Fractional Dynamics and Control of Distributed Parameter Systems

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of some distributed parameter systems.

Robot Manipulator Systems: Analysis and Control

Manipulator systems are rather complex and highly nonlinear which makes difficult their analysis and control. Classic system theory is veil known, however it is inadequate in the presence of strong nonlinear dynamics. Nonlinear controllers produce good results [1] and work has been done e. g. relating the manipulator nonlinear dynamics with frequency response [2–5]. Nevertheless, given the complexity of the problem, systematic methods which permit to draw conclusions about stability, imperfect modelling effects, compensation requirements, etc. are still lacking. In section 2 we start by analysing the variation of the poles and zeros of the descriptive transfer functions of a robot manipulator in order to motivate the development of more robust (and computationally efficient) control algorithms. Based on this analysis a new multirate controller which is an improvement of the well known “computed torque controller” [6] is announced in section 3. Some research in this area was done by Neuman [7,8] showing tbat better robustness is possible if the basic controller structure is modified. The present study stems from those ideas, and attempts to give a systematic treatment, which results in easy to use standard engineering tools. Finally, in section 4 conclusions are presented.

System Modeling and Control Through Fractional-Order Algorithms

The theory of fractional calculus goes back to the beginning of thr throry of differential calculus but its inherent complexity postponed the applications of the associated concepts. In the last decade the progress in the areas of chaos and fractals revealed subtle relationships with the fractional calculus leading to an increasing interest in the development of the new paradigm. In the area of automaticcontrol preliminary work has already been carried out but the proposed algorithms are restricted to the frequency domain. The paper discusses the design of fractional-order discrete-time controllers. The algorithms studied adopt the time domein, which makes them suited for z-transform analusis and discrete-time implementation. The performance of discrete-time fractional-order controllers with linear and non-linear systems is also investigated.

AI in power systems and energy markets

In a world increasingly conscientious about environmental effects, power and energy systems are undergoing huge transformations. Electric energy produced from power plants is transmitted and distributed to end users through a power grid. The power industry performs the engineering design, installation, operation, and maintenance tasks to provide a high-quality, secure energy supply while accounting for its systems’ abilities to withstand uncertain events, such as weather-related outages. Competitive, deregulated electricity markets and new renewable energy sources, however, have further complicated this already complex infrastructure.Sustainable development has also been a challenge for power systems. Recently, there has been a signifi cant increase in the installation of distributed generations, mainly based on renewable resources such as wind and solar. Integrating these new generation systems leads to more complexity. Indeed, the number of generation sources greatly increases as the grid embraces numerous smaller and distributed resources. In addition, the inherent uncertainties of wind and solar energy lead to technical challenges such as forecasting, scheduling, operation, control, and risk management. In this special issue introductory article, we analyze the key areas in this field that can benefi t most from AI and intelligent systems now and in the future.We also identify new opportunities for cross-fertilization between power systems and energy markets and intelligent systems researchers.

Stability of fractional order systems

The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, from the mathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled.

Fractional calculus: application in modelling and control

This contribution introduces the fractional calculus (FC) fundamental mathematical aspects and discuses some of their consequences. Based on the FC concepts, the chapter reviews the main approaches for implementing fractional operators and discusses the adoption of FC in control systems. Finally are presented some applications in the areas of modeling and control, namely fractional PID, heat diffusion systems, electromagnetism, fractional electrical impedances, evolutionary algorithms, robotics, and nonlinear system control.

Fractional Calculus: Application in modeling and control

This contribution introduces the fractional calculus (FC) fundamental mathematical aspects and discuses some of their consequences. Based on the FC concepts, the chapter reviews the main approaches for implementing fractional operators and discusses the adoption of FC in control systems. Finally are presented some applications in the areas of modeling and control, namely fractional PID, heat diffusion systems, electromagnetism, fractional electrical impedances, evolutionary algorithms, robotics, and nonlinear system control.

Modeling and Control of a Dragonfly-Like Robot

Dragonflies demonstrate unique and superior flight performances than most of the other insect species and birds. They are equipped with two pairs of independently controlled wings granting an unmatchable flying performance and robustness. In this paper it is studied the dynamics of a dragonfly-inspired robot. The system performance is analyzed in terms of time response and robustness. The development of computational simulation based on the dynamics of the robotic dragonfly allows the test of different control algorithms. We study different movement, the dynamics and the level of dexterity in wing motion of the dragonfly. The results are positive for the construction of flying platforms that effectively mimic the kinematics and dynamics of dragonflies and potentially exhibit superior flight performance than existing flying platforms.

