Most of the industrial applications are multipleinput multiple-output (MIMO) systems, that can be be identified using knowledge of the system's physics or from measured data employing statistical methods. Currently, there is the only class of statistical identification methods capable of handling the issue of vast MIMO systems -subspace identification methods. These methods, however, as all statistical methods, need data of certain quality, i.e. excitation of corresponding order, no data corruption, etc. Nevertheless, the combination of statistical methods and physical knowledge of the system could significantly improve system identification. This paper presents a new algorithm which provides remedy to insufficient data quality of certain kind through incorporating of prior information, e.g. known static gain or input-output feedthrough. The presented algorithm naturally extends classical subspace identification algorithms, that is, it adds extra equations into the computation of system matrices. The performance of the algorithm is shown on a case study and compared to current methods, where the model is used for an MPC control of a large building heating system.Index Terms-Subspace methods; Identification for control
I. MOTIVATIONWith 39 %, buildings contribute significantly to total energy usage in 2005, as stated by the U. S. Energy Information Administration [1]. This poses strong motivation for creation of advanced and energy saving HVAC (Heating, Ventilating, and Air Conditioning) systems [2]. Significant amount of energy can be saved using predictive control strategies (see project OptiControl 1 ) compared to the conventional strategies. Widely used control strategy, weathercompensated control, can lead to poor energy management or reduced thermal comfort even if properly set up, because it utilizes current outside temperatures only. In case of sharp change of weather, there is an improper control action due to the energy accumulation in large buildings, resulting in over-or underheating of the building. Even though HVAC control systems have been improved significantly during recent years, predictive controller described in [3] introduces a different approach to the heating system control design. There is, however, a crucial condition for the successful control, that is, properly identified model of the system. Model identification can be performed by variety of methods, physical modeling or statistical approach among others. This paper presents incorporation of prior information into subspace identification methods. These methods originally emerged as a conjunction of linear algebra, geometry and S. Prívara, J. Cigler, Z. Váňa, L. Ferkl and M.Šebek are with Department of Control Engineering, Faculty of Electrical Engineering of Czech Technical University in Prague, Karlovo náměstí 13, Czech Republic samuel.privara@fel.cvut.cz 1 http://www.opticontrol.ethz.ch/ system theory and compared to the classical identification methods [4], they provide user with several advantages such as numerical robustness, natu...