Tuning and auto-tuning of fractional order controllers for industry applications

Many real dynamic systems are better characterized using a non-integer order dynamic model based on fractional calculus or, differentiation or integration of non-integer order. Traditional calculus is based on integer order differentiation and integration. The concept of fractional calculus has tremendous potential to change the way we see, model, and control the nature around us. Denying fractional derivatives is like saying that zero, fractional, or irrational numbers do not exist. In this paper, we offer a tutorial on fractional calculus in controls. Basic definitions of fractional calculus, fractional order dynamic systems and controls are presented first. Then, fractional order PID controllers are introduced which may make fractional order controllers ubiquitous in industry. Additionally, several typical known fractional order controllers are introduced and commented. Numerical methods for simulating fractional order systems are given in detail so that a beginner can get started quickly. Discretization techniques for fractional order operators are introduced in some details too. Both digital and analog realization methods of fractional order operators are introduced. Finally, remarks on future research efforts in fractional order control are given.

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Fractional order control - A tutorial

Fractional Order Systems Fractional Order PID Controller Chaotic Fractional Order Systems Field Programmable Gate Array, Microcontroller and Field Programmable Analog Array Implementation Switched Capacitor and Integrated Circuit Design Modeling of Ionic Polymeric Metal Composite

Fractional Order Systems: Modeling and Control Applications

The present state-of-the-art article is devoted to the analysis of new trends and recent results carried out during the last 10 years in the field of fractional calculus application to dynamic problems of solid mechanics. This review involves the papers dealing with study of dynamic behavior of linear and nonlinear 1DOF systems, systems with two and more DOFs, as well as linear and nonlinear systems with an infinite number of degrees of freedom: vibrations of rods, beams, plates, shells, suspension combined systems, and multilayered systems. Impact response of viscoelastic rods and plates is considered as well. The results obtained in the field are critically estimated in the light of the present view of the place and role of the fractional calculus in engineering problems and practice. This articles reviews 337 papers and involves 27 figures. DOI: 10.1115/1.4000563

Application of Fractional Calculus for Dynamic Problems of Solid Mechanics: Novel Trends and Recent Results

A recent article published in this magazine has labeled fractional-order continuous-time systems as the "21st century systems". Indeed, this emerging research area is slowly gaining momentum among electrical engineers while its deeply rooted mathematical concepts also slowly migrate to various engineering disciplines. A very important aspect of research in fractional-order circuits and systems is that it is an interdisciplinary subject. Specifically, it is an area where biochemistry, medicine and electrical engineering over-lap giving rise to many new potential applications. This article aims to provide an overview of the current status of research in this area, highlighting specific problems which need to be addressed particularly by electrical engineers.

Fractional-order circuits and systems: An emerging interdisciplinary research area

Fractional order control strategies for power electronic buck converters

The objective of this work is to find out optimum settings for a fractional PIλ controller in order to fulfill three different robustness specifications of design for the compensated system, taking advantage of the fractional order, λ. Since this fractional controller has one parameter more than the conventional PI controller, one more specification can be fulfilled, improving the performance of the system and making it more robust to plant uncertainties, such as gain and time constant changes. For the tuning of the controller an iterative optimization method has been used, based on a nonlinear function minimization. Two real examples of application are presented and simulation results are shown to illustrate the effectiveness of this kind of unconventional controllers.

On Fractional PIλ Controllers: Some Tuning Rules for Robustness to Plant Uncertainties

In recent years the increasing amount of work related to the application of Fractional Calculus (FC) is remarkable in many areas of science and engineering. In relation to automatic control, the us...

Fractional PID Controllers for Industry Application. A Brief Introduction

In this paper a modified version of the classical Van der Pol oscillator is proposed, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, using phase portraits, spectral analysis and bifurcation diagrams. The fractional-order dynamics is illustrated through numerical simulations of the proposed schemes using approximations to fractional-order operators. Finally, the analysis is extended to the forced Van der Pol oscillator.

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Antonio José Calderón

Papers

Fractional order control strategies for power electronic buck converters

On Fractional PIλ Controllers: Some Tuning Rules for Robustness to Plant Uncertainties

Fractional PID Controllers for Industry Application. A Brief Introduction

Analysis of the Van der Pol Oscillator Containing Derivatives of Fractional Order

Evaluation of a hybrid photovoltaic-wind system with hydrogen storage performance using exergy analysis