Subspace Identification of Temperature Dynamics

Abstract

Data-driven modeling and control of temperature dynamics in mechatronics systems and industrial processes are challenging control engineering problems. This is mainly because the temperature dynamics is inherently infinite-dimensional, nonlinear, spatially distributed, and coupled with other physical processes. Furthermore, the dominant time constants are usually long, implying that in practice due to various economic and time constraints, we can only collect a relatively small number of data samples that can be used for data-driven modeling. Finally, since sensing and actuation of temperature dynamics are often spatially discrete, special attention needs to be given to sensor (actuator) placement and identifiability problems. Motivated by these challenges, in this manuscript, we consider the problem of data-driven modeling and validation of temperature dynamics. We have developed an experimental setup consisting of a long aluminum bar whose temperature dynamics is influenced by spatially distributed heat actuators and whose temperature is sensed by spatially distributed thermocouples. We address the noise reduction problem and perform step response and nonlinearity analyses. We combine predictor based subspace identification methods with time series analysis methods to identify a multiple-input multiple-output system model. We provide detailed treatments of model structure selection, validation, and residual analysis problems under different modeling and prediction scenarios. Our extensive experimental results show that the temperature dynamics of the experimental setup can be relatively accurately estimated by low-order models.

Subspace identification of low-dimensional Structural-Thermal-Optical-Performance (STOP) models of reflective optics

“…Additional technical details related to the used subspace identification method can be found in. 36,52,53 Our goal is to estimate the following state-space model:…”

“…We use a version of the subspace identification method that is derived and summarized in our previous papers. 34,36,52,53 We implemented the subspace identification method in Python. We used LiveLink for MATLAB module to generate data sets for testing the subspace identification method.…”

“…The VARX model is postulated such that the output of the system at the time instant k is a linear combination of the past inputs and outputs, from k − 1 until k − p, for more details, see. 34,36,52,53 Here p is referred to as the past window. The first step of the subspace identification method is to estimate the parameters of the VARX model and past window p. We use a simple least-squares technique to estimate the VARX model parameters.…”

Data-driven Estimation, Tracking, and System Identification of Deterministic and Stochastic Optical Spot Dynamics

“…Motivated by these challenges, in this manuscript we propose and experimentally verify a unified data-driven framework and tools for the estimation, tracking, and prediction of optical spots by using data-driven Kalman filters. We address the first challenge by adapting, tuning, and experimentally testing the subspace system identification algorithm [41][42][43] for estimating the Kalman filter models of stochastic disturbances. We address the second challenge by developing a method for estimating the covariance matrices of Kalman filter models.…”

A novel method for adaptive control of deformable mirrors

“…14,[21][22][23][24][25][26][27] To properly analyze, predict, and control the influence of thermal phenomena on DM behavior, it is often necessary to use data-driven techniques to estimate thermal dynamics. 21,28,29 If not properly modeled and if not taken into account when designing control algorithms, these nonlinearities and time-varying DM behavior, can significantly degrade the achievable closed-loop performance of AO systems. Widely used approaches for DM control are based on pre-estimated linear time-invariant DM models in the form of influence matrices, see for example 18,30 and references therein.…”