Dynamic Performance Characteristics, Part 2

2001 ◽  
Author(s):  
Fred V. Brock ◽  
Scott J. Richardson
Keyword(s):  
Mathematical Model ◽  
Dynamic Performance ◽  
Linear Ordinary Differential Equation ◽  
Performance Model ◽  
Physical Aspect ◽  
System Parameters ◽  
Forcing Function ◽  
Independent Variable ◽  
Time Invariant ◽  
The Mathematical Model

The first-order model discussed in chap. 6 is inadequate when there is more than one energy storage reservoir in the system to be modeled. If the sensor is linear it can be modeled with a higher-order dynamic performance model. Here the term ‘system’ refers to a physical device such as a sensor while the equation refers to the corresponding mathematical model. There exists a dual set of terms corresponding to consideration of the physical system or of the mathematical model. For example, an are coefficients of the mathematical model (see eqn. 8.1) but they also represent some physical aspect of the sensor being modeled; thus they can also be called system parameters. The general dynamic performance model is the linear ordinary differential equation where t = time, the independent variable, x = the dependent variable, an = equation coefficients or system parameters, and xi(t) = input or forcing function. This equation is ordinary because there is only one independent variable. It is linear because the dependent variable and its derivatives occur to the first degree only. This excludes powers, products, and functions such as sin(x). If the system parameters an are constant, the system is time invariant.

A High Performance Model for Task Allocation in Distributed Computing System Using K-Means Clustering Technique

2018 ◽  
Vol 9 (3) ◽  
pp. 1-23 ◽  
Author(s):  
Harendra Kumar ◽  
Nutan Kumari Chauhan ◽  
Pradeep Kumar Yadav
Keyword(s):  
Mathematical Model ◽  
Distributed Computing ◽  
High Performance ◽  
Computing System ◽  
Performance Model ◽  
Communication Costs ◽  
Clustering Technique ◽  
Proposed Model ◽  
Two Stages ◽  
The Mathematical Model

Tasks allocation is an important step for obtaining high performance in distributed computing system (DCS). This article attempts to develop a mathematical model for allocating the tasks to the processors in order to achieve optimal cost and optimal reliability of the system. The proposed model has been divided into two stages. Stage-I, makes the ‘n' clusters of set of ‘m' tasks by using k-means clustering technique. To use the k-means clustering techniques, the inter-task communication costs have been modified in such a way that highly communicated tasks are clustered together to minimize the communication costs between tasks. Stage-II, allocates the ‘n' clusters of tasks onto ‘n' processors to minimize the system cost. To design the mathematical model, executions costs and inter tasks communication costs have been taken in the form of matrices. To test the performance of the proposed model, many examples are considered from different research papers and results of examples have compared with some existing models.

scholarly journals NUMERICAL MODEL OF CURRENT AND SEDIMENT TRANSPORT IN THE WAVE BOUNDARY LAYER

2011 ◽  
Vol 1 (32) ◽  
pp. 5
Author(s):  
Yuliang Zhu ◽  
Jing Ma ◽  
Hao Wang
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Eddy Viscosity ◽  
Sediment Concentration ◽  
Wave Boundary Layer ◽  
Time Invariant ◽  
Wave Boundary ◽  
The Mathematical Model ◽  
The Relationship ◽  
Turbulent Wave

Mathematical model is one of the means to study of turbulent wave boundary layer. The paper analysis of the existing model, adopt a more reasonable boundary condition to establish a improved mathematical model of 1DV turbulent wave boundary layer using k-ε model. The paper recommends brief flow simulation and mainly introduced the simulation of the sediment concentration. The paper use the eddy-viscosity value which calculation by the mathematical model and the model of You Zaijin on time-invariant eddy-viscosity into the relationship about sediment diffusion coefficient and eddy-viscosity to calculate the sediment concentration. The calculation results turns out the way that use the eddy-viscosity value which calculation by the mathematical model into the relationship can obtain better timely sediment concentration value. When use the model simulates the time-invariant sediment concentration, the two ways have not many distinctions. It means the way that that use the eddy-viscosity value which calculation by the mathematical model into the relationship is feasible.

