A torque estimator using online tuning grey fuzzy PID for applications to torque-sensorless control of DC motors Dao Thanh Liem 1 , Dinh Quang Truong 2 , Kyoung Kwan Ahn ⇑ School of Mechanical and Automotive Engineering, University of Ulsan, Republic of Korea article info Article history: Received 30 April 2014 Accepted 19 January 2015 Available online 24 February 2015 Keywords: Torque estimation Parameters identification Grey predictor Online tuning fuzzy PID abstract DC motors are used indispensably in industrial applications because they provide such advantages as small size, high speed, low construction cost, and safe operation. A major area of research in DC motors is to determine a better method to measure the torque of motor shaft. The traditional way to measure the mechanical torque of a rotating shaft is attachment a torque transducer in the transmission system between the driving motor and the load. However, this technique requires additional parts for the trans- mission system, which makes the design more complicated, time consuming, costly in construction, and in many cases impossible to achieve. The purpose of this paper is to present a new method for estimating the load torque of a DC motor shaft by using a novel modelling method based on an adaptive control technique, named as online tuning grey fuzzy PID (OTGFPID). A test rig using a DC motor is setup to investigate the torque behaviour as well as to evaluate the developed estimator. Firstly, mathematical model is developed for the motor. Secondly, the experimental speed-torque data and the optimized motor model is used to optimize the torque estima- tor. Then the optimized estimator is used to estimate accurately the load torque. Finally, the capability of the optimized torque estimator has been validated with the practical experiments in comparison with a typical estimation method. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction DC motors are used indispensably in industrial applications because they provide such advantages as low friction, small size, high speed, low construction cost, and safe operation. DC motors also provide excellent speed control for acceleration, deceleration, and simple torque control, which is very difficult to achieve at a specified power when using inverters and AC motors. Many indus- trial processes require DC motor to operate with variable speed and variable torque machines to drive them. This reliable function has been provided by DC motors for over a century. Recent advancements in vehicle technologies have enabled DC motor applications to cast wider and wider net. One major area of research in vehicle technologies is to obtain the torque of a rotating shaft. This can be realized in several ways. One method to measure the mechanical torque of a rotating shaft is to attach an additional torque transducer in the transmission system between the driving motor and the load. However this configuration requires additional parts for the transmission system, which results in a design that is more complicated, time consuming, expensive in construction, and in many cases impossible [1–3]. Therefore, several alternative methods of torque estimation have been used [4–8]. Franco, Frankchek, and Grigoriadis [5] pre- sented a real-time engine brake torque estimation model for inter- nal combustion engines in which the instantaneous measured engine speed serves as the model input. Their model was separated into steady-state and transient torque estimations. From the immediate engine speed signal, they estimated in real-time the crankshaft torsion, due to the power stroke, and the mean engine. Flores, Reger, and Ramirez [6] introduced an algebraic approach for online load estimation and passivity, based on a boost-converter- driven DC motor system. The local estimates of the load value were achieved in a relatively short time interval by using a model-based, instantaneous estimation formula devoid of asymptotic conver- gence features. The main drawback of this method is that the uncertain load is assumed to be piecewise constant. In [7], Barcaro, Bianchi, and Magnussen discussed the potential for erroneous esti- mation of average torque in fractional-slot permanent-magnet motors. They investigated the current vector angle that allows http://dx.doi.org/10.1016/j.mechatronics.2015.01.004 0957-4158/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author at: School of Mechanical Engineering, University of Ulsan, Daehakro 93, Nam-gu, Ulsan 680-749, Republic of Korea. E-mail address: kkahn@ulsan.ac.kr (K.K. Ahn). 1 Graduate School of Mechanical Engineering, University of Ulsan, Republic of Korea. 2 School of Mechanical Engineering, University of Ulsan, Daehakro 93, Nam-gu, Ulsan 680-749, Republic of Korea. Mechatronics 26 (2015) 45–63 Contents lists available at ScienceDirect Mechatronics journal homepage: www.elsevier.com/locate/mechatronics