Design of a Fractional Order PI (FOPI) for the Speed Control of a High-Performance Electrical Drive with an Induction Motor

Abstract

This paper describes the application of the Fractional Order PIs (FOPI) in the speed loop of a high performance induction motor electrical drive. In particular the speed tracking and load rejection capability of FOPI controller has been investigated and compared with both an integer-order PI and an IP both in simulation and experimentally with constant settling time. Illustrative study proves the simplicity and efficiency of the presented design method over integer controllers.

Fractional-Order PI Control of DFIG-Based Tidal Stream Turbine

“…When the time trends to zero, the first item of the molecule will be zero. Consequently, according to the automatic control theory, the settling time t se of this second-order system can be approximated in (14) for ±5% error bandwidth [39,64,66]. Then, the parameters k pe and k ie are deduced in (15) subsequently [63].…”

“…In the last few years, the FOPI controller, the combination of the fractional calculus theory and IOPI controller, has become increasingly attractive for control systems and applied successfully in many practical systems such as power electronic converters and hard disk drive servo systems [38,39].…”

“…Some researchers have already focused on the application of FOPI controller in the machine system [39,41,[46][47][48][49][50][51][52][53][54][55][56][57][58][59]. These references mainly focused on the controller parameters tuning methods according to different criteria.…”

“…In [41,46], MATLAB optimization toolbox FMINCON was adopted to minimize the phase margin; Newton iteration method was selected to maximize the gain margin in [47]; ITAE was used as the criterion of optimal parameters tuning in [48][49][50][51]; reference [48] applied PSO to find the minimum ITAE; Dieng A. utilized PSO to optimize a special objective function which could minimize the torque ripple [52][53][54]; in [55], a new non-linear function containing ITSE, settling-time, rising time, and maximum overshoot was minimized by PSO and BFO. There are still a few papers studying on the robustness of internal parameter variations and external disturbances [39,56,57]. Indeed, most of these papers compared the performance of IOPI and FOPI controllers.…”

A Frequency criterion for analysis of stability of systems with fractional-order derivatives

“…In modern approaches to the creation of models of processes and of the synthesis of control actions in dynamic systems, there are used fractional derivatives and integrals, which describe so-called fractal peculiarities of such processes [1,2]. In particular, the design of some electromechanical systems using fractional-order regulators significantly advances the possibilities of optimization of such systems [3][4][5][6]. The problems of analysis and synthesis of dynamic systems which are described by equations with derivatives of fractional orders have recently received considerable attention [7,8].…”