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Digital realization of non-integer-order controllers is important to exploit the benefits provided by these controllers, in terms of flexibility, dynamic performance and robust stability, for applications in mechatronics, industrial and automotive systems. To realize infinite-dimensional fractional-order operators and controllers in the digital domain, a discrete-time approximation is necessary that must be characterized by stable and minimum-phase properties for control purposes. This paper provides a design method useful for a wide class of plants and applies a consolidated approximation technique. Moreover, the practical implementation problems of digital non-integer control algorithms are deeply analyzed by considering the effects of the sampling period, of the conversion between analog and digital domain (and vice versa) and the associated quantization. Results show benefits and limitations of the approach.

In the last decades noninteger differentiation became a popular tool for modeling the complex behaviours of physical systems from diverse domains such as mechanics, electricity, chemistry, biology, and economics. Numerous studies have validated the novel perspective demonstrating fractional order models that better characterize many real-world physical systems by means of differential operators of noninteger order. The long-range temporal or spatial dependence phenomena inherent to the fractional order systems (FOS) present unique and intriguing peculiarities, not supported by their integer order counterpart, which raise exciting challenges and opportunities related to the development of modelling, control, and estimation methodologies involving fractional order dynamics.

This paper introduces a new application of the Field Programmable Analog Array. Ease of design and reprogrammability are the advantages offered by this class of analog circuits, making them an ideal environment for the implementation of chaotic circuits and their experimental characterization. Chua's circuit, a well-known paradigm of nonlinear circuits, has been used as an example of application. Experimental results show the suitability of the approach, highlighting the features of the new implementation: a fully on the fly programmable Chua's circuit has been obtained.

This paper describes a soft computing approach to control a semiactive sky-hook suspension system. The fuzzy controller has been optimized by means of a genetic algorithm and implemented using a dedicated hardware device. After a preliminary study on a quarter car, a seven degree-of-freedom (7-DOF) model was implemented and used for controller simulation and optimization. The proposed control system takes the vehicle heave into account, improving the opposing requirements of comfort and drivability. The following conditions were optimized: drivability over random test roads, sine-wave holes, and sleeper-plates at different speeds. Fuzzy control makes it possible to change the characteristic parameters of the sky-hook suspension in an optimal way according to the different road conditions. The number of fuzzy controller inputs is kept as small as possible, avoiding the use of expensive sensors that increase the overall cost of the system. The proposed system is also easily applicable to existing commercial suspension systems. In addition to the comfort features, the fuzzy controller allows a reduction in load fluctuation, abnormal behavior and tire consumption.

This paper proposes an experimental analysis on the convergence of evolutionary algorithms (EAs). The effect of introducing chaotic sequences instead of random ones during all the phases of the evolution process is investigated. The approach is based on the substitution of the random number generator (RNG) with chaotic sequences. Several numerical examples are reported in order to compare the performance of the EA using random and chaotic generators as regards to both the results and the convergence speed. The results obtained show that some chaotic sequences are always able to increase the value of some measured algorithm-performance indexes with respect to random sequences. Moreover, it is shown that EAs can be extremely sensitive to different RNGs. Some t-tests were performed to confirm the improvements introduced by the proposed strategy.

