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Effective and accurate state estimation is a staple of modern modeling. On the other hand, nonlinear fractional-order singular (FOS) systems are an attractive modeling tool as well since they can provide accurate descriptions of systems with complex dynamics. Consequently, developing accurate state estimation methods for such systems is highly relevant since it provides vital information about the system including related memory effects and long interconnection properties with constraint elements. However, missing features in transforming structures such as violation of constraints in non-singular versions of such systems may affect the performance of the estimation result. This paper proposes the state estimation algorithm design for the original and non-transformed stochastic nonlinear FOS system. We introduce a deterministic data-fitting based framework which helps us to take steps directly towards Kalman filter (KF) derivation of the system, called extended fractional singular KF (EFSKF). Using stochastic reasoning, we demonstrate how to construct recursive form of the filter. Analysis of the filter shows how the proposed algorithm reduces to the nominal nonlinear filters when the system is in its usual state-space form making said algorithm highly flexible. Finally, simulation results verify that the estimation of nonlinear states can be accomplished with the proposed EFSKF algorithm with a reasonable performance.

This study considers the boundary control problem of a time fractional partial differential equation (PDE) – fractional ordinary differential equation (ODE) cascaded system with spatially varying diffusivity and Dirichlet connection. Using the backstepping transformation, a full-state feedback law is obtained. Meanwhile, the well-posedness of kernel functions in this transformation is established theoretically. Subsequently, a Mittag-Leffler convergent boundary observer is derived, which composes with the proposed state feedback law to enable stabilisation by output feedback. With the designed state and output feedback controllers, the Mittag-Leffler stability of the closed-loop system is then proved by the fractional Lyapunov method. Finally, the results of numerical simulations are provided for fractional cascaded plants when neither kernel ODE nor kernel PDE has an explicit solution.

This paper develops an extension of the bilateral control method for fractional partial differential equations (PDEs) with space-dependent coefficients by output feedback. Using a backstepping transformation, a full state feedback control law is designed. Then the fractional PDE system is folded into two subsystems and Mittag-Leffler convergent state observers of these subsystems are derived. Although the observers are coupled with boundary conditions (BCs), error subsystems are decoupled by assuming some available measurements. Hence, the observer gains are easily obtained. After this, we compose the designed state feedback controller and observers to enable Mittag-Leffler stabilization by output feedback. Finally, a fractional numerical example is provided to support the effectiveness of the proposed synthesis for the case when neither the control kernel nor the estimation kernel has an explicit solution.

Augmented reality (AR) and virtual reality (VR), collectively referred to as “extended reality” (XR), have begun to diffuse in industry. However, the current levels of awareness, perceived limitations, and use of AR and VR, as well as the potential differences on these aspects between these technologies are still not well known. Moreover, it is unknown whether small and medium-sized enterprises (SMEs) differ from large companies on these issues. This research employed a mixed methods research design to address this gap by carrying out a cross-sectional survey (n = 208) to gauge European industrial companies’ level of AR and VR awareness and adoption, and by interviewing 45 companies in nine European countries in order to identify critical enabling factors in the adoption of XR for SMEs. Results show no statistical difference between the respondents’ perceptions toward AR and VR or in their use levels. Thus, examining AR and VR under the umbrella term XR seems justified, especially in the context of their organizational use. However, larger companies were found to be using XR more than SMEs. Analysis of interviews based on the technology–organization–environment framework also yielded several enabling factors affecting XR adoption and specified whether they are particularly highlighted in the SME context. Overall, this paper contributes to XR research by providing a holistic multi-country overview that highlights key issues for managers aiming to invest in these technologies, as well as critical organizational perspectives to be considered by scholars.

