A Nonlinear Model Predictive Control Tracking Application for a System of Cascaded Tanks

Abstract

Nonlinear Model Predictive Control (NMPC) formulations through quasi-Linear Parameter Varying (qLPV) embeddings have been brought to focus in recent literature. In this brief paper, we evaluate the application of this kind of control strategy to the reference tracking problem of a cascaded tank system. This benchmark application has four states and two control inputs, which represent the fluid inlets to the upper tanks. The levels of each of the four tanks dependent not only on these input flows, but also on bounded disturbance variables. The system exhibits nonlinearities due to the fluid dynamics, which are incorporated as state-dependent qLPV variables. This case study serves to illustrate how a Sequential Quadratic Program (SQP) is an elegant solution to NMPC design: the qLPV realisation of the nonlinear dynamics yields linear predictions at each sampling instant, which can be refined through sequential operations of a single QP. The resulting numerical toughness is much smaller than the Nonlinear Programs generated with “regular” NMPC design, which is very convenient. Moreover, the SQP solution provides estimates of the future scheduling parameters, with convergence properties. Using realistic simulations, we demonstrate the effectiveness of this control approach with respect to piecewise constant reference tracking and disturbance rejection, which are assessed using standard performance indexes.