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Control algorithms for programmable logic controllers are still developed based on the experience of those responsible for control in the industry. The IEC-61131-3 standard considers five programming languages: Ladder Diagram, Structured Text, Function Block Diagram, Instruction List, and Sequential Function Diagram, which use different function blocks to develop control algorithms. Within the control algorithms for discrete event systems, there are two types of blocks: those with discrete inputs and outputs, and those with discrete and analog inputs and discrete output. Of the latter, the present research shows the analysis and formal model of the blocks including the problems of accumulation of tokens and the restoration of the coils. This proposal includes logical blocks of timers, counters, positive and negative transition detectors and bistable elements, which, together with the AND, OR, AND-OR, contact lock, auto-loop and Set-Reset logics, can be modeled and analyzed control algorithms with a greater degree of complexity. This guarantees the safety of workers as well as machines.

This study developes and validates an Automation Studio-based critical thinking assessment instrument for electrical engineering students, focusing on the ladder diagram concepts in automation control systems. The multiple-choice instrument emphasises the significance of critical thinking in engineering education, particularly in the design and analysis of logic control systems. A quantitative methodology was employed with content validation conducted by experts, in addition to construct validity and reliability analysed statistically using SPSS. Out of the 45 items, 35 were deemed valid with item correlation values exceeding the significance threshold (r > 0.3). The reliability, measured using Cronbach's alpha, was 0.926, indicating excellent internal consistency. Difficulty levels and question differentiation confirmed the efficacy of the instrument in assessing critical thinking skills. This study contributes to the development of technology-based critical thinking evaluation tools that are appropriate for contemporary engineering education. Future research directions include adapting the instrument to other engineering disciplines, and refining it through broader population testing. The findings underscore the relevance of validated and reliable instruments for fostering critical thinking among engineering students.

Powerful advantages of programmable logic controller (PLC) dominate process industries. Scan time of PLC increases with the number of inputs, rungs added in ladder diagram (LD). Researchers have identified and proved that field programmable gate array (FPGA) is more suitable than PLC for high speed applications. PLC executes the instructions represented through LD. PLC programmers are not familiar with FPGA programming. But, FPGA does not support LD based programming. This work has developed application software to generate equivalent VerilogHDL code for LD using LabVIEW. Novelty in this work is that each rung is defined using an \"assign\" statement which helps simultaneous execution of all the rungs. A data acquisition system was created to monitor the digital signals handled by the FPGA. The software was verified with a case study of substances mixing and traffic light control system.

Programmable logic controller (PLC) has become commonly used in industrial machinery for sequence control. However, the PLC program is easy to replicate and to analyse. This factor should become a security consideration for using it as a platform for a nuclear power reactor for the Instrumentation and Control (I&C) system. Since the PLC-based system has the possibility of common cause failure, as well as cybersecurity attacks and PLCs, have to handle many complex systems. Therefore field programmable gate array (FPGA) technology is possible to be implemented as a control program with hard-wired logic for experimental power reactor (RDE) I&C system. However, another factor should become a consideration. This trade-off analysis studies are presents a systematic method to compare the performance of implement a hard-wired sequence control with FPGA and PLC using a ladder diagram. Productive PLC programs were examined with Omron CQM1 and Altera Stratix II FPGA and were shown to fit into a common FPGA chip. Straightforward Sequential design and a performance-oriented flat design was estimated to be used for time response performance. By this analysis, it hope that development of I&C system for RDE will have a unanimous decision to determine which platform to be implemented, with the consideration that the chosen platform meets the criteria as the requirement analysis from the stakeholders which it refers to the user needs to develop an availability, maintainability and reliability system essential to safety.

Automated systems based on programmable logic controllers (PLC) are still applied in discrete event systems (DES) for controlling and monitoring of industrial processes signals. PLC-based control systems are characterized for having physical input and output signals coming from and going to sensors and actuators, respectively, which they are in direct contact with the production or manufacturing process. The input subsystem to PLC consists of sensor-wiring-physical inputs module, and it can present two kinds of faults: short circuit or open circuit, in one or more signals of the process physical inputs, which it causes faults in the control and/or in the control algorithms behavior. Ladder diagram (LD) is one of the five programming languages supported by the International Electrotechnical Commission (IEC) through the IEC-61131-3 standard, and it remains being used at industry for control algorithm design of PLC-based systems. This paper proposes the simulation and validation of control algorithms developed in LD by using Petri Nets (PN) in order to deal with the possible fault options (short circuit and/or open circuit) in the physical inputs subsystem of a PLC-based control system. One control algorithms in LD have been analyzed in order to show the advantages of the proposed approach.

