Blas M. Vinagre

Analogue Realizations of Fractional-Order Controllers

An approach to the design of analogue circuits, implementingfractional-order controllers, is presented. The suggestedapproach is based on the use of continued fraction expansions;in the case of negative coefficients in a continued fractionexpansion, the use of negative impedance converters is proposed.Several possible methods for obtaining suitable rational appromixationsand continued fraction expansions are discussed. An exampleof realization of a fractional-order Iλ controlleris presented and illustrated by obtained measurements.The suggested approach can be used for the control of veryfast processes, where the use of digital controllers isdifficult or impossible.

Two direct Tustin discretization methods for fractional-order differentiator/integrator

This paper deals with fractional calculus and its approximate discretization. Two direct discretization methods useful in control and digital filtering are presented for discretizing the fractional-order differentiator or integrator. Detailed mathematical formulae and tables are given. An illustrative example is presented to show the practically usefulness of the two proposed discretization schemes. Comparative remarks between the two methods are also given.

A new IIR-type digital fractional order differentiator

A new infinite impulse response (IIR)-type digital fractional order differentiator (DFOD) is proposed by using a new family of first-order digital differentiators expressed in the second-order IIR filter form. The integer first-order digital differentiators are obtained by the stable inversion of the weighted sum of Simpson integration rule and the trapezoidal integration rule. The distinguishing point of the proposed DFOD lies in an additional tuning knob to compromise the high-frequency approximation accuracy.

Fractional order control strategies for power electronic buck converters

This paper presents several alternative methods for the control of power electronic buck converters applying fractional order control (FOC). For achieving this goal, the controller design will be carried out by two strategies. On the one hand, the design of a linear controller for the DC/DC buck converter will be considered. In that sense, the Bodes ideal function will be used as reference system. On the other hand, the fractional calculus is proposed in order to determine the switching surface applying a fractional sliding mode control (FRSMC) scheme to the control of such devices. In that sense, switching surfaces based on fractional order PID and PI structures are defined. An experimental prototype has been developed and the experimental and simulation results confirm the validity of the proposed control strategies.

Using Fractional Order Adjustment Rules and Fractional Order Reference Models in Model-Reference Adaptive Control

This paper investigates the use of Fractional Order Calculus (FOC) inconventional Model Reference Adaptive Control (MRAC) systems. Twomodifications to the conventional MRAC are presented, i.e., the use offractional order parameter adjustment rule and the employment offractional order reference model. Through examples, benefits from theuse of FOC are illustrated together with some remarks for furtherresearch.

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

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.

Fractional PID Controllers for Industry Application. A Brief Introduction

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 use of Fractional Order Control (FOC) needs, for real applications, to develop methods for controller design and parameter tuning, and efficient strategies for controller implementation. On the other hand, the Proportional Integral Derivative (PID) controller is currently by far the most widely used form of feedback controller in industrial applications. This paper, after an introduction to FC and FOC, briefly presents methods for fractional PID controller tuning, including auto-tuning, and some software and hardware strategies for efficient implementations of controllers in industrial applications.

Stability of linear time invariant systems with interval fractional orders and interval coefficients

This paper considers the stability of the fractional-order linear time-invariant systems with interval type uncertainties in both fractional orders and the relevant coefficients. It is an extension of our previous result on the robust stability analysis of the interval type uncertain fractional order LTI systems with crisply known fractional orders. We have proposed a stability check procedure for uncertain LTI systems with interval fractional orders and interval coefficients. The procedure is demonstrated with some simple examples

Improved fractional Kalman filter and its application to estimation over lossy networks

This paper presents improvements on the fractional Kalman filter (FKF) based on the infinite dimensional form of a linear discrete fractional order state-space system. Furthermore, taking into account the considerable interest in estimation over networks with packet losses, the application and extension of the improved FKF are included. Some simulation cases are given in order to demonstrate the effectiveness of the proposed algorithms, with significant improvements in terms of estimation and smoothing results.

A Fractional Adaptation Scheme for Lateral Control of an AGV

Lateral control of an autonomous guided vehicle is influenced strongly by both the longitudinal speed and the position input command (magnitude of the reference signal) of the vehicle. For that reason some suitable strategies for governing the vehicle are adaptive and robust controllers. In this article, an adaptive scheme which combines a model reference approach with a fractional order adjustment rule for a feedforward gain adjustment is proposed. Two parameters can be tuned to obtain robustness with respect to variations in speed and magnitude of the reference signal: Adaptation gain, and derivative order of the adjustment rule. A model is developed for the vehicle, the design procedure is discussed, and simulation results are obtained to show the advantages the proposed fractional adaptation scheme.