Mathematical Modeling of a DC Motor With Encoder Feedback Using Real Time Simulation

2001 ◽  
Author(s):  
Kourosh Rahnamai ◽  
Brian Yanke
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Dc Motor ◽  
Actual System ◽  
Math Model ◽  
Real Time Simulation ◽  
System Parameters ◽  
Time Simulation ◽  
The Mathematical Model ◽  
Permanent Magnet Dc Motor

Abstract Real-time simulation is used to model and perform parameter identification of a dc motor with encoder feedback. Using a fast DSP board, a permanent-magnet dc motor is controlled through a proportional position feedback, while running in parallel a real-time simulation of the mathematical model of the same system. Parameters of the mathematical model are adjusted in real time, such that the error between actual system and math model are minimized. This method allows a fast and efficient method for calculating and verifying math model of a dynamic system.

Modeling and Simulation of Educational Linear Motion Module

2009 ◽  
Author(s):  
Dian-sheng Chen ◽  
Yu-xin Chen ◽  
Tian-miao Wang
Keyword(s):  
Mathematical Model ◽  
Dynamic Performance ◽  
Linear Motion ◽  
Motion Model ◽  
Load Case ◽  
Know How ◽  
Working Principle ◽  
And Control ◽  
The Mathematical Model ◽  
Control Accuracy

In order to let the student understand the linear motion module’ principles and know how to improve the dynamic performance and control accuracy, a mathematical model is established based on the analysis of the composition and working principle of linear motion module. On the load and unload conditions, we simulate and analyze the system respectively. In the load case, PID parameters are obtained after the PID regulation. The correction of establishing the mathematical model and simulating the system are verified so that the linear motion model’ precision is effectively enhanced.

scholarly journals A Novel Method for Changing the Dynamics of Slender Elements Using Sponge Particles Structures

Materials ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 4874
Author(s):  
Mateusz Żurawski ◽  
Bogumił Chiliński ◽  
Robert Zalewski
Keyword(s):  
Mathematical Model ◽  
Dynamic Properties ◽  
Experimental Studies ◽  
Continuous Model ◽  
Particle Structure ◽  
System Parameters ◽  
Mass Redistribution ◽  
Novel Method ◽  
The Mathematical Model ◽  
Theoretical Considerations

The paper concerns problems related to controlling the dynamic properties of beam-like elements. The parameters of the investigated system can be changed by external factors, resulting in partial changes in the system mass redistribution. It is assumed that it is possible to control the system dynamics by shaping the object frequency structure. The paper introduces the mathematical model of the investigated cantilever beam filled with a Sponge Particle Structure. The continuous model has been simplified to a discrete multi-degree of freedom system. The influence of the system parameters on its behavior is discussed in details. The possible applications of the presented concept are proposed. The spectral vibration analyses were carried out. Theoretical considerations enabled the use of the preliminary semi-active method for controlling the vibration frequencies through a mass redistribution. Experimental studies were carried out to verify the proposed mathematical model.

The Mechanics of Spiral Springs and Its Application in Timekeeping

2013 ◽  
Vol 81 (3) ◽  
Author(s):  
Longhan Xie ◽  
Puihang Ko ◽  
Ruxu Du
Keyword(s):  
Mathematical Model ◽  
Natural Frequency ◽  
Critical Parameter ◽  
Dynamic Deformation ◽  
Dynamic Performance ◽  
Spiral Spring ◽  
Simulation Results ◽  
Experimental Validations ◽  
The Mathematical Model ◽  
Castigliano’S Theorem

Spiral spring is widely used in mechanisms, such as mechanical watch movements and clocks where the spiral spring is used for timekeeping. According to literature, there are only a few studies on spiral springs. In this paper, the mechanics of spiral springs is analyzed in details, and its dynamic performance in mechanical watch movements is further studied to find out its natural frequency, which is the most critical parameter for mechanical watch movements. Based on Castigliano's theorem, the mathematical model of dynamic deformation and natural frequency of the spiral spring under external axial torque is developed, and computer simulation with Matlab® is also conducted. Experimental validations are carried out, which confirm the simulation results. Experiments show that the analytical method in this paper can be used to guide and facilitate the design of spiral spring.

scholarly journals Mathematical model of explanation of the world’s structure in Plato’s Timaeus

2019 ◽  
Vol 62 (2) ◽  
pp. 163-188
Author(s):  
Aleksandar Kandic
Keyword(s):  
Mathematical Model ◽  
Physical World ◽  
Human Organism ◽  
Physical Aspect ◽  
Natural Phenomena ◽  
The Status ◽  
Psychological Origin ◽  
Micro Structures ◽  
The Mathematical Model ◽  
The Relationship