Fractional integro-differentiation (or, non-integer order integro-differentiation) is a mathematical framework that leads to efficient tools for modeling and control many of physical systems. Nevertheless, the overall area is commonly refereed as Fractional Calculus (FC) and become popular during the last years. In fact, FC can be used to describe in a solid and compact form systems characterized by long-range temporal or spatial dependence phenomena. Furthermore, the extension of classical and modern control theories to the new perspective, allows the development of algorithms applicable both integer and non-integer order systems. The application of fractional calculus can have a considerable impact on everyday life namely in technology, social and health issues. Therefore, important challenges are still posed to the scientific community that motivate researchers to explore new features of fractional systems. The special issue Challenges in Fractional Dynamics and Control Theory includes a selection of nine papers addressing topics that recently emerged in this area and is organized as follows. Lopes and Machado (2015) contribute with the manuscript entitled State space analysis of forest fires. Burnt area, precipitation and atmospheric temperatures are interpreted as state variables of a complex system and the correlations between them are investigated. The study sheds light about a complex phenomenon that needs to be better understood in order to mitigate its devastating consequences, at both economical and environmental levels. Balachandran et al. (2015) present the paper Controllability of nonlinear implicit neutral fractional Volterra integrodifferential systems. The control problem of non-linear neutral fractional Volterra integrodifferential systems with implicit fractional derivative is established. Sufficient conditions for controllability are obtained by means of the notions of condensing map and measure of noncompactness of a set. Meerschaert, et al. (2015) have the study Anisotropic fractional diffusion tensor imaging. Traditional diffusion tensor imaging (DTI) maps brain structure by fitting a diffusion model to the magnitude of the electrical signal acquired in magnetic resonance imaging (MRI). Fractional DTI employs anomalous diffusion models to obtain a better fit to real MRI data, which can exhibit anomalous diffusion in both time and space. The paper describes the challenge of developing and employing anisotropic fractional diffusion models for DTI. Pinto and Carvalho (2015) develop the work Fractional complex-order model for HIV infection with drug resistance during therapy. They propose a fractional complex-order model for drug resistance in HIV infection. The fractional complex-order system reveals rich dynamics and variation of the value of the complex-order derivative sheds new light on the modeling of the intracellular delay. Muresan et al. (2015) contribute with Design and analysis of a multivariable fractional order controller for a non-minimum phase system. Two control strategies for multivariable processes are proposed, based on a decentralised and a steady state decoupling approach. The designed controllers are fractional order PIs. The efficiency and robustness of the fractional algorithms is tested and validated using a non-minimum phase process. Ventura et al. (2015) add the work Fractional direct and inverse models of the dynamics of a human arm. The paper presents a comparative study of both direct and inverse models of the human arm at the elbow joint.

An enhanced model for the heating process on heterogeneous materials based on fractional order PDEs has been identified through an optimization algorithm. Experimentation has been carried out on a finite length beam filled with a composite material in order to obtain a model in the frequency domain. The obtained results confirm the fractional nature of the heating processes when diffusion occurs in not continuous composite materials.

This presentation focuses on two approaches, both based on second order sliding modes, for detecting faults and controlling certain classes of infinite dimensional systems. Two concrete applications will be presented. The first approach considers a three-dimensional distributed-parameter model of an industrial furnace and addresses the problem of detecting faults in the heaters by using a certain number of suitably located temperature probes internal to the furnace. A second order sliding mode observer is designed, which produces suitable residual signals allowing to detect faults in the furnace electrical heating system. Simulation results will be illustrated. Secondly, a novel electro-active polymer, Ionic Polymer-Metal Composite (IPMC), is considered. This class of materials bends when solicited by an external electric field, and it is well known to exhibit fractional-order systems behaviour. Second order sliding mode algorithms, suitably tailored to the fractional order systems setting, are exploited to address the positioning problem of an IPMC membrane. Experimental results demonstrates the effectiveness of the latter approach.

In this paper, systems formed by networks of simple nonlinear cells are studied. Using lattice models, some of the fundamental features of complex systems such as self-organization and pattern formation are illustrated. In the first part of this work, a lattice of identical Chua's circuit is used to experimentally study its global spatiotemporal dynamics, according to the variation of some macroparameters, like the coupling coefficient or the neighboring dimension. The second part of the paper deals with the remarkable improvements regarding regularization and pattern formation, obtained in networks of nonlinear systems by introducing some spatial diversity, especially generated by deterministic, unpredictable dynamics. Simulation results show that synchronization and self-organization occur in networks with a few nonlocally connected cells, with irregular topology and small spatial diversity.

This letter deals with the remarkable effects observed in arrays of circuits and systems when parameter spatial diversity is induced by using chaos, leading to pattern formation and regularization. The communication emphasizes the fact that generating spatial dissymmetries by using chaos enhances regularity and pattern formation capability with respect to the case in which diversity is generated by random processes. Several examples are reported showing the previous conjecture. A further aim of the paper is to emphasize that the introduction of a small amplitude chaotic spatial diversity could control chaos in both 1D and 2D large scale connected arrays of nonlinear circuits like Cellular Neural Network (CNN).

Ionic Polymer-Metal Composites (IPMCs) are electro-active polymers transforming mechanical forces into electric signals and vice versa. This paper proposes an improved electro-mechanical grey-box model for IPMC membrane working as actuator. In particular the IPMC nonlinearity has been characterized through experimentation and included within the electric model. Moreover identification of the model parameters has been performed via optimization algorithms using both single- and multi-objective formulation. Minimization was attained via the Nelder-Mead simplex and the Genetic Algorithms considering as cost functions the error between the experimental and modeled absorbed current and the error between experimental and modeled displacement. The obtained results for the different formulations have been then compared.

