Deliverables

Within each Working Group, the Tasks were defined that are to be solved by its members inside the Working Group or through efficient cooperation between the Working Groups. Although some Deliverables are understood to be delivered, you may still become a valuable member of our COST Action and contribute the secific Tasks, Delivebrales and finally the Objectives of this COST Action. In total, 21 deliverables were identified and can be linked to individual Working Groups (WGs) as folows:

  • WG1 – Fractional calculus and mathematical models
    • D1 – Development and implementation of a general framework for global, non-adaptive identification of fractional and non-rational systems in general
    • D6 – Development and implementation of a general framework of adaptive identification of fractional and non-rational systems
    • D13 – Approximation of derivatives and integrals of fractional orders by new numerical and analytical methods; Fractionized models
    • D17 – Development of methods for PID controllers’ synthesis, Matlab toolboxes and discretization algorithms
  • WG2 – Fractional-order systems’ synthesis and analysis
    • D2 – Presentation of optimized low-order approximations of fractional Laplacian operator featuring lower circuit complexity
    • D7 – Presentation of tools for analysis and synthesis of the fractional-order function blocks
    • D14 – Increased approximation accuracy of fractional Laplacian operator for analogue circuit design, discrete rational approximations
    • D16 – Presentation of new fractional-order elements based on the IMPC, graphene and RC-EDP design approach
  • WG3 – Design of analogue and digital fractional-order function blocks
    • D3 – Development of integrators and differentiators, initial implementation of digital fractional order blocks
    • D9 – Development of fractional-order analogue and digital filter topologies using basic building blocks
    • D11 – Optimal dynamic control – methods for solution and numerical computation of optimal dynamic control
    • D18 – Application of FO linear and non-linear blocks in sensors, actuators and control systems
  • WG4 – Utilization of fractional-order systems in engineering and biomedical research areas
    • D4 – Development of preliminary models for automotive injection systems and of physical and mathematical knowledge on models of Havriliak
    • D8 – Detailed models and virtual prototypes; low-order models for FO controllers, development of simulation tools for systems of Havriliak-Negami type
    • D12 – Advanced FO control algorithms and realization techniques for automotive applications; model of pain pathways and corresponding software
    • D19 – Modelling and control of injection systems; Schemes for analysing propagation of electro-magnetic fields in biological tissues; Report on correlation analysis and corresponding software
  • Deliverables common for all WGs
    • D5 – Contribution of each working group to the proceedings of the Year 1 Workshop co-located with the Action meeting
    • D10 – Contribution of each working group to the proceedings of the Year 2 Workshop co-located with the Action meeting
    • D15 – Contribution of each working group to the proceedings of the Year 3 Workshop co-located with the Action meeting
    • D20 – Contribution of each working group to the proceedings of the Year 4 Workshop co-located with the Action meeting
    • D21 – Finalization of the book summarizing Action activities and scientific results achieved during its four years span

D1 – Development and implementation of a general framework for global, non-adaptive identification of fractional and non-rational systems in general (expected by July 2017)

Mainly the members and their activities done within the Working Group 1 contribute to this deliverable. Currently, it is not delivery fully but is foreseen before the end of the Action.

A general framework for global, non-adaptive identification of fractional and non-rational systems in general is being developed in two specific directions. The first is non-parametric analysis, in which an overall shape of the frequency characteristic is analyzed first, and then suitable explicit or implicit fractional order model is proposed and optimized by means of a PSO algorithm. Relevant study was reported in 10.1016/j.ifacol.2017.08.2084 in collaboration between Serbian and Italian COST action members. Parts of the research were also reported in 10.1016/j.aeue.2017.05.036. Another path under investigation is to develop specific forms of transfer functions related to various distributed-parameter systems, with or without fractional spatio-temporal dynamics. Initial results are reported in 10.1109/ECCTD.2017.8093252, 10.1007/s11071-016-3322-z.

