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 fastgrowing 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.

B-like minimum energy conformations of deoxydinucleoside monophosphate anions (dDMPs) containing Gua and/or Cyt and their Na+ complexes have been studied by the DFT PW91PW91/DZVP method. The optimized geometry of the dDMPs is in close agreement with experimental observations and the obtained minimum energy conformations are consistent with purine-purine, purine-pyrimidine, and pyrimidine-purine arrangements in crystals of B-DNA duplexes. All the studied systems are characterized by pyramidalization of the amino groups, which participate in the formation of unusual hydrogen bond between the carbonyl oxygen of the second base in the dGpdC, dCpdG dDMPs, and their Na+ complexes. In all the obtained structures the bases assume a nearly parallel disposition to each other and this effect is independent on the degree of their spatial superposition. From this it is concluded that the parallel disposition of the bases in the B-like single-stranded conformations is dictated by the sugar-phosphate backbone. Correspondingly, the base-base interactions attain a secondary role in the formation of these spatial structures. The formation of a weak C6-H6...O5' hydrogen bond between cytosine and the phosphate oxygen is reported, in agreement with experimental observations.

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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.

ABSTRACT:We apply DFT calculations to deoxydinucleoside monophosphates (dDMPs) which represent minimal fragments of the DNA chain to study the molecular basis of stability of the DNA duplex, the origin of its polymorphism and conformational heterogeneity. In this work, we continue our previous studies of dDMPs where we detected internal energy minima corresponding to the ''classical'' B conformation (BI-form), which is the dominant form in the crystals of oligonucleotide duplexes. We obtained BI local energy minima for all existing base sequences of dDMPs. In the present study, we extend our analysis to other families of DNA conformations, successfully identifying A, BI, and BII energy minima for all dDMP sequences. These conformations demonstrate distinct differences in sugar ring puckering, but similar sequence-dependent base arrangements. Internal energies of BI and BII conformers are close to each other for nearly all the base sequences. The dGpdG, dTpdG, and dCpdA dDMPs slightly favor the BII conformation, which agrees with these sequences being more frequently experimentally encountered in the BII form. We have found BII-like structures of dDMPs for the base sequences both existing in crystals in BII conformation and those not yet encountered in crystals till now. On the other hand, we failed to obtain dDMP energy minima corresponding to the Z family of DNA conformations, thus giving us the ground to conclude that these conformations are stabilized in both crystals and solutions by external factors, presumably by interactions with various components of the media. Overall the accumulated computational data demonstrate that the A, BI, and BII families of DNA conformations originate from the corresponding local energy minimum conformations of dDMPs, thus determining structural stability of a single DNA strand during the processes of unwinding and rewinding of DNA.

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Abstract:As it results from many research works, the majority of real dynamical objects are fractional-order systems, although in some types of systems the order is very close to integer order. Application of fractional-order models is more adequate for the description and analysis of real dynamical systems than integer-order models, because their total entropy is greater than in integer-order models with the same number of parameters. A great deal of modern methods for investigation, monitoring and control of the dynamical processes in different areas utilize approaches based upon modeling of these processes using not only mathematical models, but also physical models. This paper is devoted to the design and analogue electronic realization of the fractional-order model of a fractional-order system, e.g., of the controlled object and/or controller, whose mathematical model is a fractional-order differential equation. The electronic realization is based on fractional-order differentiator and integrator where operational amplifiers are connected with appropriate impedance, with so called Fractional Order Element or Constant Phase Element. Presented network model approximates quite well the properties of the ideal fractional-order system compared with e.g., domino ladder networks. Along with the mathematical description, OPEN ACCESSEntropy 2013, 15 4200 circuit diagrams and design procedure, simulation and measured results are also presented.