Modelling and Control of Freeway Traffic

This paper presents the most recent developments of the Simulator of Intelligent Transportation Systems (SITS). The SITS is based on a microscopic simulation approach to reproduce real traffic conditions in an urban or non-urban network. In order to analyse the quality of the microscopic traffic simulator SITS a benchmark test was performed. A dynamical analysis of several traffic phenomena, applying a new modelling formalism based on the embedding of statistics and Laplace transform, is then addressed. The paper presents also a new traffic control concept applied to a freeway traffic system.

Multi-agent systems and birtual producers in electronic marketplaces

This paper presents an agent-based simulator designed for analyzing agent market strategies based on a complete understanding of buyer and seller behaviours, preference models and pricing algorithms, considering user risk preferences. The system includes agents that are capable of improving their performance with their own experience, by adapting to the market conditions. In the simulated market agents interact in several different ways and may joint together to form coalitions. In this paper we address multi-agent coalitions to analyse Distributed Generation in Electricity Markets

Copper, nickel and zinc removal by peanut hulls: batch and column studies in mono, tri-component systems and with real effluent

The main goal of this research study was the removal of Cu(II), Ni(II) and Zn(II) from aqueous solutions using peanut hulls. This work was mainly focused on the following aspects: chemical characterization of the biosorbent, kinetic studies, study of the pH influence in mono-component systems, equilibrium isotherms and column studies, both in mono and tri-component systems, and with a real industrial effluent from the electroplating industry. The chemical characterization of peanut hulls showed a high cellulose (44.8%) and lignin (36.1%) content, which favours biosorption of metal cations. The kinetic studies performed indicate that most of the sorption occurs in the first 30 min for all systems. In general, a pseudo-second order kinetics was followed, both in mono and tri-component systems. The equilibrium isotherms were better described by Freundlich model in all systems. Peanut hulls showed higher affinity for copper than for nickel and zinc when they are both present. The pH value between 5 and 6 was the most favourable for all systems. The sorbent capacity in column was 0.028 and 0.025 mmol g-1 for copper, respectively in mono and tri-component systems. A decrease of capacity for copper (50%) was observed when dealing with the real effluent. The Yoon-Nelson, Thomas and Yan’s models were fitted to the experimental data, being the latter the best fit.

Modeling and control of a dragonfly-like robot

Dragonflies demonstrate unique and superior flight performances than most of the other insect species and birds. They are equipped with two pairs of independently controlled wings granting an unmatchable flying performance and robustness. In this paper, the dynamics of a dragonfly-inspired robot is studied. The system performance is analyzed in terms of time response and robustness. The development of computational simulation based on the dynamics of the robotic dragonfly allows the test of different control algorithms. We study different movements, the dynamics, and the level of dexterity in wing motion of the dragonfly. The results are positive for the construction of flying platforms that effectively mimic the kinematics and dynamics of dragonflies and potentially exhibit superior flight performance than existing flying platforms.

On the robustness of the slotine-Li and the FPT/SVD-based adaptive controllers

A comparative study concerning the robustness of a novel, Fixed Point Transformations/Singular Value Decomposition (FPT/SVD)-based adaptive controller and the Slotine-Li (S&L) approach is given by numerical simulations using a three degree of freedom paradigm of typical Classical Mechanical systems, the cart + double pendulum. The effects of the imprecision of the available dynamical model, presence of dynamic friction at the axles of the drives, and the existence of external disturbance forces unknown and not modeled by the controller are considered. While the Slotine-Li approach tries to identify the parameters of the formally precise, available analytical model of the controlled system with the implicit assumption that the generalized forces are precisely known, the novel one makes do with a very rough, affine form and a formally more precise approximate model of that system, and uses temporal observations of its desired vs. realized responses. Furthermore, it does not assume the lack of unknown perturbations caused either by internal friction and/or external disturbances. Its another advantage is that it needs the execution of the SVD as a relatively time-consuming operation on a grid of a rough system-model only one time, before the commencement of the control cycle within which it works only with simple computations. The simulation examples exemplify the superiority of the FPT/SVD-based control that otherwise has the deficiency that it can get out of the region of its convergence. Therefore its design and use needs preliminary simulation investigations. However, the simulations also exemplify that its convergence can be guaranteed for various practical purposes.