D2 – Presentation of optimized low-order approximations of fractional Laplacian operator featuring lower circuit complexity (expected by July 2017)

Mainly the members and their activities done within the Working Group 2 contribute to this deliverable. Currently, it is not delivery fully but is foreseen before the end of the Action.

The results presented in 10.1016/j.ifacol.2017.08.1422 and 10.1109/ECCTD.2017.8093324 provide efficient techniques to obtain accurate and low-order approximations of fractional operators and compensators that are useful for control and other applications.

Partially also delivered by presenting the comprehensive analysis of the approximation of low-pass magnitude response. These results were presented in 10.1016/j.aeue.2017.04.031. The further analysis of specific transfer function types continues, see e.g. 10.5755/j01.eie.24.2.20634.

D3 – Development of integrators and differentiators, initial implementation of digital fractional order blocks (expected by July 2017)

Mainly the members and their activities done within the Working Group 3 contribute to this deliverable. Currently, it is not delivery fully but is foreseen before the end of the Action.

Partially delivered by presenting the efficient circuit solutions to design analogue fractional-order integrator and differentiators using opams, CCIIs, CFOAs and OTAs and published in 10.1109/TSP.2017.8076081. As variuos types of active elements may be used for the practical design of such, even if in principle simple, function blocks, the activities within this deliverable still continue. The proposal of digital fractional blocks will proceed.

D4 – Development of preliminary models for automotive injection systems and of physical and mathematical knowledge on models of Havriliak (expected by July 2017)

Mainly the members and their activities done within the Work Grouping 4 contribute to this deliverable. Currently, this deliverable is understood to be delivered, but further progress in this area may be expexted.

Preliminary mathematical developments and properties regarding Havriliak-Negami type of time-domain or frequency-domain models were obtained by putting together the best results from the following previous publications 10.1007/978-3-319-45474-0_38, 10.1515/fca-2016-006, 10.1109/ICFDA.2014.6967399. Some advancements were proposed in the current output 10.1515/fca-2016-0060. In details, numerical methods are now available to give an approximate but accurate solution to differential equations in which the Prabhakar derivative is used to better describe anomalous relaxation in Havriliak-Negami models of dielectric materials or biological tissues. Moreover, the time-domain relaxation and response functions of the most common materials that show anomalous relaxation are now well known and described.

D5 – Contribution of each working group to the proceedings of the Year 1 Workshop co-located with the Action meeting (expected by September 2017)

The members from all Working Groups have contributed the Annual Workshop to share their experience and achievements. This deliverable is understood to be delivered.

The Annual Workshop 2017 was organized in San Sebastian by the Spain representatives of the Action, Dr Karmele Lopez de Ipina and Dr. Pilar Ma Calvo, at University of the Basque Country. Following the tasks and expected deliverables described within the individual Working Groups, 19 speakers from the member countries presented the progress in the description and utilization of fractional-order systems and function blocks. Next to that also representatives of the 3 local companies – Technalia (by Hector Herrero), Stago (by Pablo Martinez Santoja) and OTRI (by Gorka Artola), gave a speech on the possible utilization of fractional-order approach in controlling their designs. For more information, please see Annual Workhop 2017.

D6 – Development and implementation of a general framework of adaptive identification of fractional and non-rational systems (expected by May 2018)

Mainly the members and their activities done within the Working Group 1 contribute to this deliverable. Currently, it is not delivery fully but is foreseen before the end of the Action.

A general framework for adaptive identification of fractional and non-rational systems in general is being developed. The research is targeting algorithms that are capable of identifying unknown parameters in transfer functions of arbitrary form, including rational, fractional, transfer functions, transfer functions with “fractional delay”, and other forms of transfer functions which are derived from partial differential equations describing distributed parameter systems. The proposed algorithm is gradient based, and novel convergence conditions are derived generalizing well known results regarding input richness. Relevant study was reported in 10.1016/j.aeue.2017.04.008, while additional publications are in the review phase at this moment.

D7 – Presentation of tools for analysis and synthesis of the fractional-order function blocks (expected by July 2018)

Mainly the members and their activities done within the Working Group 2 contribute to this deliverable. Currently, this deliverable is understood to be delivered, but further progress in this area may be expexted.