A bstract We present new computations for Feynman integrals relevant to Higgs plus jet production at three loops, including first results for a non-planar class of integrals. The results are expressed in terms of generalised polylogarithms up to transcendental weight six. We also provide the full canonical differential equations, which allows us to make structural observations on the answer. In particular, we find a counterexample to previously conjectured adjacency relations, for a planar integral of the tennis-court type. Additionally, for a non-planar triple ladder diagram, we find two novel alphabet letters. This information may be useful for future bootstrap approaches.

A bstract We develop an operator approach to the evaluation of multiple integrals for multiloop Feynman massless diagrams. A commutative family of graph building operators H α for ladder diagrams is constructed and investigated. The complete set of eigenfunctions and the corresponding eigenvalues for the operators H α are found. This enables us to explicitly express a wide class of four-point ladder diagrams and a general two-loop propagator-type master diagram (with arbitrary indices on the lines) as Mellin-Barnes-type integrals. Special cases of these integrals are explicitly evaluated. A certain class of zig-zag four-point and two-point planar Feynman diagrams (relevant to the bi-scalar D -dimensional “fishnet” field theory and to the calculation of the β -function in ϕ 4 -theory) is considered. The graph building operators and convenient integral representations for these Feynman diagrams are obtained. The explicit form of the eigenfunctions for the graph building operators of the zig-zag diagrams is fixed by conformal symmetry and these eigenfunctions coincide with the 3-point correlation functions in D -dimensional conformal field theories. By means of this approach, we exactly evaluate the diagrams of the zig-zag series in special cases. In particular, we find a fairly simple derivation of the values for the zig-zag multi-loop two-point diagrams for D = 4. The role of conformal symmetry in this approach, especially a connection of the considered graph building operators with conformal invariant solutions of the Yang-Baxter equation is investigated in detail.

A bstract We study correlation functions in the one-dimensional N = 2 supersymmetric SYK model. The leading order 4-point correlation functions are computed by summing over ladder diagrams expanded in a suitable basis of conformal eigenfunctions. A novelty of the N = 2 model is that both symmetric and antisymmetric eigenfunctions are required. Although we use a component formalism, we verify that the operator spectrum and 4-point functions are consistent with N = 2 supersymmetry. We also confirm the maximally chaotic behavior of this model and comment briefly on its 6-point functions.

A bstract We discuss specific hypergeometric solutions of the conformal Ward identities (CWI’s) of scalar 4-point functions of primary fields in momentum space, in d spacetime dimensions. We determine such solutions using various dual conformal ansätze (DCA’s). We start from a generic dual conformal correlator, and require it to be conformally covariant in coordinate space. The two requirements constrain such solutions to take a unique hypergeometric form. They describe correlators which are at the same time conformal and dual conformal in any dimension. These specific ansätze also show the existence of a link between 3- and 4-point functions of a CFT for such class of exact solutions, similarly to what found for planar ladder diagrams. We show that in d = 4 only the box diagram and its melonic variants, in free field theory, satisfies such conditions, the remaining solutions being nonperturbative. We then turn to the analysis of some approximate high energy fixed angle solutions of the CWI’s which also in this case take the form of generalized hypergeometric functions. We show that they describe the behaviour of the 4-point functions at large energy and momentum transfers, with a fixed − t/s . The equations, in this case, are solved by linear combinations of Lauricella functions of 3 variables and can be rewritten as generalized 4K integrals. In both cases the CWI’s alone are sufficient to identify such solutions and their special connection with generalized hypergeometric systems of equations.

A bstract We continue the study of AdS loop amplitudes in the spectral representation and in position space. We compute the finite coupling 4-point function in position space for the large- N conformal Gross Neveu model on AdS 3 . The resummation of loop bubble diagrams gives a result proportional to a tree-level contact diagram. We show that certain families of fermionic Witten diagrams can be easily computed from their companion scalar diagrams. Thus, many of the results and identities of [ 1 ] are extended to the case of external fermions. We derive a spectral representation for ladder diagrams in AdS. Finally, we compute various bulk 2-point correlators, extending the results of [ 1 ].