Grey-box model identification of temperature dynamics in a photobioreactor

•A grey-box model identification strategy is presented.•A model structure is derived from first principles.•An UKF is used as the training algorithm.•A Schur method for calculating the matrix square root in the UKF is proposed.•The identification approach is experimentally validated. This article presents a general strategy for grey-box model identification and deals with some issues that might be present in real life applications. An Unscented Kalman Filter (UKF) is used to train a grey-box temperature model with experimental data from an internally illuminated photobioreactor. The model structure is derived by means of heat balance analysis with the aid of a heat flow diagram. Then, the model is discretized and given an alternative state space representation in such a way that parameters can be readily estimated with an UKF. In order to avoid performance degradation and to improve the stability of the UKF algorithm, the prediction error covariance matrix is estimated and the state covariance matrix square root is calculated with a method based on Schur spectral decomposition to ensure positive semi-definiteness.