—This paper presents a novel control algorithm for high-torque low-speed permanent magnet synchronous motors for direct drive applications. A new induced voltage based formulation of the electromagnetic torque is developed and a novel current control algorithm is designed to reduce the torque ripples which are originated from the flux harmonics. A prototype motor with relatively high induced voltage harmonics is designed and constructed and the experiment results of the Harmonic control algorithm are compared to the results of a conventional Field Oriented Control. Keywords—control; torque ripple; traction; current harmonic; permanent magnet synhcronous motor I. INTRODUCTION With the growing of Electric Vehicle (EV) industry and direct drive applications the requirement of high performance, low torque ripple motors is growing rapidly. Permanent Magnet Synchronous Motor (PMSM) has been considered as a proper candidate for EV applications due to its compactness, high torque and dynamic, robustness and high efficiency. Considering the EV application not only a fast torque response is required but also a smooth performance with minimum torque ripple at low speed is essential. However, PMSMs usually show a considerable torque ripple if it is not compensated. Torque ripples due to the cogging torque, current torque, current measurement and flux harmonics restrict the application of the PMSMs [1], [2], [3], [4]. These torque ripples cause undesirable mechanical vibration at low speed [1]. This paper deals with the torque ripples which are originated from non-sinusoidal and asymmetrical back EMFs. The tolerances and limitations in design and manufacturing of an electrical motor lead to asymmetrical EMFs in three phases which can consequently lead to torque ripples [5]. Also the ferromagnetic components are typically driven near or above the saturation flux density at least at nominal load operation. This leads to non-sinusoidal linked fluxes in the stator coils and, hence, creates disruptive torque ripple during operation when the motor is fed with sinusoidal currents developed by Field Oriented Control (FOC) [6]. Several methods are proposed to deal with this pulsating torques. These methods can be categorized into two main groups. The first group includes methods which deal with the motor design aspects such as winding modification, skewing etc. However, the applicability of these techniques is limited to newly developed motors, and they can result in a further complicated realization and higher manufacturing cost [1]. The second type includes the optimization of control algorithm to deal with non- sinusoidal EMFs. Due to the non-sinusoidal linked fluxes and the therefrom caused non-constant torque during operation when using sinusoidal phase currents, the standard dq- transformation is not suitable for an accurate control. Some authors have used a modified dq-model in order to overcome this problem [6]. Another approach is developing a modified non-sinusoidal EMF model of PMSM using dependent voltage and current sources [7]. Another similar approach is developing a back-stepping model of the motor [8]. It is also possible to calculate the actual non-sinusoidal air gap flux density distribution using extended Kalman filter [9]. Furthermore, the phase asymmetries are considered using recursive least square method [5]. There are also different efforts to reduce the torque pulsation by modification the control algorithm. An iterative learning control algorithm for torque ripple reduction caused by stator saturation is proposed in [6] and [1]. Predicative control for torque ripple reduction using the derivative of the currents is discussed in [10]. In [11] a closed-loop control strategy is developed to suppress the circulation of zero sequence currents and amplitude of the dominant current harmonics caused by the non-sinusoidal EMFs. The zero sequence component is considered as one additional degree of freedom that has to be managed. A method based on the third harmonic current to improve the torque performance of a five phase PMSM is discussed in [12]. Reference [13] uses the speed harmonic by a proper injection of current harmonics into the motor for the direct calculation of maximum torque per ampere angle. Variable frequency methods are also addressed in some works [14]. The advantages of using instantaneous voltage control technique for torque ripple reduction in PMSM are discussed in [15]. Time error signals are generated directly from the different phase voltages. In [16] the abilities of pseudo derivative feedback controller to improve the performance of PMSMs at standstill and low speed regions are discussed. A predictive current control for torque ripple reduction of a PMSM with variable This article is accepted and will published on the IEEE eXplore. All rights reserved. © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. switching frequency is addressed in [17]. The proposed control scheme is based on a FOC and optimizes the switching frequency on each sample. However, many authors suggest the modification of Direct Torque Control to reduce the torque ripple [18], [19]. Reference [20] considers the asymmetry of a six phase motor and design a modified DTC to deal with that. Another possibility to receive a low torque ripple is to make use of higher harmonics in the stator phase currents [6]. This paper presents a control algorithm which energizes the motor with three phase non-sinusoidal currents to compensate the non-sinusoidal EMFs. The motor torque formulation is derived using output active power principal and the current controller is designed to generate a very smooth torque at low speed. A motor prototype with a non-sinusoidal EMF is constructed and the control algorithm is validated using an electromechanical test bench. II. ELECTROMAGNETIC TORQUE FORMULATION The conventional FOC is based on the assumption of a sinusoidal phase flux linkage and currents. Benefiting from sinusoidal electrical properties, the park transformation can be used and the FOC can be applied. However, this is not always the case. The harmonics of the induced voltage cause the torque pulsation. The electromagnetic torque of a PMSM can be calculated using induced voltage. (1) P, T and ω are the output power, torque and rotational speed of the motor and Ei and Ii are the three phase EMFs and currents. Considering the total harmonics of currents and the derivation of fluxes and describing them using the Fourier series, we can achieve a more general form of the torque. It is supposed that the normalized induced voltages and the current are odd and symmetric as it is always the case in PMSM. Thus the general equation of the motor active power can be formulated as the multiplication of phase currents and induced voltages. This is given by: (2) An and Bm are the harmonic amplitudes of currents and induced voltages. In the case of n=m the first part of the power equation is given by: (3) In the case of n≠m the other term of the power is given by: (4) Both terms of power which are indicated in the equation (3) and (4) include zero terms which can be eliminated and the power can be given by: (5) It can be simply shown that in the case of sinusoidal currents and EMFs the famous torque formulation of PMSM can be achieved from equation (5) [21]. Once the order and the amplitude of harmonics of induced voltage are determined, the order and amplitude of current are computed in order to result in a constant torque. The general block diagram of the control algorithm is indicated in Fig. 1. III. HARMONIC CURRENT CONTROLLER The reference values of the three phase currents are calculated by the current estimator unit shown in Fig. 1. The current estimator unit receives the harmonics of the three phase induced voltages as well as cogging torque as inputs. These values are functions of motor position and speed. The reference value of the torque is computed by the speed control loop which can also be arbitrarily realized. The main part of the proposed control algorithm is the current estimator unit. It predicts the three reference currents of the three phases. The current calculation depends on the order and amplitude of the harmonics of the induced voltage. It is clear that the higher order harmonic terms require a very fast response of the current controller which due to the limited current and voltage capability of the power electronic device and predefined values of the motor inductances is not always realizable. The EMF harmonic spectrum of the prototype motor is indicated in Fig. 2 [22]. The functionality of the current estimator is described by assuming the 1th and 11th harmonics of the induced voltage. Now taking a look at the equation (5) it is possible to select the order of the current harmonics. It can easily be deduced with a good compromise between complexity and realizeability that the current should include the 1st and 11th harmonics. Now these known B1 and B11 and unknown A1 and A11 are put into the equation (5) and the rest of coefficients are set to zero. Fig. 1. Block Diagram of the control algorithm Hence, according to the equation (5) the power is given by: (5) The torque consists of a constant and a position dependent term including the 12th harmonic. The term corresponding to the 10th harmonic is eliminated automatically. Therefore, the amplitude and order of the current harmonics term can be determined to eliminate the position dependent term. This leads to a system of equations given by: (6) A1 and A 11 are calculated in each step and sent as the reference value of current to the current controller. Supposing a pure open loop torque controller, the reference value of torque is sent to the current estimator in case of the proposed controller. The optimized current