The FOMCON toolbox for MATLAB®, initially developed by Aleksei Teplakov, the current MC member for Estonia, was further improved. The FOMCON toolbox for MATLAB® is a fractional-order calculus based toolbox for system modeling and control design. For more details about the Matlab Toolbox you may check the MathWorks® File Exchange or the FOMCON hopepage

D8 – Detailed models and virtual prototypes; low-order models for FO controllers, development of simulation tools for systems of Havriliak-Negami type (expected by July 2018)

Mainly the members and their activities done within the Working Group 4 contribute to this deliverable. Currently, this deliverable is understood to be delivered, but further progress in this area may be expexted.

The results shown in the previous publications 10.1016/j.ifacol.2016.08.071, 10.1109/CDC.2015.7403160, 10.3182/20150218-3-AU-30250//978-3-902823-71-70075, 10.3182/20140824-6-ZA-1003.00889 are based on simulation models developed in the Matlab/Simulink environment or on virtual prototypes built by the AMESim software package. The mentioned tools also allow an easy and fast prototyping of the control systems on the basis of a model-based approach that guarantees accuracy and effectiveness of the results. Namely, the implemented simulation models allow an accurate representation of the complex, nonlinear, time-varying dynamical processes that occur in the considered common rail injection systems and characterize their operation in different working points. In this sense, the models can be considered very close to the hardware and real systems they represent.

To simulate Havriliak-Negami models in the time domain, efficient numerical schemes were developed. Firstly, a convolution quadrature rule was derived on the basis of the Laplace transform representation of the response function. The method allows to discretize fractional Havriliak-Negami models in the time domain and then obtain a numerical approximation useful to simulate the time-domain response of these models. Secondly, a Prabhakar function was employed to describe anomalous relaxation properties of dielectric materials with Havriliak-Negami type of behaviour.

D9 – Development of fractional-order analogue and digital filter topologies using basic building blocks (expected by August 2018)

Mainly the members and their activities done within the Working Group 3 contribute to this deliverable. Currently, it is not delivery fully but is foreseen before the end of the Action.

Partially delivered by presenting analogue or digitally controlled analogue fractional-order filters providing the low-, band- and high-pass frequency response. Some of the results reached by Action members can be found here: 10.1016/j.aeue.2017.04.031, 10.5755/j01.eie.24.2.20634, 10.1109/TSP.2018.8441421, 10.1515/jee-2018-0001. The research in this area has a close link to the deliverable D3 and therefore, also here the activities will further continue to propose circuit complexity optimized solutions.

D10 – Contribution of each working group to the proceedings of the Year 2 Workshop co-located with the Action meeting (expected by September 2018)

The members from all Working Groups have contributed the Annual Workshop to share their experience and achievements. This deliverable is understood to be delivered.

The Annual Workshop 2018 was organized in Bialystok by the Polish representative of the Action, Dr Dorota Mozyrska, at University of Bialystok. Following the tasks and expected deliverables described within the individual Working Groups, 16 speakers from the member countries presented the progress in analysis and design of optimized fractional-order function blocks and system control.

D11 – Optimal dynamic control – methods for solution and numerical computation of optimal dynamic control (expected by July 2019)

Mainly the members and their activities done within the Working Group 3 contribute to this deliverable. Currently, it is not delivery fully but is foreseen before the end of the Action.

The activities within this deliverable mainly base on further development of the FOMCON toolbox for MATLAB® that was originally developed by Aleksei Teplakov.

D12 – Advanced FO control algorithms and realization techniques for automotive applications; model of pain pathways and corresponding software (expected by July 2019)

Mainly the members and their activities done within the Working Group 4 contribute to this deliverable. Currently, it is not delivery fully but is foreseen before the end of the Action.