Ionic polymer-polymer composites (IP2Cs) are electroactive polymers which can be used both as sensors and as actuators. In this paper, a new multiphysics model of IP2Cs working as an actuator is presented and implemented using a finite element methods solver (COMSOL Multiphysics). The model involves electrical, mechanical, chemical, and thermal effects and yields a unique solution. Knowledge acquired by measuring campaigns has been included in the model. More specifically the frequency dependence of Young's modulus was experimentally determined and introduced in such a model. A frequency-domain investigation is performed and a model optimization procedure that integrates the Nelder-Mead simplex method with the COMSOL Multiphysics models is exploited to identify IP2C model parameter by fitting experimental data. A fractional order dynamics has been identified in the model, confirming previous studies on IPMC gray box modeling and on electroactive polymeric devices.

1Department of Electrical, Electronics and Computer Engineering, University of Catania, Viale A. Doria 6, 95125 Catania, Italy 2ISEP-Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Rua Dr. Antonio Bernardino de Almeida 431, 4200-072 Porto, Portugal 3Department of Mathematical Analysis, University of La Laguna, C/Astr. Francisco Sanchez s/n, La Laguna, 38271 Tenerife, Spain

The street light system, using a Power Line network, requires detailed knowledge about transmission medium, such as: transfer function, parasitic capacity, induced inductances and noise due to capacitive coupling between phases, in order to undertake a reliable master/slave communication. This paper proposes an innovative algorithm useful for a network dynamic configuration. It will allow to reduce impact noise, facing problems related to the attenuation, increasing with frequency and distance square, and cross coupling between phases, making network communication between master and slave nodes (street lights) reliable and more noise immune.

Modern aerospace vehicles are expected to have non-conventional flight envelopes and, in order to operate in uncertain environments, they must guarantee a high level of robustness and adaptability. A Neural Networks (NN) controller, with real-time learning capability, can be used in applications with manned or unmanned aerial vehicles. In this paper we propose a realtime system, based on a NN model, in order to control the trajectories of a hexacopter. The paper shows a performance evaluation, through a real experimental testbed, of the proposed approach in terms of error measures and obtained coordinates of the hexacopter.

In this paper an integrated circuit (IC) design of the fractional order proportional-integral-derivative (PID) controller is proposed. The development of the IC device is realized in Cadence environment, using the switched capacitors (SC) technology in order to reduce the area on the silicon wafer and to improve the electrical controllability. In order to obtain transfer functions that describe the fractional order of the differ-integral operator it is necessary to use interpolation methods, in particular, the choice in this work has fallen on the Oustaloup interpolation. This procedure is aimed at implementing a series of pole-zero blocks that approximate the non-integer order. The realized approach is able to guarantee a good approximation of the fractional order PID and simultaneously propose a detailed circuit analysis of the influence of the non-idealities, in particular the phenomenon of warping. This takes into account the distortion introduced by the s-domain to the z-domain transition, acting on the positions of poles and zeros, especially those at a higher frequency. Time and frequency domain result tests confirm the feasibility and reliability of the SC implementation.

In this paper the fundamentals of Cellular Neural Networks (CNNs) are introduced. Subsequently it is shown that, due to their locally distributed way of exchanging signals, such structures can be used as powerful devices to simulate and to reproduce, in an analog fashion and low cost, complex behaviors, i.e. dynamics commonly encountered in living systems, such as autonomous wave formation and propagation as well as morphogenetical pattern development. In fact it is proven that both of these behaviours can be simulated with CNNs with the same cell structure, and the thoroughly different dynamics can arise only suitably modulating the CNN cell parameters. Therefore a unifying approach to pattern formation and active wave propagation phenomena is presented. The derivation of the complex phenomena is analytically addressed and several simulation results are also reported.

IPMCs are electroactive polymers which can be used both as sensors and as actuators. The modeling of IPMC transducers is an open issue relevant to the development of effective applications. A multiphysics model of IPMC actuators is here implemented. It integrates the description of the electrical, mechanical, chemical and thermal coupled physics domains in a unique solution and, as a novelty, it allows the study in the frequency domain and the comparison with experimental response of the IPMC device. The IPMC white box modeling requires several macro- and microscopic parameters, not always accessible via theoretical approaches or experimentation. This work presents a new model optimization procedure which integrates the Nelder–Mead simplex method with the COMSOL Multiphysics®models. The proposed procedure uses experimental data and fits model simulations to IPMC real behavior for microscopic parameters’ identification. The model is developed for IPMCs with ethylene glycol as the solvent.