This paper considers observer-based output feedback stabilization and stability robustness against small diffusivity perturbations of coupled time fractional partial differential equations (PDEs) with space-dependent (non-constant) parameters. Herein, the plant is equipped with the only available measurement at x=0 and actuation at x=1 . By backstepping transformation, the well-posedness of the kernel matrix PDE and the observer gains are obtained. Then an output feedback controller is introduced and the Mittag-Leffler stability of the closed-loop system is proved by the fractional Lyapunov method. Robustness analysis of diffusion coefficients uncertainty (with a small perturbation in the diffusion coefficient) is also provided. The output feedback stabilization of the closed-loop system is tested by a numerical example.

Článek přináší systematickou revizi stavu vývoje PID regulátorů neceločíselného řádu a možností jeho průmyslové implementace The interest in fractional-order (FO) control can be traced back to the late nineteenth century. The growing tendency towards using fractional-order proportional-integral-derivative (FOPID) control has been fueled mainly by the fact that these controllers have additional “tuning knobs” that allow coherent adjustment of the dynamics of control systems. For instance, in certain cases, the capacity for additional frequency response shaping gives rise to the generation of control laws that lead to superior performance of control loops. These fractional-order control laws may allow fulfilling intricate control performance requirements that are otherwise not in the span of conventional integer-order control systems. However, there are underpinning points that are rarely addressed in the literature: (1) What are the particular advantages (in concrete figures) of FOPID controllers versus conventional, integer-order (IO) PID controllers in light of the complexities arising in the implementation of the former? (2) For real-time implementation of FOPID controllers, approximations are used that are indeed equivalent to high-order linear controllers. What, then, is the benefit of using FOPID controllers? Finally, (3) What advantages are to be had from having a near-ideal fractional-order behavior in control practice? In the present paper, we attempt to address these issues by reviewing a large portion of relevant publications in the fast-growing FO control literature, outline the milestones and drawbacks, and present future perspectives for industrialization of fractional-order control. Furthermore, we comment on FOPID controller tuning methods from the perspective of seeking globally optimal tuning parameter sets and how this approach can benefit designers of industrial FOPID control. We also review some CACSD (computer-aided control system design) software toolboxes used for the design and implementation of FOPID controllers. Finally, we draw conclusions and formulate suggestions for future research.

In the present paper, a software framework comprising the implementation of Model Predictive Control—a popular industrial control method—is presented. The framework is versatile and can be run on a variety of target systems including programmable logic controllers and distributed control system implementations. However, the main attractive property of the framework stems from the goal of achieving smooth technology transfer from the academic setting to real industrial applications. Technology transfer is, in general, difficult to achieve, because of the apparent disconnect between academic studies and actual industry. The proposed software framework aims at bridging this gap for model predictive control—a powerful control technique which can result in substantial performance improvement of industrial control loops, thus adhering to modern trends for reducing energy waste and fulfilling sustainable development goals. In the paper, the proposed solution is motivated and described, and experimental evidence of its successful deployment is provided using a real industrial plant.

In the manuscript, the issue of detecting and segmenting out pavement defects on highway roads is addressed. Specifically, computer vision (CV) methods are developed and applied to the problem based on deep learning of convolutional neural networks (ConvNets). A novel neural network structure is considered, based on a pipeline of three ConvNets and endowed with the capacity for context awareness, which improves grid-based search for defects on orthoframes by considering the surrounding image content&mdash, an approach, which essentially draws inspiration from how humans tend to solve the task of image segmentation. Also, methods for assessing the quality of segmentation are discussed. The contribution also describes the complete procedure of working with pavement defects in an industrial setting, involving the workcycle of defect annotation, ConvNet training and validation. The results of ConvNet evaluation provided in the paper hint at a successful implementation of the proposed technique.