Some advanced fractional order control techniques can be applied to automotive engines using the common rail injection system technology and compressed natural gas, which gives a solution to reduce emissions of polluting gases and particulate matter. In this case, the injection process is strongly non-linear, time-variant and highly coupled, so suitable control systems must be designed to guarantee the desired performance. The main controlled variable affecting emissions and consumption of the engines is the common rail pressure in the injection system.

An approach was made available to synthesize and realize fractional order controllers. Synthesis of the controller is based on a loop-shaping technique, which is applied on the open-loop transfer function to achieve frequency-domain performance and robustness specifications. The technique pursues an optimal feedback system in a specified bandwidth and takes advantage of the fractional integrator to achieve enhanced robustness. Moreover, the design approach is reinforced by the D-decomposition methodology that guarantees robust stability of the closed-loop system. Finally, the design formulas are specified by closed-form expressions. As regards the realization of the synthesized controllers, accuracy and simplicity are both considered, to allow an efficient and easy implementation as required by industry. Last but not least, the realization formulas guarantee stability and minimum-phase properties of the controllers.

The performance indexes, the robustness (sensitivity to parametric changes) and disturbance rejection capability are tested by simulation of virtual prototypes that are based on very accurate non-linear models of the considered injection systems. Results indicate that fractional-order controllers allow a higher accuracy in metering the injected fuel and better promptness in setting the rail pressure to the desired reference values.

The variation between different working points of the injection system (in terms of the reference rail pressure) is compensated by a model-based fractional-order gain scheduling control strategy, which allows switching from one controller to another each time the working point associated to the rail pressure changes. In case of small variations, only one switch is necessary; if large variations occur, then more controllers are considered such that variations of the injection timings and the rail pressure are limited. In this way, nonlinearity effects, oscillations and instability problems in the rail pressure are prevented.

The preliminar results linked to this deliverable were discussed e.g. in 10.1016/j.ifacol.2017.08.2084 and as chapter will also be part  of the book Handbook of Fractional Calculus with Applications, Vol. 6, Applications in Control (chapter by Fractional-Order Controllers for Mechatronics and Automotive Applications by P. Lino, G. Maione).

 

D13 – Approximation of derivatives and integrals of fractional orders by new numerical and analytical methods; Fractionized models (expected by September 2019)

Mainly the members and their activities done within the Working Group 1 contribute to this deliverable. Currently, it is not delivery fully but is foreseen within 2 years after the end of the Action.

Numerous novel approaches for the numerical handling of fractional operators have been proposed recently by research groups outside of the COST Action. These methods differ in their structure and in the interpretation of their respective parameters greatly from the traditional approaches. Therefore a comparison of the performance is difficult and appropriate concepts for such a sensible comparison need to be designed. This work is currently ongoing together with a research group from Pakistan that intends to join the COST Action in the near future. We expect to have publishable results within the two years after the end of the action. The outcome will then be published in suitable international peer reviewed journals.

D14 – Increased approximation accuracy of fractional Laplacian operator for analogue circuit design, discrete rational approximations (expected by September 2019)

Mainly the members and their activities done within the Working Group 2 contribute to this deliverable. Currently, it is not delivery fully but is foreseen before the end of the Action.

The initial results on this deliverable were reached by the comprehensive analysis of the Oustaloup approximation and defining the equations to determine the initial parameters of this approximation technique to obtain a response that satisfies the designers’ requirements of approximation error in magnitude and/or phase in a specific frequency range for the minimal possible order N of the approximation as presented in J. Koton, J. H. Stavnesli, T. Freeborn, Performance Analysis of Oustaloup Approximation for the Design of Fractional-Order Analogue Circuits, in Proc. ICUMT 2018, Nov 2018, Moscow, Russia.

D15 – Contribution of each working group to the proceedings of the Year 3 Workshop co-located with the Action meeting (expected by September 2019)

The Annual Workshop 2019 that will summarize the level of achievements within individual tasks and deliverables is to be planned within the upcoming Grant Period. The members from all Working Groups are expected to contribute to the Annual Workshop 2019 to share their experience and achievements with other members and Anual Workshop participants. Currently, it is not delivery fully but is foreseen before the end of the Action.

