ScienceDirect IFAC-PapersOnLine 48-28 (2015) 484–489 Available online at www.sciencedirect.com 2405-8963 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2015.12.175 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Blind Identification, Sensors, Temperature Measurement, System Identification. 1. INTRODUCTION Temperature measurement is a fundamental measurement quantity and one of the seven SI base units in the physi- cal world. Traditionally, the measurement of temperature would involve the insertion of a thermometer into the measurement environment and taking the reading when the measurement has stabilised. Although considered ad- equate for many applications, this may not be sufficiently accurate enough when the temperature fluctuates. Among several alternative technologies, thermocouples provide an inexpensive and robust method of measuring tempera- ture over a wide range and at low cost (Childs (2001)). However, the design of a thermocouple-based temperature measurement system involves a compromise between ro- bustness and speed of response. This presents major chal- lenges when measuring temperature fluctuations that have a frequency significantly greater than the sensor band- width. The challenge of obtaining an accurate temperature measurement is not restricted to the case of fluctuat- ing temperature variations. For example in semiconductor manufacturing, the accuracy of an in situ temperature measurement system that utilizes contact temperature sensors, such as thermocouples or resistance temperature detectors (RTDs), depends on the amount of thermal con- tact between the transducer and the wafer surface (Tan et al. (2006)). If a good thermal contact between the sensor and the wafer is not achieved, the measurement errors can potentially be significant thereby requiring some method of correction. One approach that can be used to compensate for the sensor measurement error is to increase the effective band- width of the sensor using software-based compensation techniques. A requirement of this method is that a dy- namic model of the sensor is available and the sensor model parameters are known before the compensation can be performed. Additionally, the estimated parameters should take into account the measurement environment and any other factors that influence the dynamic characteristics of the sensor. In other words, the parameters of the model should be estimated when the sensor is in situ. A method known as the loop current step response (LCSR) is often used for this purpose. It involves injecting a current into the sensor that is much larger than the one used under Abstract: Compensation for the dynamic response of a temperature sensor usually involves the estimation of its input on the basis of the measured output and model parameters. In the case of temperature measurement, the sensor dynamic response is strongly dependent on the measurement environment and fluid velocity. Estimation of time-varying sensor model parameters therefore requires continuous in situ identification. This can be achieved by employing two sensors with different dynamic properties, and exploiting structural redundancy to deduce the sensor models from the resulting data streams. Most existing approaches to this problem assume first-order sensor dynamics. In practice, however second-order models are more reflective of the dynamics of real temperature sensors, particularly when they are encased in a protective sheath. As such, this paper presents a novel difference equation approach to solving the blind identification problem for sensors with second-order models. The approach is based on estimating an auxiliary ARX model whose parameters are related to the desired sensor model parameters through a set of coupled non-linear algebraic equations. The ARX model can be estimated using conventional system identification techniques and the non-linear equations can be solved analytically to yield estimates of the sensor models. Simulation results are presented to demonstrate the efficiency of the proposed approach under various input and parameter conditions. * School of Electronics, Electrical Engineering and Computer Science, Queen’s University, Belfast (e-mail: pgillespie05@qub.ac.uk) ** Department of Electronic Engineering, National University of Ireland Maynooth, Maynooth, Co. Kildare, Ireland (e-mail: phung@eeng.nuim.ie) *** School of Mechanical and Aerospace Engineering, Queen’s University, Belfast (e-mail: r.kee@qub.ac.uk) **** School of Electronics, Electrical Engineering and Computer Science, Queen’s University, Belfast (e-mail: s.mcloone@qub.ac.uk) Philip D. Gillespie * Peter C. Hung ** Robert J. Kee *** Se´ an F. McLoone **** Blind Characterisation of Sensors with Second-Order Dynamic Response