach is demonstrated by simulating the problem of controlling a continuously operated fermenter system at its optimum operating point. Analysis of the simulation study shows that in contrast to the conventional nonlinear MPC (NMPC), the proposed ADNMPC scheme injects perturbation to the process whenever a model update is needed while meeting the control objectives. Moreover, with reference to a non-adaptive NMPC controller, the proposed ADNMPC schemes achieve better servo control performance while controlling the fermenter at the singular optimum operating point.