The paper proposes a new procedure which allows to define the parameters of a Fractional Order Proportional Integrative Derivative (FO-PID) controller that stabilizes a first-order plant with time-delay. The stabilizing FO-PID parameters complete set has been determined by the application of the Hermite–Biehler theorem to fractional order systems. The proposed procedure has been verified by computer simulations that confirm the effectiveness of the approach. The diffused PID controller industrial use and the verified capability of their non-integer order form justifies the timely FO-PID controller interest.

Fractional-order differential equations are interesting for their applications in the construction of mathematical models in finance, materials science or diffusion. In this paper, an application of a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equation is employed for calculating Lyapunov exponents of fractional order systems. It is known that the Lyapunov exponents, first introduced by Oseledec, play a crucial role in characterizing the behaviour of dynamical systems. They can be used to analyze the sensitive dependence on initial conditions and the presence of chaotic attractors. The results reveal that the proposed method is very effective and simple and leads to accurate, approximately convergent solutions.

IPMC actuators suffer because of a large number of influencing factors that do not allow adequate open loop working conditions and they require the use of controlling strategies. IPMC controllers can be designed by using suitable device models. Here a non integer order transfer function is used to model IPMC actuators. In the present paper the IPMC model is scaled as a function of the actuator length and the control law has been parameterized according to this physical parameter

IPMCs are electroactive polymers which can be used both as sensors and as actuators. A multiphysics model of IPMC devices working as actuators is here presented. The model integrates electrical, mechanical, chemical and thermal effects in a unique solution and attention is focused on the coupling factors among the physics domains. The model was validated through experimentation.

IPMCs are a novel class of composite materials capable of electromechanical reversible transduction. It has been suggested in literature that they can be modeled by using fractional transfer functions. In this paper a gray box approach is used to identify IPMC actuators. Moreover the proposed transfer functions are ruled by using the device geometrical parameters, in such a away to guarantee the control of the transducer behavior during the design phase. Experimental validation of the proposed approach is reported.

An FPGA based system has been developed in order to characterize, in real time, Electrocardiographic (ECG) signals. These signals are analyzed by using nonlinear data analysis to extract the d ∞ parameter, characterizing their asymptotic chaotic behaviour. The FPGA implemented algorithm has been applied on a statistically significant number of ECG signals taken from the MIT-BIH database and including normal subjects and subjects affected by arrhythmia and ventricular arrhythmia. The real time feature of the proposed approach allows a clinical applications of such methodology in the early diagnosis of cardiac pathologies.

Many researches have highlighted the influence of climate on mortality, showing a high increase in mortality in the summer time during “heat waves”, periods of very high temperature and humidity levels. The bioclimatic indexes are used in urban climate studies to describe the level of thermal sensation that a person experiences due to the modified climatic conditions of an urban area. The index provides a meaningful and realistic indicator that can not only be used as an information as to how hot it feels, but also as a readily identifiable warning for individuals subject to the physiological dangers of heat exposure. The authors have developed a methodology that, by means of the Neural Network (NN), permits one to predict the values of meteorological data and then the calculation of the bioclimatic indexes. The meteorological data required for the calculation of the bioclimatic index concerning hourly values of air temperature, relative humidity, wind speed have been used according to the records of the meteorological station of the Pergusa Lake (EN), for the year from 2003 to 2006 NN-estimated, the bioclimatic indexes values were compared with coincident bioclimatic indexes values obtained from air temperature and relative humidity observations recorded at standard meteorological stations. Statistical analysis showed a good agreement between the NN-estimated and the station-observed bioclimatic indexes values, with a root mean square error (RMSE) < 1%.

In this chapter a Switched Capacitors (SC) implementation of fractional differintegral operator is proposed. Time and frequency domain result tests validate the feasibility and reliability of the SC circuit implementation. A detailed analysis of the influence of the non-idealities is proposed in order to obtain a design ready for Integrated Circuit (IC) implementation. The proposed approach may guarantee a good degree of approximation of fractional differintegral operator and therefore the possibility to realize PI λ D μ controller IC based on switched capacitors technology.

A Switched Capacitors (SC) implementation of fractional integrator is proposed in this paper. Time and frequency domain result tests validate the feasibility and reliability of the SC circuit implementation. A detailed analysis of the influence of the non-idealities is proposed in order to obtain a design fit for Integrated Circuit (IC) implementation. The proposed approach may guarantee a good degree of approximation of the fractional differ-integral operator and therefore the possibility to realize a PIλDμ controller IC based on switched capacitors technology.