Real control systems require robust control performance to deal with unpredictable and altering operating conditions of real-world systems. Improvement of disturbance rejection control performance should be considered as one of the essential control objectives in practical control system design tasks. This study presents a multi-loop Model Reference Adaptive Control (MRAC) scheme that leverages a nonlinear autoregressive neural network with external inputs (NARX) model in as the reference model. Authors observed that the performance of multi-loop MRAC-fractional-order proportional integral derivative (FOPID) control with MIT rule largely depends on the capability of the reference model to represent leading closed-loop dynamics of the experimental ML system. As such, the NARX model is used to represent disturbance-free dynamical behavior of PID control loop. It is remarkable that the obtained reference model is independent of the tuning of other control loops in the control system. The multi-loop MRAC-FOPID control structure detects impacts of disturbance incidents on control performance of the closed-loop FOPID control system and adapts the response of the FOPID control system to reduce the negative effects of the additive input disturbance. This multi-loop control structure deploys two specialized control loops: an inner loop, which is the closed-loop FOPID control system for stability and set-point control, and an outer loop, which involves a NARX reference model and an MIT rule to increase the adaptation ability of the system. Thus, the two-loop MRAC structure allows improvement of disturbance rejection performance without deteriorating precise set-point control and stability characteristics of the FOPID control loop. This is an important benefit of this control structure. To demonstrate disturbance rejection performance improvements of the proposed multi-loop MRAC-FOPID control with NARX model, an experimental study is conducted for disturbance rejection control of magnetic levitation test setup in the laboratory. Simulation and experimental results indicate an improvement of disturbance rejection performance.

Due to unpredictable and fluctuating conditions in real-world control system applications, disturbance rejection is a substantial factor in robust control performance. The inherent disturbance rejection capacity of classical closed loop control systems is limited, and an increase in disturbance rejection performance of single-loop control systems affects the set-point control performance. Multi-loop control structures, which involve model reference control loops, can enhance the inherent disturbance rejection capacity of classical control loops without degrading set-point control performance, while the classical closed Proportional Integral Derivative (PID) control loop deals with stability and set-point control, the additional model reference control loop performs disturbance rejection control. This adaptive disturbance rejection, which does not influence set-point control performance, is achieved by selecting reference models as transfer functions of real control systems. This study investigates six types of multi-loop model reference (ML-MR) control structures for PID control loops and presents straightforward design schemes to enhance the disturbance rejection control performance of existing PID control loops. For this purpose, linear and non-linear ML-MR control structures are introduced, and their control performance improvements and certain inherent drawbacks of these structures are discussed. Design examples demonstrate the benefits of the ML-MR control structures for disturbance rejection performance improvement of PID control loops without severely deteriorating their set-point performance.

The interest towards using Fractional-order (FO) PID controllers in the industry is mainly fueled by the fact that these controllers have two additional “tuning knobs” that can be used to adjust the control law in a way that would benefit the control loop. However, there are certain points that are rarely addressed in literature, namely: (1) What are the particular advantages (in concrete numbers) of FOPID controllers versus conventional, integer-order (IO) PID controllers in the light of complexities arising in the implementation of the former? (2) For real-time implementation of FOPID controllers, approximations are used that are equivalent to high order linear controllers. What, then, is the benefit of using FOPID controllers? In the present paper, we attempt to address these issues by reviewing recent literature in the field and by providing relevant analysis and recommendations.

A stunning outcome of fractional calculus for control practice are fractional-order PID (FOPID) controllers. Based on their experimental and numerical results, several studies have reported improvements in control performance of closed loop control systems by FOPID controllers compared to classical PID controllers. However, the industry at large is still cautious about adopting FOPID controllers because of the lack of concrete data about the related cost-benefit trade-off. Main concerns arise at the point that there have not been a quantitative evaluation scheme that clearly demonstrates for which concrete cases FOPID controllers can provide considerable improvements in control. Therefore, there is a need for more thorough theoretical and quantitative demonstrations. To that end, this study presents a plant function independent evaluation methodology to reveal inherent advantages of FOPID control. Impacts of two additional controller coefficients, namely fractional orders of differentiator and integrator, are analyzed in the frequency domain and their contributions to open loop gain maximization, phase margin and Reference to Disturbance Rate (RDR) performance are investigated.

The problem of changing the dynamics of an existing DC motor control system without the need of making internal changes is considered in the paper. In particular, this paper presents a method for incorporating fractional-order dynamics in an existing DC motor control system with internal PI or PID controller, through the addition of an external controller into the system and by tapping its original input and output signals. Experimental results based on the control of a real test plant from MATLAB/Simulink environment are presented, indicating the validity of the proposed approach.

