scholarly journals Parallel mathematical models of dynamic objects

2018 ◽  
Vol 4 (2) ◽  
pp. 120 ◽  
Author(s):  
Roman Voliansky ◽  
Andri Pranolo
Keyword(s):  
Mathematical Model ◽  
Transfer Function ◽  
High Accuracy ◽  
Parallel Model ◽  
Partial Fraction ◽  
Dynamic Object ◽  
Calculation Time ◽  
Dynamical Object ◽  
Object Usage ◽  
Partial Fraction Decomposition

The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for transforming the serial mathematical model into parallel ones. This algorithm is based on partial fraction decomposition of the transfer function of a dynamic object. Usage of proposed algorithms is one of the ways to decrease calculation time and improve PC usage while a simulation is being performed. We prove our approach by considering the example of modeling and simulating of fourth order dynamical object with various eigenvalues. This example shows that developed parallel model is stable, well-convergent, and high-accuracy model. There is no defined any calculation errors between well-known serial model and proposed parallel one. Nevertheless, the proposed approach’s usage allows us to reduce calculation time by more than 20% by using several CPU’s cores while calculations are being performed.

Information dualism of the problem of optimum terminal control of dynamic object

2021 ◽  
pp. 85-90
Author(s):  
V.P. Ivanov
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Law ◽  
Computational Algorithms ◽  
Terminal Control ◽  
Dynamic Object ◽  
Nonlinear Mathematical Model ◽  
Dynamical Object

The article deals with the problem of synthesis of terminal control. A functional, a nonlinear mathematical model of a dynamic object, restrictions on the maximum permissible values of control are given. The control law is synthesized. The following statement is proved: the synthesis of the optimal control is carried out using the entire initial mathematical model of the dynamical object, but to calculate the control at any particular moment of time, it is possible to use a reduced (truncated) model, which simplifies the computational algorithms. Thus, there is an informational dualism of the manage- ment task. The approach is an extension of the principle of information redefinition of Yu.B. Germeier to the area of optimal terminal control.

Pulse-Width Modulated Amplifier for DC Servo System and Its Matlab Simulation

2015 ◽  
Vol 9 (1) ◽  
pp. 625-631
Author(s):  
Ma Xiaocheng ◽  
Zhang Haotian ◽  
Cheng Yiqing ◽  
Zhu Lina ◽  
Wu Dan
Keyword(s):  
Mathematical Model ◽  
Transfer Function ◽  
Input Signal ◽  
Pulse Width ◽  
Rotation Speed ◽  
Servo Motor ◽  
Matlab Simulation ◽  
Pulse Width Modulated ◽  
Signal Changes ◽  
The Relationship

This paper introduces a mathematical model for Pulse-Width Modulated Amplifier for DC Servo Motor. The relationship between pulse-width modulated (PWM) signal and reference rotation speed is specified, and a general model of motor represented by transfer function is also put forward. When the input signal changes, the rotation speed of the servo motor will change accordingly. By changing zeros and poles, transient performance of this system is discussed in detail, and optimal ranges of the parameters is recommended at the end of discussion.

scholarly journals Two-loop leading colour QCD corrections to $$ q\overline{q} $$ → γγg and qg → γγq

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Bakul Agarwal ◽  
Federico Buccioni ◽  
Andreas von Manteuffel ◽  
Lorenzo Tancredi
Keyword(s):  
Numerical Code ◽  
Tree Level ◽  
Partial Fraction ◽  
Integration By Parts ◽  
Analytic Expressions ◽  
Partial Fraction Decomposition ◽  
Loop Amplitudes

Abstract We present the leading colour and light fermionic planar two-loop corrections for the production of two photons and a jet in the quark-antiquark and quark-gluon channels. In particular, we compute the interference of the two-loop amplitudes with the corresponding tree level ones, summed over colours and polarisations. Our calculation uses the latest advancements in the algorithms for integration-by-parts reduction and multivariate partial fraction decomposition to produce compact and easy-to-use results. We have implemented our results in an efficient C++ numerical code. We also provide their analytic expressions in Mathematica format.

