IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 57, NO. 3, MARCH 2010 975 Adaptive Nonlinear Direct Torque Control of Sensorless IM Drives With Efﬁciency Optimization Masood Hajian, Jafar Soltani, Member, IEEE, Gholamreza Arab Markadeh, and Saeed Hosseinnia Abstract—Efﬁciency optimization of induction motor (IM) drives is a major subject based on these drives’ extensive use in the industry. Among the different proposed methods, a model- based approach (MBA) seems to be the fast one. However, this method needs the motor parameters that must be correctly iden- tiﬁed. On the other hand, a search-based approach (SBA) is a parameter-independent method but needs a greater convergence time. In this paper, a novel model-based loss-minimization ap- proach is presented, which is combined with a backstepping direct torque control of the IM drive. An improved search-based method for efﬁciency optimization is also introduced. The proposed con- troller is realized in the stationary reference frame and has a fast-tracking capability of rotor ﬂux and electromagnetic torque. Moreover, a sliding-mode rotor-ﬂux observer is introduced, which is employed for simultaneous determination of rotor-ﬂux space vector, rotor speed, and rotor time constant. The proposed control idea is experimentally implemented in real time using a ﬁeld- programmable gate-array board synchronized with a personal computer. Simulation and experimental results are ﬁnally pre- sented to verify the effectiveness of the method proposed. Index Terms—Direct torque control (DTC), efﬁciency optimiza- tion, induction motor (IM), integrator backstepping, rotor ﬂux, sliding mode (SM). I. I NTRODUCTION T HREE-PHASE induction motors (IMs) are extensively used in the industry and consume more than 60% of industrial electricity [1]. This is why considerable efforts are being done to improve their efﬁciency [2]–[9]. The efﬁciency of electrical drives is greatly reduced at light loads, where the reference ﬂux magnitude is held on its initial value. Loss minimization is performed using high-quality materials and ex- cellent design procedures in the manufacturing process [2]–[5]. Moreover, expert control algorithms are employed in order to improve drive performance. The main approach in the latter ﬁeld is the adaptation of motor ﬂux to the load and speed variations [5]–[9]. It is worthwhile to mention that most of the proposed methods for this purpose have been presented in a rotating reference frame, particularly in the rotor-ﬂux-oriented (RFO) reference frame [5]–[7]. Manuscript received December 25, 2008; revised July 21, 2009. First published August 21, 2009; current version published February 10, 2010. M. Hajian, J. Soltani, and S. Hosseinnia are with the Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan 84154, Iran (e-mail: m.hajian@ec.iut.ac.ir; j1234sm@cc.iut.ac.ir; hoseinia@cc.iut.ac.ir). G. A. Markadeh is with the Department of Electrical Engineering, Faculty of Engineering, University of Shahrekord, Shahrekord 88186-34141, Iran (e-mail: arab-gh@eng.sku.ac.ir). Digital Object Identiﬁer 10.1109/TIE.2009.2029592 Control strategies to improve motor efﬁciency can be di- vided into three categories: 1) model-based methods; 2) search methods; and 3) power-factor improvement methods [5]. A model-based energy-optimal control of IMs has been described in [5]. Based on this method, for a given load torque and a given rotor speed, using the steady-state IM model in the rotor-ﬂux ﬁeld-orientation coordinate frame and considering a speed-dependent iron-loss shunt resistance, the average of motor input real power is minimized. The method of [5] conﬁrms that the IM efﬁciency becomes maximized when the averages of two-axis power-loss components obtained in the RFO reference frame are equal. Abrahamsen et al. [5] proposed a conventional PI controller to generate the rotor-ﬂux reference in order to make the real input power minimized. One may note that the motor cur- rents and power-loss components are harmonic polluted, and therefore, it is extremely difﬁcult to precisely tune the afore- mentioned PI controller. In addition, because, at any step of time, the method needs to know the average of two-axis power- loss components, it is required to store the voltage and current samples, which results in some phase lag. In [8], a so-called fast ﬂux search controller has been pre- sented for a conventional DTC-based IM drive, in which a simple ﬂux search method is employed to maximize the IM efﬁciency. Kaboli et al. [8] claimed that, for a given value of output power (a given load torque and a given rotor speed), the IM efﬁciency becomes maximized when the motor input current reaches its minimum value. However, considering the IM iron losses, this is not perfectly true for induction drives, and the reason can be found in [5] and [10]. Furthermore, in the conventional DTC method, using the bang-bang or hysteresis torque and ﬂux controllers, in order to have a good tracking and a fast dynamic response, one is required to have a narrow hysteresis band [11]–[14]. This results in a large chattering, as well as a high variable switching frequency. Loss minimization of the IM drive is presented in this paper for each given value of load torque and rotor speed. That is achieved by adjusting the magnitude of the rotor-ﬂux reference using both a model-based method and a simple search one. The IM model in the rotating reference frame attached to the rotor- ﬂux space vector is employed in the model-based approach (MBA). According to this model, the optimal motor slip is determined using an algebraic quadratic equation and is used in the steady-state model of IM to calculate the optimal motor ﬂux for each speciﬁc load torque. Efﬁciency optimization is also presented using an online search method. However, stator real input power instead of stator input current is selected as the objective function in the 0278-0046/$26.00 © 2010 IEEE