In this paper, we present our findings related to the problem of localization and visualization of a sound source placed in the same room as the listener. The particular effect that we aim to investigate is called synesthesia—the act of experiencing one sense modality as another, e.g., a person may vividly experience flashes of colors when listening to a series of sounds. Towards that end, we apply a series of recently developed methods for detecting sound source in a three-dimensional space around the listener.We also apply a Kalman filter to smooth out the perceived motion. Further, we transform the audio signal into a series of visual shapes, such that the size of each shape is determined by the loudness of the sound source, and its color is determined by the dominant spectral component of the sound. The developed prototype is verified in real time. The prototype configuration is described and some initial experimental results are reported and discussed. Some ideas for further development are also presented.

Practical performances of controller design methods strongly depend on relevancy of identified models. Fractional order system models promise advantage of more accurate modeling of real systems. This study presents a discussion on utilization of two fundamental numerical solution methods of fractional calculus in identification problems of One Noninteger Order Plus Time Delay with one pole (NOPTD-I) models. The identification process is carried out by estimating parameters of a NOPTD-I type transfer function template so that the step response of the NOPTD-I model can sufficiently fit experimental step response data. In the study, step responses of NOPTD-I models are numerically calculated according to two fundamental methods, which are Mittag-Leffler (ML) function and Grunwald–Letnikov (GL) definition. Particle swarm optimization (PSO) algorithm is used to perform data fitting. Illustrative examples are presented to evaluate model parameter estimation performances of these two methods for synthetically generated noisy test data. An experimental study is conducted for modeling pitch rotor of TRMS to compare experimental performances.

The modern nonlinear control theory provides various powerful frameworks. Some of them are still either out of sight of the industry or too complex to be implemented. In this paper, we present and explain the key points of an algebraic framework of differential forms. Together with Mathematica based software package NLControl it forms a powerful basis toward the employment in analysis and control of various complex processes. The application is illustrated on the basis of the laboratory model of three serially connected water tanks. DOI: http://dx.doi.org/10.5755/j01.itc.45.2.13212

This study demonstrates the utilization of model reference adaptive control (MRAC) for closed-loop fractional-order PID (FOPID) control of a magnetic levitation (ML) system. Design specifications of ML transportation systems require robust performance in the presence of environmental disturbances. Numerical and experimental results demonstrate that incorporation of MRAC and FOPID control can improve the disturbance rejection control performance of ML systems. The proposed multiloop MRAC–FOPID control structure is composed of two hierarchical loops which are working in conjunction to improve robust control performance of the system in case of disturbances and faults. In this multiloop approach, an inner loop performs a regular closed-loop FOPID control, and the outer loop performs MRAC based on Massachusetts Institute of Technology (MIT) rule. These loops are integrated by means of the input-shaping technique and therefore no modification of any parameter of the existing closed-loop control system is necessary. This property provides a straightforward design solution that allows for independent design of each loop. To implement FOPID control of the ML system, a retuning technique is used which allows transforming an existing PID control loop into an FOPID control loop. This paper presents the simulation and experimental results and discusses possible contributions of multiloop MRAC–FOPID structure to disturbance rejection control of the ML system.

In the present paper, the problem of digital implementation of retuning fractional-order (FO) controllers for an unstable plant — a real-life laboratory model of a Magnetic Levitation System (MLS) — is investigated. Retuning control is applied to an existing closed-loop PID control system through the use of a hardware FO controller prototype. An implementation method for the retuning controller is proposed. Three types of hardware-in-the-loop (HIL) experiments are considered. First, the plant is simulated using a suitable dynamic model. Second, the real-life laboratory model of the MLS is controlled. In the third type of experiment, a MATLAB implementation of the retuning controller is evaluated as a benchmark. Three controllers obtained in an earlier work are tested with this setup. Experimental results are compared and discussed.