Abstract
Efficient temperature control requires more than air temperature measurements. Relevant variables, such as wall, ceiling, and other construction temperature evolution are usually unmeasured. Estimation of such quantities is often difficult because they are not observable with respect to available data. Their availability however would allow efficient control design. In this paper, we propose a method for designing state observers that efficiently estimate not only observable but also nonobservable (but detectable) state variables. Our method uses contraction semigroup, to obtain observer with a monotonic error reduction. Proposed approach gives twice as fast estimation as pure simulation and avoids transitional error standard observer would have. Problem of state estimation in building control applications is an important one. Attractiveness of obtaining values of physically unmeasurable variables is easily visible, as it would allow more efficient methods of temperature control. In this paper, authors discuss the problem of such estimation using a lumped capacitance model. This type of model is usually only detectable but not observable. Methods of observer tuning for such systems are not discussed properly in the literature and require special consideration. In this paper, three approaches for estimation are compared: pure model, eigenvalue shifting, and contraction semigroup observer. Results are illustrated with numerical experiments.
Highlights
One of the currently important areas of control and electrical engineering is the problem of efficient energy usage in building installations [1, 2]
E idea of using dedicated control strategies for housing buildings is not yet popular; it is believed that it would lead to both increase in comfort and more efficient energy usage
It is often suggested to decompose the system into observable and unobservable subspaces; such decomposition for our case is not practical. Another way to solve the problem with lack of observability was presented in article [12] where indistinguishable states were aggregated into one state. e decomposed system has its own observable state variables that cannot be used for the determination of values of physical state variables
Summary
One of the currently important areas of control and electrical engineering is the problem of efficient energy usage in building installations [1, 2]. We Mathematical Problems in Engineering present a methodology for estimating state under much weaker detectability condition. In such case, only asymptotic state estimation is possible. We present a contraction semigroup-based approach allowing estimation of the entire state vector (including nonobservable states) with continuous reduction of estimation error. We present three methods of constructing state estimator for a detectable system, including contraction semigroupbased approach. We verify its application for the analysed system and present discussion of methods’ effectiveness
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