Hadi Malek

Performance analysis of fractional order extremum seeking control.

Extremum-seeking scheme is a powerful adaptive technique to optimize steady-state system performance. In this paper, a novel extremum-seeking scheme for the optimization of nonlinear plants using fractional order calculus is proposed. The fractional order extremum-seeking algorithm only utilizes output measurements of the plant, however, it performs superior in many aspects such as convergence speed and robustness. A detailed stability analysis is given to not only guarantee a faster convergence of the system to an adjustable neighborhood of the optimum but also confirm a better robustness for proposed algorithm. Furthermore, simulation and experimental results demonstrate that the fractional order extremum-seeking scheme for nonlinear systems outperforms the traditional integer order one.

A fractional order maximum power point tracker: Stability analysis and experiments

This paper presents a fractional order extremum seeking control scheme for maximum power point tracking tasks to better accommodate rapid varying solar irradiance for photovoltaic (PV) arrays. The stability analysis of the proposed control algorithm is presented first. Then the new algorithm is benchmarked against the integer order extremum seeking control. Our extensive simulation and experimental results show that, our proposed maximum power point tracker has faster convergence speed in comparison with integer order one.

Tuning Fractional Order Proportional Integral Controllers for Time Delayed Systems With a Fractional Pole

First order plus time delay model is widely used to model systems with S-shaped reaction curve. Its generalized form is the use of a single fractional pole to replace the first order (single-time constant) model, which is believed to better characterize the reaction curve. Using time delayed system model with a fractional pole as the starting point, in this paper, designing fractional order controllers for this class of fractional order systems is investigated. The novelty of this paper is on designing the integer order PID and fractional order PI and [PI] controllers for these class of systems. The simulation and lab experimental results are both included to illustrate the effectiveness of the proposed tuning method. By comparing the results of PID controller, fractional order PI and [PI] controllers, the advantages of the fractional order controller are clearly demonstrated in the case of controlling the single fractional pole plants with constant time delay.© 2011 ASME

Fractional Order Extremum Seeking Control: Performance and Stability Analysis

In this paper, a novel extremum-seeking control algorithm called fractional order extremum-seeking control is analyzed and benchmarked against the traditional integer order one. Utilizing fractional order operators in extremum-seeking scheme improves the convergence speed, robustness, and performance of this method without employing additional blocks. Using averaging model, the detailed analysis of fractional order extremum-seeking control is presented. Simulation and experimental results support the mathematical analysis and demonstrate that the proposed scheme outperforms the traditional extremum-seeking algorithm.

BICO MPPT: A Faster Maximum Power Point Tracker and Its Application for Photovoltaic Panels

This paper develops a maximum power point tracking (MPPT) algorithm to optimize photovoltaic (PV) array performance and make it more compatible to rapidly varying weather conditions. In particular, a novel extremum seeking controller (ESC), which uses a Bode ideal cutoff (BICO) filter in its structure, is designed and tested on a simulated PV array. The new algorithm is compared against the commonly used ESC MPPT algorithm with first-order filters. The BICO extremum seeking controller achieves transient rise to the MPP faster than the common extremum seeking MPPT, which is the faster and more robust method among all other methods. This claim has been discussed and proved mathematically in this paper, in addition to simulation illustrations. This faster extremum seeking algorithm enables PV systems to detect rapid variations in the environmental conditions like irradiation and temperature changes.

An Improved Maximum Power Point Tracking Based on Fractional Order Extremum Seeking Control in Grid-Connected Photovoltaic (PV) Systems

This paper presents a fractional order extremum seeking control scheme for grid-connected photovoltaic (PV) systems tasks to better accommodate rapid varying solar irradiance for photovoltaic (PV) arrays. The stability analysis of the proposed control algorithm is presented first. Then the new algorithm is benchmarked against the integer order extremum seeking control. Our extensive simulation and experimental results show that, our proposed maximum power point tracker has faster convergence speed in comparison to integer order and incremental conductance algorithm and also less total harmonic distortion (THD) in the injected current to the grid.Copyright

Design of optimal lighting control strategy based on multi-variable fractional-order extremum seeking method

