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