Several papers reviewing fractional order calculus in control applications have been published recently. These papers focus on general tuning procedures, especially for the fractional order proportional integral derivative controller. However, not all these tuning procedures are applicable to all kinds of processes, such as the delicate time delay systems. This motivates the need for synthesizing fractional order control applications, problems, and advances completely dedicated to time delay processes. The purpose of this paper is to provide a state of the art that can be easily used as a basis to familiarize oneself with fractional order tuning strategies targeted for time delayed processes. Solely, the most recent advances, dating from the last decade, are included in this review.

The paper proposes a mathematical framework for the use of fractional-order impedance models to capture fluid mechanics properties in frequency-domain experimental datasets. An overview of non-Newtonian (NN) fluid classification is given as to motivate the use of fractional-order models as natural solutions to capture fluid dynamics. Four classes of fluids are tested: oil, sugar, detergent and liquid soap. Three nonlinear identification methods are used to fit the model: nonlinear least squares, genetic algorithms and particle swarm optimization. The model identification results obtained from experimental datasets suggest the proposed model is useful to characterize various degree of viscoelasticity in NN fluids. The advantage of the proposed model is that it is compact, while capturing the fluid properties and can be identified in real-time for further use in prediction or control applications. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

The present manuscript aims at raising awareness of the endless possibilities of fractional calculus applied not only to system identification and control engineering, but also into sensing and filtering domains. The creation of the fractance device has enabled the physical realization of a new array of sensors capable of gathering more information. The same fractional-order electronic component has led to the possibility of exploring analog filtering techniques from a practical perspective, enlarging the horizon to a wider frequency range, with increased robustness to component variation, stability and noise reduction. Furthermore, fractional-order digital filters have developed to provide an alternative solution to higher-order integer-order filters, with increased design flexibility and better performance. The present study is a comprehensive review of the latest advances in fractional-order sensors and filters, with a focus on design methodologies and their real-life applicability reported in the last decade. The potential enhancements brought by the use of fractional calculus have been exploited as well in sensing and filtering techniques. Several extensions of the classical sensing and filtering methods have been proposed to date. The basics of fractional-order filters are reviewed, with a focus on the popular fractional-order Kalman filter, as well as those related to sensing. A detailed presentation of fractional-order filters is included in applications such as data transmission and networking, electrical and chemical engineering, biomedicine and various industrial fields.

Fractional order proportional integral and proportional derivative controllers are nowadays quite often used in research studies regarding the control of various types of processes, with several papers demonstrating their advantage over the traditional proportional integral/proportional derivative controllers. The majority of the tuning techniques for these fractional order proportional integral/fractional order proportional derivative controllers are based on three frequency-domain specifications, such as the open-loop gain crossover frequency, phase margin and the iso-damping property. The tuning parameters of the controllers are determined as the solution of a system of three nonlinear equations resulting from the performance criteria. However, as with any system of nonlinear equations, it might occur that for a certain process and with some specific performance criteria, the computed parameters of the fractional order proportional integral/fractional order proportional derivative controllers do not fall into a range of values with correct physical meaning. In this article, a study regarding this limitation, as well as the existence conditions for the fractional order proportional integral/fractional order proportional derivative parameters are presented. The method could also be extended to the more complex fractional order proportional–integral–derivative controller. The aim of this research is directed toward demonstrating that when designing fractional order proportional integral/fractional order proportional derivative controllers, the choice of the performance specifications should be done based on some specific design constraints. The article shows that given a specific process and open-loop modulus and phase specifications, the gain crossover frequency (or in general, a certain test frequency used in the design), specified as a performance specification, must be selected such that the process phase fulfills an important condition (design constraint). Once this is met, the proposed approach ensures that the tuning parameters of the fractional order controller will have a physical meaning. Illustrative examples are included to validate the results.

Cyber-physical systems revolve around context awareness, empowering objective-oriented services, products and operations based on real data. Self-aware and self-control systems are core elements in the Industry 4.0 framework towards self-sustainable adaptive manufacturing and personalized services. This development is witnessed by the context-aware pervasive assistance to users and machines in decisions making process for optimizing product performance and economic yield. While integration of the virtual and the physical world entails smart sensors communication and complex data analytics, it relies on artificial intelligence tools to manage process operations. The objective of the article is to create awareness that systems & control community must address theoretical and practical aspects from a larger perspective. Context aware control is emerging as a natural solution to maximize the use of available sensing instrumentation and the relatively low cost data logging, i.e. an important source for extracting information, interpreting and using context information and adapt its functionality to the current context of use. This article presents a concise overview of applications where context aware systems and control methodologies are relevant in the seven societal challenges acknowledged by European policy-makers: Digital Society;

Fractional order calculus has been used to generalize various types of controllers, including internal model controllers (IMC). The focus of this manuscript is towards fractional order IMCs for first order plus dead-time (FOPDT) processes, including delay and lag dominant ones. The design is novel at it is based on a new approximation approach, the non-rational transfer function method. This allows for a more accurate approximation of the process dead-time and ensures an improved closed loop response. The main problem with fractional order controllers is concerned with their implementation as higher order transfer functions. In cases where central processing unit CPU, bandwidth allocation, and energy usage are limited, resources need to be efficiently managed. This can be achieved using an event-based implementation. The novelty of this paper resides in such an event-based algorithm for fractional order IMC (FO-IMC) controllers. Numerical results are provided for lag and delay dominant FOPDT processes. For comparison purposes, an integer order PI controller, tuned according to the same performance specifications as the FO-IMC, is also implemented as an event-based control strategy. The numerical results show that the proposed event-based implementation for the FO-IMC controller is suitable and provides for a smaller computational effort, thus being more suitable in various industrial applications.

Graphical abstract

Classical fractional order controller tuning techniques usually consider the frequency domain specifications (phase margin, gain crossover frequency, iso-damping) and are based on knowledge of a process model, as well as solving a system of nonlinear equations to determine the controller parameters. In this paper, a novel auto-tuning method is used to tune a fractional order PI controller. The advantages of the proposed auto-tuning method are two-fold: There is no need for a process model, neither to solve the system of nonlinear equations. The tuning is based on defining a forbidden region in the Nyquist plane using the phase margin requirement and determining the parameters of the fractional order controller such that the loop frequency response remains out of the forbidden region. Additionally, the final controller parameters are those that minimize the difference between the slope of the loop frequency response and the slope of the forbidden region border, to ensure the iso-damping property. To validate the proposed method, a case study has been used consisting of a pick and place movement of an UR10 robot. The experimental results, considering two different robot configurations, demonstrate that the designed fractional order PI controller is indeed robust.