Real-time nonlinear global state observer design for solar heating systems

Abstract Nowadays it is important to investigate and develop solar water heating systems as an environmentally friendly technology. For this reason we introduce a physically-based nonlinear mathematical model that applies to a wide range of solar heating systems. In commercial solar heating systems not all state variables are monitored by direct measurements, since some of them may be technically difficult or expensive to measure. For a better monitoring and more efficient control of the system it may be useful to estimate the unmeasured state variables. As a novelty, we apply a global nonlinear state observer to a solar domestic water heating system. The state observer has been established relatively recently in the field of control theory. The state observer we worked out enables us to estimate the unmeasured state variables in real-time. This observer is global in the sense that it works starting from any initial state. A further contribution of this work is a rather general algorithm for the practical application of the real-time estimation process, and we also give bounds of the estimation error and a practical method to decrease this error. Comparing calculated and measured values for a real particular solar heating system, we justify the usability of the state observer and the estimation process. On the basis of measured data, we show that the nonlinear mathematical model corresponding to the applied nonlinear observer is more accurate than the linear model corresponding to the classical linear Luenberger-type observer, so it is reasonable to apply the nonlinear observer.