An analytical solution for stability-performance dilemma of hydronic radiators

Thermostatic radiator valves (TRV) have proved their significant contribution in energy savings for several years. However, at low heat demand conditions, an unstable oscillatory behavior is usually observed and well known for these devices. This closed-loop instability is due to the nonlinear dynamics of the radiator which result in a large time constant and a large gain for the radiator at small flow rates. In order to improve stability of radiators under the low demand circumstance, one way is to replace the fixed-parameter controller of TRV with an adaptive controller. This paper presents a gain scheduling controller based on a proposed linear parameter varying model of radiator dynamics. The model is parameterized based on the operating flow rate, room temperature and radiator specifications. Parameters of the model are derived based on the proposed analytic solution that describes dissipated heat by a radiator to ambient air. It is shown via simulations that the designed controller based on the proposed linear parameter varying (LPV) model performs excellent and remains stable in the whole operating conditions.