Multi-Object Multi-Discipline Probabilistic Design of High-Pressure Turbine Blade-Tip Radial Running Clearance

2013 ◽  
Vol 572 ◽  
pp. 551-554
Author(s):  
Wen Zhong Tang ◽  
Cheng Wei Fei ◽  
Guang Chen Bai
Keyword(s):  
Mathematical Model ◽  
High Pressure ◽  
Optimal Design ◽  
Mechanical System ◽  
High Accuracy ◽  
Probabilistic Design ◽  
High Pressure Turbine ◽  
Surface Method ◽  
Blade Tip ◽  
The Mathematical Model

For the probabilistic design of high-pressure turbine (HPT) blade-tip radial running clearance (BTRRC), a distributed collaborative response surface method (DCRSM) was proposed, and the mathematical model of DCRSM was established. From the BTRRC probabilistic design based on DCRSM, the static clearance δ=1.865 mm is demonstrated to be optimal for the BTRRC design considering aeroengine reliability and efficiency. Meanwhile, DCRSM is proved to be of high accuracy and efficiency in the BTRRC probabilistic design. The present study offers an effective way for HPT BTRRC dynamic probabilistic design and provides also a promising method for the further probabilistic optimal design of complex mechanical system.

Dynamic Requisition-Compensation Balance Theory of Mining-under Village Relocation Planning Based on PSO Algorithm

2014 ◽  
Vol 587-589 ◽  
pp. 128-131
Author(s):  
Ya Kai Chen ◽  
Dong Wen Liu ◽  
Zhi Yong Qiao ◽  
Ting Ting Wang ◽  
Shu Jiang
Keyword(s):  
Mathematical Model ◽  
Arable Land ◽  
Pso Algorithm ◽  
High Accuracy ◽  
Balance Theory ◽  
Land Area ◽  
Swarm Optimization ◽  
Land Conflict ◽  
Reclamation Project ◽  
Per Capita

This study has improved traditional ‘requisition first compensation later’ theory and ‘compensation first requisition later’ theory, and proposed dynamic requisition-compensation balance theory. Mathematical model of mining-under village relocation is established, and the particle swarm optimization (PSO) algorithm is used to optimize the stage relocation planning of dynamic requisition-compensation balance theory. The result shows that, this new theory can effectively solve land using problems such as land requisition difficulty and land compensation difficulty, reduce the human-land conflict, ensure execute relocation smoothly, promote reclamation project implementation, and can guarantee a certain amount of arable land surplus; The PSO algorithm can maximize both the surplus land area and the per capita building land area of farmer with high accuracy.

Exact Solutions of the Vibration Problem of Beam Structures

2013 ◽  
Vol 390 ◽  
pp. 242-245 ◽  
Author(s):  
Alexander V. Chekanin
Keyword(s):  
Mathematical Model ◽  
Exact Solutions ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Numerical Solutions ◽  
High Accuracy ◽  
Displacement Method ◽  
Actual Problem ◽  
Beam Structures ◽  
The Mathematical Model

The article deals with the actual problem of improving the accuracy of determining the dynamic characteristics of beam structures. To solve such problems the displacement method is used. Defining matrices are calculated with the Godunovs scheme. Numerical solutions in this case can be obtained practically with any accuracy within accepted hypotheses of the mathematical model of the calculated object. This suggests that the resulting solutions are standard. The examples of determining the natural frequencies of vibrations of beam structures that demonstrate an extremely high accuracy of the proposed algorithm are given.

Modeling and Simulation of a Micro-Actuator with Long-Travel

2008 ◽  
Vol 392-394 ◽  
pp. 804-809
Author(s):  
W.R. Jiang ◽  
Ze Sheng Lu
Keyword(s):  
Mathematical Model ◽  
High Resolution ◽  
Transfer Function ◽  
Friction Model ◽  
Theory Analysis ◽  
Stick Slip ◽  
Micro Actuator ◽  
Transmission Part ◽  
Speed Change ◽  
Set Up

A microactuator with long-travel and high-resolution based on the principle of tribology is presented, which stroke is up to 300mm and displacement resolution is 0.01μm. It resolves the contradiction of large-stroke and high-resolution in macro/micro drive successfully. The dynamic model of the microactuator is set up. The theory analysis on the dynamic character of the system is carried out based on Karnopp “stick-slip” friction model. The physical and mathematical model of the drive part and transmission part are set up respectively by the method of modularization. The transfer function of the system is attained. The tacking simulation is carried out based on fuzzy control with speed change integral, the result is proved that error is 0.004μm.

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