关键词: 热电偶, 分数阶微积分, 传递函数, 参数估计

Abstract: The fractional order model of thermocouple is used to study the dynamic characteristics of thermocouple. In dynamic system temperature measurement, a delay of temperature response exists when the thermocouple is used to measure the transient temperature. The process of measurement is a time-delay process or genetic process. When thermocouple wires come into contact with an object being measured, the heat transfer occurs through the wires. The temperature on measuring junction results from the heat transfer between medium and measuring junction and the heat conduction between measuring junction and wires. A fractional order model of semi-infinite solid heat conduction is established based on the theory of fractional calculus. The proposed model describes the heat transfer between the measuring junction and the measured medium, including the heat transfer between the measuring junction and the wire. A fractional order transfer function is obtained by fractional Laplace transform. The transfer function describes the time lag of thermal inertia and the phase delay of thermal diffusion. An experimental system for measuring the surface temperature by thermocouple is built to collect the input and output data of thermocouple under the step perturbationed. Based on measured input and output data, the parameters and order of fractional order transfer function are estimated by using the new Luus-Jaakola algorithm. The experimental and calculated results show that the fitting results of variable fractional order transfer function are better than those of invariable fractional order transfer function.Key

Key words: thermocouple, fractionalcalculus, transferfunction, parameterestimation