Abstract In recent years, the light-energy consumption accounts for quite a large proportion of total electricity consumption. In this paper, an optimal lighting control strategy is designed for a lighting system with multiple lighting sources, to decrease electric energy consumption and increase energy efficiency. In the proposed control strategy, a novel multi-variable fractional-order extremum seeking control (FO ESC) strategy is implemented in minimizing the light-energy consumption by separately regulating the brightness of multi-lighting sources, while a PID method is applied to guarantee the desired lighting level. The proposed scheme is presented to not only raise the convergence rate and enhance the control accuracy, but also to improve the search efficiency of the minimum light-energy consumption by manipulating the fractional-order. Experimental results including comparison with the corresponding integer-order (IO) ESC show that the light-energy consumption under the proposed strategy can approach a smaller neighborhood of the minimum lighting-energy point more quickly.

A Note on the Lyapunov Stability of Fractional-Order Nonlinear Systems

In this paper, stability of fractional order (FO) systems is investigated in the sense of the Lyapunov stability theory. A new definition for exponential stability of the fractional order systems is given and sufficient conditions are obtained for the exponential stability of the FO systems using the notion of Lyapunov stability. Besides, a less conservative sufficient condition is derived for asymptotical stability of FO systems. The stability analysis is done in the time domain. Numerical examples are given to show that the obtained conditions are effective and applicable in practice. INTRODUCTION Although the idea of differentiation and integration of arbitrary (fractional) order faces difficulty to find a real-world application for more than 300 years, recently, these operators have gained interests among engineering scientist and researchers for their superior results in control and modeling of physical systems [1-5]. With the increasing trend of introduced FO models for electrical, mechanical and chemical processes, in depth study of these systems from different points of view such as control [6-9], dynamical behavior analysis [10-12], and stability analysis [13-16] is noticeably growing. One of the fundamental topics, which should be taken into consideration in all dynamic systems, is the stability analysis. There are limited published works in the area of FO systems [14-20] that are mainly concentrated on the stability analysis of FO linear systems [17-20]. From literature, the main approach for stability analysis of FO LTI systems mostly depends on calculating eigenvalues of state equations. However, Lyapunov stability of linear fractional systems based on an energy balance approach has been studied in [21], [22]. Nonetheless, seeking a direct systematic approach for stability analysis of FO nonlinear systems is still under development and investigation [23], [24]. The most well-known method to analyze the stability of nonlinear integer order systems is the Lyapunov stability technique. Very recently, the Lyapunov stability problem for the FO systems has been investigated in literature [25-28]. Fractional Lyapunov direct method for checking the stability problem in FO systems has been introduced in [25], [26]. Furthermore, FO systems have been studied from the aspect of Mittag-Leffler stability problem in [25]. In [26], introducing the class-K functions to the fractional Lyapunov direct method, asymptotical stability of the FO systems is discussed in the sense of fractional Lyapunov direct method. In [27], uniform stability of fractional order systems is studied proposing a complement theorem for [25]. This paper deals with the problem of stability, i.e. asymptotical stability and, in particular, exponential stability of nonlinear FO systems utilizing the extension of the Lyapunov stability notion. To the authors’ best knowledge, the notion of exponential stability is not extended for fractional order systems, yet. Using the concept of fractional integration operator and GrownwallBellman lemma, different stability conditions are obtained for the FO systems. All the analyses are done in the time domain and the conditions are derived for asymptotical and exponential stability of the FO systems. In the case of asymptotical stability,

A single-stage three-phase grid-connected photovoltaic system with fractional order MPPT

This paper propose a new maximum power point tracker called fractional order extremum seeking control for grid-connected photovoltaic (PV) systems tasks to better accommodate rapid varying solar irradiance for photovoltaic (PV) arrays. The new algorithm is benchmarked against the integer order extremum seeking control and incremental conductance algorithms. Our extensive simulation results show that the proposed maximum power point tracker has faster convergence speed in comparison to integer order and incremental conductance algorithm and also less total harmonic distortion (THD) in the injected current to the grid.

A model for calculating the magnetic & copper losses of an Inductive Power Transfer (IPT) pad

In this paper, an analytical expression is proposed to compute the total losses of a circular pad for Inductive Power Transfer (IPT) system. These losses can be separated into winding losses and core losses. The proposed analytical expression includes both conduction and induction losses due to eddy current effects at high frequency in the winding and ferrite core. Experimental results are shown to confirm the validity of the analytical model.