Control of the temperature in the hot liquid tank by using a digital PID controller considering the random errors of the thermometer indications

• Published in: Energy (Oxford) Vol. 239; p. 122771
• Main Authors: Taler, Dawid, Sobota, Tomasz, Jaremkiewicz, Magdalena, Taler, Jan
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 15.01.2022; Elsevier BV
• Subjects: A mathematical model of the thermometer; Conduction heating; Conductive heat transfer; Control stability; Control systems; Controllers; Digital filters; Digital smoothing of thermometer readings; Domestic water heater; Electric filters; energy; Fluid filters; Fluid temperature control; Fluid temperature measurement; heat transfer; Inverse problems; liquids; Proportional integral derivative; Quotients; Random errors; thermometers; Water temperature; Fluid temperature control; Fluid temperature measurement; A mathematical model of the thermometer; Digital smoothing of thermometer readings; Domestic water heater
• ISSN: 0360-5442; 1873-6785
• DOI: 10.1016/j.energy.2021.122771

A digital PID (Proportional-Integral-Derivative) controller to maintain a constant hot water temperature in the tank was proposed. The thermometer's indications are subject to random errors. The water temperature is determined by solving the inverse problem for a thermometer in the form of a solid cylinder inside which the temperature is measured. The water temperature is determined using a first or second-order thermometer model. The use of differential quotients to calculate the first or second derivative after time causes the controller to be unstable. To increase the stability of the PID system operation, digital filters were used to eliminate the influence of random disturbances of the temperature indicated by the thermometer. This ensures stable, much faster, and more accurate operation of the controller. The operation of the PID controller with the proposed technique for determining the medium temperature was illustrated by using the example of an electric storage heater in which the water temperature should be equal to the pre-set temperature. The novelty of the presented PID control system is the determination of the fluid temperature based on the solution of the inverse problem of heat conduction formulated for a thermometer. As a result, the speed and accuracy of the PID controller are significantly improved. •The random errors in thermometer indication can make the PID controller inaccurate.•A novel inverse method for fluid temperature determination was developed.•A digital PID controller is resistant to random errors in thermometer indications.•A mathematical model of the hot water tank-thermometer system was developed.•The operation of the PID controller was tested for disturbed thermometer data.