A direct method for computing the L∞ norm of a transfer matrix is presented. The proposed procedure allows the norm to be computed through the introduction of strategy to solve the problem numerically in terms of a generalized eigenvalue problem. At the same time, the procedure also makes it possible to determine certain particular frequencies where the singular values of the transfer matrix assume peculiar properties. Accuracy is guaranteed since it does not depend on searching strategies. The complete procedure does not involve complicated computational tools, thus resulting in numerical efficiency. Two examples are given showing the suitability of the proposed approach.

In this chapter a new model for Ionic Polymer Metal Composites (IPMC) actuators, based on non-integer order models is proposed. IPMCs are very interesting polymer because of their capability to transform electrical energy into mechanical energy and vice-versa, making them particularly attractive for possible applications in different fields, such as robotics, aerospace, biomedicine, etc. An experimental setup has been realized to study the IPMCs behavior and an algorithm has been developed in Matlab environment in order to identify a fractional order model of IPMC actuators.

A new strategy to realize an FPGA implementation of a soft sensor for an industrial process is proposed. The proposed approach is based on the integration on Field Programmable Gate Array (FPGA) of a neural networks. The proposed method has been applied to develop a soft sensor for the estimation of the freezing point of kerosene in an atmospheric distillation unit (topping) working in a refinery in Sicily, Italy.

In this paper the fractional order integrative operator s−m , where m is a real positive number, is approximated via a mathematical formula and then an hardware implementation of fractional integral operator is proposed using Field Programmable Gate Array (FPGA). Digital hardware implementation of fractional-order integral operator requires careful consideration of issue of system performance, hardware cost, and hardware speed. FPGA-based implementation are up to one hundred times faster than implementations based on micro-processors; this extra speed can be exploited to allow higher performance in terms of digital approximations of fractional-order systems.Copyright © 2009 by ASME

The paper presents an hardware realization of a self-tuning control system implemented on a development board, Field Programmable Gate Arrays (FPGAs) based, able to adapt the control rules for an uncertain and disturbance affected plant. In the paper the on-line estimation of the plant parameters is realized by applying the “Recursive Least Squares with exponential forgetting” method and the control law is designed by using the “Pole Placement” procedure. These algorithms require a greater computational load, justifying therefore the FPGA utilization, especially in the case of high speed variation of the plant parameters. In order to test the FPGA hardware implementation of Self-Tuning regulators the process is implemented on DSPACE and the parameter variations are produced via an Human Machine Interface (HMI) console. Besides, thanks to the reprogrammability of FPGAs, these devices allow the use of such adaptive control systems in hazardous area.Copyright © 2009 by ASME

A new strategy to realize an FPGA implementation of a soft sensor for an industrial process is proposed. In order to cope with the problem of small data sets in the identification of a non linear model the proposed approach is based on the integration of bootstrap re-sampling, noise injection and stacked neural networks (NNs), using the Principal Component Analysis (PCA). The aggregated final NN-PCA system has been implemented on Field Programmable Gate Array (FPGA). The proposed method has been applied to develop a soft sensor for the estimation of the freezing point of kerosene in an atmospheric distillation unit (topping) working in a refinery in Sicily, Italy.

The paper proposes a new model for IPMC actuators, based on non-integer order models. IPMCs are very interesting because of their capability to transform electrical energy into mechanical energy and vice-versa, making them particularly attractive for possible applications in different fields, such as robotics, aerospace, biomedicine, etc. A great interest has been devoted to non-integer, or fractional, order systems because they well model a lot of physical systems. An experimental setup has been realized to study the IPMCs behavior and an algorithm has been developed in Matlab Environment to identify a fractional order model of IPMC actuators.

In this paper a remote control equipment for monitoring and managing a street lighting system is presented. It is composed by a local control, realized by master boards located inside electrical panels and slave boards mounted on each lamppost, and by a remote control realized by a central unit for the remote communication with the local control system. The communication between master and slave boards is realized using power line modems, while the remote control central unit is connected to master boards via a GPRS-GSM communication. Master board allows to choice the electrical phase for the power line communication and to send the control commands to the slave boards on each lamppost. Slave boards allow to turn on/off the lamppost, to reduce power consumption using a device developed by ALBATROS Italia S.r.L., and to detect the lamp status, checking the current flow on the lamp itself.