D16 – Presentation of new fractional-order elements based on the IMPC, graphene and RC-EDP design approach (expected by June 2020)

Mainly the members and their activities done within the Working Group 2 contribute to this deliverable. Currently, it is not delivery fully but is foreseen before the end of the Action.

The hardware design of fractional-order elements based on the Resistive-Capacitive Elements with Distributed Parameters (RC-EDP) was already initiated, where the first results were presented in 10.1109/ECCTD.2017.8093314. A software developed by prof. Ushakov is utilized to design RC-EDPs that are produced as using thick-film technology.

RC-EDP samples were taken into account to optimize the design. Currently these improved samples are being manufactured based on the thick-film technology at Brno University of Technology. The delivery is partially achieved by the publications and further publications are planned after the fabrication of new samples and verification of their functionality.

D17 – Development of methods for PID controllers’ synthesis, Matlab toolboxes and discretization algorithms (expected by July 2020)

Mainly the members and their activities done within the Working Group 1 contribute to this deliverable. Currently, it is not delivery fully but is foreseen before the end of the Action.

The activities on this deliverable have been already initiated with the development of a set of Matlab codes for the solution of fractional differential equations, in particular for multi-order systems (systems in which each differential equation has a different order) and multi-term equations (when in the same equation there are several fractional derivatives). This is a set of general purposes codes, with a similar usage to those of other built-in Matlab codes for classical ordinary differential equations, and their use is therefore very simple and possible also by users with no particular experience in numerical analysis (mainly for Action participants from other WG). The codes are available here.

D18 – Application of FO linear and non-linear blocks in sensors, actuators and control systems (expected by July 2020)

Mainly the members and their activities done within the Working Group 3 contribute to this deliverable. Currently, it is not delivery fully but is foreseen before the end of the Action.

The activities on this deliverable were already initiated by utilizing fractional-order function blocks in the PID control: see e.g. 10.1142/S0218126618501761, 10.1016/j.ifacol.2018.06.151, 10.1109/TSP.2018.8441247.

D19 – Modelling and control of injection systems; Schemes for analysing propagation of electro-magnetic fields in biological tissues; Report on correlation analysis and corresponding software (expected by July 2020)

Mainly the members and their activities done within the Working Group 4 contribute to this deliverable. Currently, it is not delivery fully but is foreseen before the end of the Action.

Currently, the contribution to accurate modelling of the electro-injectors that are used in common rail injection systems of Diesel engines were made .and presented e.g. in 10.1016/j.ifacol.2016.08.071. The model takes into account the fuel properties, the nonlinear dynamics of the fuel flow, the electro-hydraulic elements and the mechanical components subject to displacement and deformation. But it also considers fractional-order representation of the high-pressure fuel propagation inside a peculiar annular pipe of the electro-injectors, which is given by fractional-order differential equations. The new model shows a better prediction capability than a rigid body model, which is based on assuming that some relevant coupled mechanical elements behave as rigid bodies, and a nominal model, which uses nominal values of the parameters that are here fixed by conventional expressions but that can be subject to optimization. Model-based simulation shows the improvement in prediction by the help of real data. The contributions to the propagation of electro-magnetic fields will be initiated in the second half of the COST Action duration.

D20 – Contribution of each working group to the proceedings of the Year 4 Workshop co-located with the Action meeting (expected by September 2020)

The Annual Workshop 2020 that will summarize the level of achievements within individual tasks and deliverables is to be planned within the upcoming Grant Period. The members from all Working Groups are expected to contribute to the Annual Workshop 2020 to share their experience and achievements with other members and Anual Workshop participants. Currently, it is not delivery fully but is foreseen before the end of the Action.

D21 – Finalization of the book summarizing Action activities and scientific results achieved during its four years span (expected by September 2020)

The book that will summarize the achievements, deliverables and reached results of this COST Action will be prepared by the members from all Working Groups. The book starts to be prepared in the year 2019 first. Currently, it is not delivery fully but is foreseen before the end of the Action.