Design guidelines for physical implementation of fractional-order integrators and its application in memristive systems

Author(s):  
Ciro Fabian Bermúdez-Márquez ◽  
Jesus Manuel Muñoz-Pacheco
Author(s):  
Calvin Coopmans ◽  
Ivo Petra´sˇ ◽  
YangQuan Chen

Memristor is a new electrical element which has been predicted and described in 1971 by Leon O. Chua and for the first time realized by HP laboratory in 2008. Chua proved that memristor behavior could not be duplicated by any circuit built using only the other three elements (resistor, capacitor, inductor), which is why the memristor is truly fundamental. Memristor is a contraction of memory resistor, because that is exactly its function: to remember its history. The memristor is a two-terminal device whose resistance depends on the magnitude and polarity of the voltage applied to it and the length of time that voltage has been applied. The missing element—the memristor, with memristance M—provides a functional relation between charge and flux, dφ = Mdq. In this paper, for the first time, the concept of (integer-order) memristive systems is generalized to non-integer order case using fractional calculus. We also show that the memory effect of such devices can be also used for an analogue implementation of the fractional-order operator, namely fractional-order integral and fractional-order derivatives. This kind of operators are useful for realization of the fractional-order controllers. We present theoretical description of such implementation and we proposed the practical realization and did some experiments as well.


PCI Journal ◽  
2020 ◽  
Vol 65 (6) ◽  
pp. 35-61
Author(s):  
Chungwook Sim ◽  
Maher Tadros ◽  
David Gee ◽  
Micheal Asaad

Ultra-high-performance concrete (UHPC) is a special concrete mixture with outstanding mechanical and durability characteristics. It is a mixture of portland cement, supplementary cementitious materials, sand, and high-strength, high-aspect-ratio microfibers. In this paper, the authors propose flexural design guidelines for precast, prestressed concrete members made with concrete mixtures developed by precasters to meet minimum specific characteristics qualifying it to be called PCI-UHPC. Minimum specified cylinder strength is 10 ksi (69 MPa) at prestress release and 18 ksi (124 MPa) at the time the member is placed in service, typically 28 days. Minimum flexural cracking and tensile strengths of 1.5 and 2 ksi (10 and 14 MPa), respectively, according to ASTM C1609 testing specifications are required. In addition, strain-hardening and ductility requirements are specified. Tensile properties are shown to be more important for structural optimization than cylinder strength. Both building and bridge products are considered because the paper is focused on capacity rather than demand. Both service limit state and strength limit state are covered. When the contribution of fibers to capacity should be included and when they may be ignored is shown. It is further shown that the traditional equivalent rectangular stress block in compression can still be used to produce satisfactory results in prestressed concrete members. A spreadsheet workbook is offered online as a design tool. It is valid for multilayers of concrete of different strengths, rows of reinforcing bars of different grades, and prestressing strands. It produces moment-curvature diagrams and flexural capacity at ultimate strain. A fully worked-out example of a 250 ft (76.2 m) span decked I-beam of optimized shape is given.


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