Receding Horizon Control of Bilinear System with Hydraulic Delays

Abstract

All flow systems are subject to transport delays, which are determined by the flow rates in the system. When the flow rates themselves are control inputs, the system becomes subject to input-dependent state delays, which poses significant theoretical problems. In this paper we propose a model predictive control scheme for a generic multi-variable heat transport system, where flows to the individual consumers can be manipulated by a centralized controller. The control design takes the transport delay into account by means of an explicit discretization of the transport equation, which is a partial differential equation. Different discretization methods are considered, giving rise to a high-order bilinear system model in discrete time. The control problem is formulated as a linear quadratic receding horizon problem with terminal cost. Simulation studies show that the control problem can be solved using standard software and that the Lax-Friedrichs discretization method appears to be the most suitable of the investigated methods.