Fractional control of heat diffusion systems

The concept of differentiation and integration to non-integer order has its origins in the seventeen century. However, only in the second-half of the twenty century appeared the first applications related to the area of control theory. In this paper we consider the study of a heat diffusion system based on the application of the fractional calculus concepts. In this perspective, several control methodologies are investigated and compared. Simulations are presented assessing the performance of the proposed fractional-order algorithms.

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.

On the fractional order control of heat systems

The differentiation of non-integer order has its origin in the seventeenth century, but only in the last two decades appeared the first applications in the area of control theory. In this paper we consider the study of a heat diffusion system based on the application of the fractional calculus concepts. In this perspective, several control methodologies are investigated namely the fractional PID and the Smith predictor. Extensive simulations are presented assessing the performance of the proposed fractional-order algorithms.

Fractional control with a smith predictor

The advantageous use of fractional calculus (FC) in the modeling and control of many dynamical systems has been recognized. In this paper, we study the control of a heat diffusion system based on the application of the FC concepts. Several algorithms are investigated and compared, when integrated within a Smith predictor control structure. Simulations are presented assessing the performance of the proposed fractional algorithms.

Some applications of fractional calculus in engineering

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 FC in the study of system dynamics and control. In this perspective, this paper investigates the use of FC in the fields of controller tuning, legged robots, redundant robots, heat diffusion, and digital circuit synthesis.

Impact of using solar heat pumps for domestic hot water in Portuguese residential buildings

In recent years, we have seen an improvement of existing facilities in dwellings in Portugal. Within the heat pumps systems, there is a special type known as direct expansion heat pump assisted by Solar Collector (DX-SAHP). It was calculate the SPF indicator for 30 regions of Portugal. It was analyses the potential of reductions of CO2 and primary energy use for the retrofitting of DHW preparation systems. It was found that the performances of this type of equipment are benefiting from the Portuguese climate conditions, especially in the South and in the Autonomous Regions. Best SPF was obtained for Beja. It was found in all regions of the high potential for reducing CO2 emissions and verifying a potential significant reduction of primary energy consumption.

Finite Element Analysis (FEA) applied to heat transfer optimization process of pultrusion die systems

The aim of this study is to optimize the heat flow through the pultrusion die assembly system on the manufacturing process of a specific glass-fiber reinforced polymer (GFRP) pultrusion profile. The control of heat flow and its distribution through whole die assembly system is of vital importance in optimizing the actual GFRP pultrusion process. Through mathematical modeling of heating-die process, by means of Finite Element Analysis (FEA) program, an optimum heater selection, die position and temperature control was achieved. The thermal environment within the die was critically modeled relative not only to the applied heat sources, but also to the conductive and convective losses, as well as the thermal contribution arising from the exothermic reaction of resin matrix as it cures or polymerizes from the liquid to solid condition. Numerical simulation was validated with basis on thermographic measurements carried out on key points along the die during pultrusion process.

Combined heat and power and consumption optimization in a SCADA-based system

The operation of power systems in a Smart Grid (SG) context brings new opportunities to consumers as active players, in order to fully reach the SG advantages. In this context, concepts as smart homes or smart buildings are promising approaches to perform the optimization of the consumption, while reducing the electricity costs. This paper proposes an intelligent methodology to support the consumption optimization of an industrial consumer, which has a Combined Heat and Power (CHP) facility. A SCADA (Supervisory Control and Data Acquisition) system developed by the authors is used to support the implementation of the proposed methodology. An optimization algorithm implemented in the system in order to perform the determination of the optimal consumption and CHP levels in each instant, according to the Demand Response (DR) opportunities. The paper includes a case study with several scenarios of consumption and heat demand in the context of a DR event which specifies a maximum demand level for the consumer.

Microstructure, mechanical properties and chemical degradation of brazed AISI 316 stainless steel/alumina systems

The main aims of the present study are simultaneously to relate the brazing parameters with: (i) the correspondent interfacial microstructure, (ii) the resultant mechanical properties and (iii) the electrochemical degradation behaviour of AISI 316 stainless steel/alumina brazed joints. Filler metals on such as Ag–26.5Cu–3Ti and Ag–34.5Cu–1.5Ti were used to produce the joints. Three different brazing temperatures (850, 900 and 950 °C), keeping a constant holding time of 20 min, were tested. The objective was to understand the influence of the brazing temperature on the final microstructure and properties of the joints. The mechanical properties of the metal/ceramic (M/C) joints were assessed from bond strength tests carried out using a shear solicitation loading scheme. The fracture surfaces were studied both morphologically and structurally using scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS) and X-ray diffraction analysis (XRD). The degradation behaviour of the M/C joints was assessed by means of electrochemical techniques. It was found that using a Ag–26.5Cu–3Ti brazing alloy and a brazing temperature of 850 °C, produces the best results in terms of bond strength, 234 ± 18 MPa. The mechanical properties obtained could be explained on the basis of the different compounds identified on the fracture surfaces by XRD. On the other hand, the use of the Ag–34.5Cu–1.5Ti brazing alloy and a brazing temperature of 850 °C produces the best results in terms of corrosion rates (lower corrosion current density), 0.76 ± 0.21 μA cm−2. Nevertheless, the joints produced at 850 °C using a Ag–26.5Cu–3Ti brazing alloy present the best compromise between mechanical properties and degradation behaviour, 234 ± 18 MPa and 1.26 ± 0.58 μA cm−2, respectively. The role of Ti diffusion is fundamental in terms of the final value achieved for the M/C bond strength. On the contrary, the Ag and Cu distribution along the brazed interface seem to play the most relevant role in the metal/ceramic joints electrochemical performance.

Control and dynamics of fractional order 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 nonlinear dynamics. This article discusses several applications of fractional calculus in science and engineering, namely: the control of heat systems, the tuning of PID controllers based on fractional calculus concepts and the dynamics in hexapod locomotion.

Fixed point transformations in the adaptive control of fractional-order MIMO systems

Though the formal mathematical idea of introducing noninteger order derivatives can be traced from the 17th century in a letter by L’Hospital in which he asked Leibniz what the meaning of D n y if n = 1/2 would be in 1695 [1], it was better outlined only in the 19th century [2, 3, 4]. Due to the lack of clear physical interpretation their first applications in physics appeared only later, in the 20th century, in connection with visco-elastic phenomena [5, 6]. The topic later obtained quite general attention [7, 8, 9], and also found new applications in material science [10], analysis of earth-quake signals [11], control of robots [12], and in the description of diffusion [13], etc.

Analysis of diffusion process in fractured reservoirs using fractional derivative approach

The fractal geometry is used to model of a naturally fractured reservoir and the concept of fractional derivative is applied to the diffusion equation to incorporate the history of fluid flow in naturally fractured reservoirs. The resulting fractally fractional diffusion (FFD) equation is solved analytically in the Laplace space for three outer boundary conditions. The analytical solutions are used to analyze the response of a naturally fractured reservoir considering the anomalous behavior of oil production. Several synthetic examples are provided to illustrate the methodology proposed in this work and to explain the diffusion process in fractally fractured systems.

Control and Dynamics of Fractional Order 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 nonlinear dynamics. This article discusses several applications of fractional calculus in science and engineering, namely: the control of heat systems, the tuning of PID controllers based on fractional calculus concepts and the dynamics in hexapod locomotion.