Eliminating oscillations in TRV controlled hydronic radiators

Thermostatic Radiator Valves (TRV) have proved their significant contribution in energy savings for several years. However, at low heat demands, an unstable oscillatory behavior is usually observed and well known for these devices. The instability happens due to the nonlinear dynamics of the radiator itself which result in a large time constant and high gain for radiator at low flows. Taking the radiator heat as its output, we have developed this term analytically. The result is achieved by solving the partial differential equation describing the distributed radiator system with boundary conditions. Exploiting the analytic solution of the output heat, a linear parameter varying (LPV) model is parameterized in a systematic way. Time constant and radiator gain are appeared explicitly in this model. A gain schedule control is designed for TRV, inspired by the proposed LPV model. It is shown via simulations that the controller will guarantee both performance and stability in the whole operating conditions.