IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 6, JUNE 2014 3041 Tuning Method Aimed at Optimized Settling Time and Overshoot for Synchronous Proportional-Integral Current Control in Electric Machines Alejandro G. Yepes, Member, IEEE, Ana Vidal, Student Member, IEEE, Jano Malvar, Student Member, IEEE, Oscar L ´ opez, Member, IEEE, and Jes ´ us Doval-Gandoy, Member, IEEE Abstract—Implementation of proportional-integral controllers in synchronous reference frame is a well-established current con- trol solution for electric machines. Nevertheless, their gain selection is still regarded to be poorly reported, particularly in relation to the influence of the computation and modulation delay. To fill this gap, a design procedure to set the maximum gains for an accept- able damped response, with the delay being considered, has been recently proposed. In contrast, this paper presents a simple rule of thumb to achieve nearly the minimum settling time in combination with negligible overshoot for reference changes. This conclusion is theoretically demonstrated by the analysis of root locus diagrams and of overshoot versus settling time trajectories for sweeps of gain values. The design approaches aimed at gain maximization and the one developed here are compared, revealing that the lat- ter provides shorter settling time and much lower overshoot in the command tracking response, while allowing greater stability margins. On the other hand, the proposed tuning method leads to a worse disturbance rejection, but by including an active resis- tance with enhanced pole/zero cancellation as a second degree of freedom, both design procedures attain comparable and optimized attenuation of disturbances. Matching simulation and experimen- tal results validate the theoretical study. Index Terms—Current control, digital control, machine vector control, pulse width modulation converters, variable speed drives. I. INTRODUCTION I N electric drives for high-performance industrial applica- tions, both steady-state and transient characteristics provided by the control are crucial. Improving the control performance of ac drives has been the focus of comprehensive research during the last decades, and it still continues to receive a lot of atten- tion from the research community and industry. Field oriented control (FOC), which is one of the most established strategies, consists in a dual-loop involving an outer regulator in charge of Manuscript received March 26, 2013; revised June 13, 2013; accepted July 26, 2013. Date of current version January 29, 2014. This work was supported in part by the Spanish Ministry of Science and Innovation and in part by the European Commission, European Regional Development Fund (ERDF) under the project DPI2012-31283 and the FPI scholarship BES-2010-031334. This paper was presented in part at the IEEE Energy Conversion Congress and Exposition, Denver, CO, USA, September 2013. Recommended for publication by Associate Editor J. R. Espinoza. The authors are with the Department of Electronics Technology, University of Vigo, Vigo 36310, Spain (e-mail: agyepes@uvigo.es; anavidal@uvigo.es; janomalvar@uvigo.es; olopez@uvigo.es; jdoval@uvigo.es). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPEL.2013.2276059 torque/flux regulation and an inner current controller [1], [2]. The performance of the current control determines the over- all system performance, so special care should be devoted to its design in order to achieve fast and accurate current regula- tion [3], [4]. Several current control techniques for ac drives are able to achieve a very fast response in combination with negligible steady-state error. The hysteresis controller, for instance, attains an almost instantaneous tracking of the reference and is quite robust to instability problems, at the expense of either a vari- able switching frequency (fixed band) or a certain complexity (variable band) [2], [5], [6]. Predictive and deadbeat regula- tors ideally also provide a very fast dynamic response, but they are usually very sensitive to uncertainties in the plant parame- ters [7]–[10]. Minimum time current control was introduced to theoretically obtain the fastest transient response by finding the optimal control voltage for tracking the current reference un- der the voltage limit constraint [3], [11]; nevertheless, its large computational load may be a significant drawback in industrial applications [4]. In any case, the most widely spread current control technique for FOC is that based on PI control in syn- chronous reference frame (SRF) [1], [2], [4], [12]–[20]. A considerable research effort has been devoted to compare and develop alternative PI controllers in SRF, with particular focus on the internal model control (IMC) [14], complex-vector analysis [12], [13], [17], and high ratios of fundamental-to- sampling frequencies [15]–[18]. Some improvements have been successively incorporated in the conventional PI current control structures, such as axes cross-coupling decoupling [12]–[14], time delay compensation [15], [16], [18], active resistance for a better disturbance rejection [13], [16], [19]–[22], a reference modification for faster response under the converter voltage con- straint [4], and enhanced pole/zero cancellation in the discrete- time domain with the fundamental frequency being close to the sampling one [15]. However, despite the widespread us- age of synchronous PI controllers, their gain tuning is still a topic that is regarded to be poorly reported [2]. Some basic design guidelines that relate the PI gains with the time- and frequency-domain specifications have been previously obtained by assuming a first-order approximation of the system [14], but the time delay should not be disregarded when attempting to obtain the best gain adjustment [23]. Furthermore, when ac- tive resistance is implemented, it has been recommended to select its value so that the poles of the disturbance rejection response are mapped in the same locations as those given by the 0885-8993 © 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.