# Offline Identification of a Laboratory Incubator
## 1 Introduction  
Laboratory incubators provide controlled-environment conditions for microorganisms. Biological materials have specific temperature requirements for cultivation and growth processes [1]. Despite the fact that incubators are insulated and enclosed, the material loading processes can cause significant thermal disturbances in the incubator chambers. This effect is called the door-opening effect, and the recovery from this effect is one of the most challenging problems in the design of high-performance laboratory incubators [2; 3; 4]. System identification methods are used to construct mathematical models for dynamic systems from collected input-output data [5]. These methods have been used in a wide variety of research fields, from material science to biomedical engineering and neuroscience to automatic control for linear and nonlinear systems, e.g., [6; 7; 8; 9; 10; 11; 12; 13]. In [6], system identification methods are used to obtain the behavior of the entire molten salt electrolysis process. In [7], a sleep stage classification method is proposed. The method employs a system identification model, which is the state-space model, to obtain a basic model giving the discrimination features for the further classification stage. In [8; 9], the identification problems in nonlinear systems by using nonlinear system identification models are examined in detail. In [10], the sample complexity of linear system identification using input-output data is analyzed. In [11], the potential to successfully use nonlinear system identification for nonlinear neural circuits is demonstrated. In [12], two model predictive control algorithms are compared to each other, and it is shown that the algorithm employing the system identification methodoutperforms the other. In [13], an open-source system identification software package is presented. The package includes system identification methods for input-output transfer function models and state-space models. Prediction error methods (PEM) are one of the most popular families of system identification methods in the community. They have been applied successfully in the context of system modeling in the literature, e.g., [14; 15; 16; 17; 18]. In [14], a linear system identification procedure based on a full Bayesian framework is proposed. The procedure is applied for neural activity prediction and temperature prediction purposes. In [15], a study of model identification for two electrical vehicle battery types is presented. The equivalent circuit battery model is parameterized by PEM. In [16], a heat exchange system is parameterized through system identification. The task of parameter estimation for applied model structures is made by using PEM. In [17], the development of a flight dynamics model for an unmanned aerial vehicle is considered. System identification is applied to actual flight data, and various models with different structures are examined. In [18], the identification of a quadcopter autopilot system is presented. It is demonstrated that the proposed method has the ability to capture the autopilot dynamics and predict the outputs accurately. In [19], short-term room temperature models are obtained by using PEM. It is shown that k-step-ahead prediction gives successful performance results. The dynamics of systems can be modeled by using previous experiences and physical knowledge that are derived from similar systems. To the best of the authors' knowledge, no research has been found in the published literature to conduct the modeling of laboratory incubators. Besides, the multi-layered structure of laboratory incubators makes it difficult to perform mathematical modeling based on physical equations. Therefore, the studies targeting the modeling of laboratory incubators using system identification methods will make a significant contribution to the literature. In this study, we aim to find a model for a laboratory incubator.