Contents I. Introduction
Amongst all other types of electrical motors, the SRMs are the simplest in the structure. Where they have no windings nor permanent magnets in the rotor. They can offer a reliable, low-cost, less maintenance, and extended-speed range drives. These great features made them optimal candidates to be adopted in electric vehicles applications [1]. However, due to the salient nature of both the stator and the rotor, their magnetic characteristics are nonlinear function of rotor position. Therefore, a major deterrent of wider usage of SRM drives is the significant ripple in the motor torque specially at high speed ranges. Many strategies have been proposed to reduce the torque ripple of SRMs, these strategies can be categorized under two main headings, first the machine design optimization and second the control algorithms. The machine design such as modifications on its geometry or the winding configuration of the machine [2]–[4] can reduce the torque ripple of the machine to some extent, but after the machine have been already manufactured, it is very challenging to modify its geometric dimensions. More effective ways can greatly minimize the torque of an existing machine is based on control techniques [5]–[9], but some of these techniques may be very complicated and therefore, the cost and complexity of the controller increases, a simpler control techniques based only on the optimization of the switching angles are developed [10]–[13], but these techniques still have some ripples in the torque waveform. Over the past few years, TSFs are gaining attention in the field of torque quality improvement in SRM drives. TSF intelligently divides a commanded reference torque between all the phases of the machine by reshaping the commanded current waveform to each phase. Where, if the current controller tracked this waveform ideally, then the summation of the torques set up by each phase will add up to a total constant torque, in this way the machine torque is controlled indirectly and therefore, eliminating torque ripple. Several TSFs profiles have been introduced by previous works. The selection of a suitable TSF is challenging specialty at high speed drives. Because as the speed increases the induced voltage will also increases and therefore, the phase current cannot follow the commanded current. As a result, the effectiveness of any TSF will decrease at high speed drive. Previous authors suggested two metrics to evaluate the TSFs, they are the rate of change of flux linkage and the copper losses. These two metrics can be included as a second obj ectives beside reducing the torque ripple. TSF can be modified online or offline, online TSF [14]–[16], are modified online by means of torque and speed feedback. In the areas of offline TSFs, both the switch-on and the overlap angles can be optimized to improve the torque quality of the machine in addition to other secondary objectives. In [17], various TSFs types such as linear, cubic, sinusoidal, and exponential TSFs are discussed and assessed. A genetic algorithm is employed to optimize the switch-on and the overlap angles of these TSFs, the objective is to minimize the value of the rate of change of flux linkage and the copper losses. In [18] a new group of TSFs is introduced, amongst these TSFs, the best one is specified and proposed to minimize both the motor torque ripple and copper losses, the author used an analytical expression to convert the commanded torque directly in to its corresponding current waveform. In [19], offline TSF is proposed to minimize torque ripple of SRM while operating at high speed range, a multi-objective function is formed by combining two secondary objectives, first the RMS phase current (i.e. copper loss), second the rate of change of flux linkage. In this paper the sinusoidal TSF is selected and then offline optimized. The control variables are the switch-on angle and the overlap angle, the two variable optimization problem is solved using an improved version of the ant colony optimization (ACO), the main obj ective of this work is to enhance the torque profile of SRM specially at high speed range. Besides, a second objective is to reduce the RMS phase current as possible without effecting the average value of the motor torque. In addition, the optimized switch-on and overlap angles are applied to the online TSF in a closed loop speed controller to improve the dynamic torque waveform over an extended speed range. Simulation is carried out on a 4 kW, 1500 rpm, four-phase 8/6 SRM.
