An Extended Luenberger Observer for HVAC Application using FMI

In this paper we show how a Functional Mockup Unit (FMU) may be used for the realization of an Extended Luenberger Observer (ELO), which may be considered the deterministic version of an Extended Kalman Filter (EKF). The ELO has advantages over an EKF in some situations, such as lower computational burden and improved convergence. Nonlinear observers, such as those that make use of changes of coordinates to linearize, or approximately linearize the estimate error, are continuoustime dynamical systems that use so-called output injection to modify the dynamics of a model. Output injection provides a similar feedback effect as the correction step of an EKF. However, nonlinear output injection is a slightly FMU different use case because the ELO is a continuous time object. It is realized by feedback around a modelsharing type of continuous time FMU, in contrast with the algorithmic realization of a discrete-time EKF, which uses the co-simulation form of FMU. We illustrate the design and realization of an ELO for a building HVAC example, in which we estimate unmeasured heat flows and unmeasured boundary conditions for use in a building “digital twin.” We also make some remarks about model reduction and the challenges in realizing a conventional EKF for these types of models.