Plato?s cosmological dialogue The Timaeus initiates, among other things, the question of the status of mathematical entities: do they exist completely independently of the physical world whose structure they supposedly explain, are they present in a certain sense within the physical world, or are they, perhaps, exclusively psychological in nature. The author of the paper critically examines Johansen?s interpretation according to which the inherent structure of the human psyche, in the case of Plato?s Timaeus, is already mathematically ideal. Although Johansen?s interpretation is pervasive and well-grounded, the relationship between mathematical and sensory entities is considered mainly in the context of astronomy, disregarding Plato?s theory of micro-structures (the so-called geometric atomism). Thus, the author confronts Johansen?s interpretation with the opinions of other influential researchers of ancient philosophy, such as Cornford, Vlastos, Popper, Lloyd, Brisson, as well as the philosophers of the ancient era, Proclus, Aristotle, and others, in an effort to develop an interpretation that is as close as possible to the whole of Plato?s text. It seems that, when it comes to Plato?s Timaeus, one cannot discuss about the psychological origin of the mathematical model of explanation of natural phenomena without realizing that, in a quite complicated way, such mathematical model possesses a physical aspect as well. Plato himself, at the end of The Timaeus, claims that psychological disorders are caused by disruptions of the mathematically ideal proportions of bodily parts of the human organism (86b), which is only one of his claims that points to the psychophysical nature of mathematical entities.

scholarly journals MATHEMATICAL MODEL OF ESTIMATION THE DYNAMIC PARAMETERS OF MACHINE AND TRACTOR UNIT’S ENGINE UNDER UNSTEAD LOAD

2019 ◽  
Vol 14 (2) ◽  
pp. 106-110 ◽  
Author(s):  
Владимир Медведев ◽  
Vladimir Medvedev ◽  
Станислав Синицкий ◽  
Stanislav Sinickiy
Keyword(s):  
Mathematical Model ◽  
Dynamic Characteristics ◽  
Theoretical Basis ◽  
Theoretical Calculations ◽  
Dynamic Performance ◽  
Transition Process ◽  
Theoretical Studies ◽  
The Mathematical Model ◽  
Regulatory Characteristic ◽  
The Ideal

The article provides an analysis of the existing methods and techniques for assessing the dynamic characteristics of engines of mobile machines, and also presents theoretical calculations for estimating the dynamic performance of an machine and tractor unit’s engine under unsteady load. The proposed mathematical model describes the change in the performance of the engine of machine and tractor unit with a linear law of loading and allows you to compare an engine’s operation at unsteady load with the ideal. The quasi-dynamic characteristic was laid as the theoretical basis for study to assess the dynamic performance of machine and tractor unit’s engine under unsteady load. Comparison of the dynamic performance of engines at unsteady load with ideal performance, which have no dynamic losses. It is proposed to apply the “quasi-dynamic” characteristics. The quasidynamic (ideal) characteristic is called - the change in the performance of machine and tractor unit’s engine, in the transition process, occurring in accordance with the change in the frequency of rotation of the crankshaft on the stationary characteristics. The mathematical model for estimating the dynamic performance of an machine and tractor unit’s engine using a correcting branch with an unsteady load is experimental equations for load buildup. Theoretical relationships have been developed for evaluating the dynamic performance of an engine with an unsteady load on the correcting branch of the regulatory characteristic. Using the proposed theoretical dependences, it is possible to carry out theoretical studies of the effect of load on the dynamic performance of an machine and tractor unit’s engine and determine the total dynamic losses.

Numerical Analysis on the Performance of Control Valve in Variable Displacement Wobble Plate Compressor

2005 ◽  
Vol 127 (2) ◽  
pp. 326-333 ◽  
Author(s):  
Chunpeng Dou ◽  
Xinjiang Yang ◽  
Changqing Tian ◽  
Xianting Li
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Dynamic Performance ◽  
Control Point ◽  
Control Valve ◽  
Effective Area ◽  
Suction Pressure ◽  
Study Characteristics ◽  
Variable Displacement ◽  
The Mathematical Model

The performance of control valve is analyzed in this paper in order to study characteristics of the variable displacement wobble plate compressor. The forces acting on the control valve are analyzed and the mathematical model to analyze its performance is developed. A test bench is set up to get the steady and dynamic performance of control valve. The steady-state performances predicted by the mathematical model agree well with the experimental data while the predicted dynamic performances agree with the experimental results qualitatively. With the mathematical model, the steady-state performances of the control valve with four different preset control points and three different effective areas of the evacuated bellows have been analyzed, and the dynamic behavior of one type control valve has been studied. It is shown that: (1) the suction pressure at preset control point is inversely proportional to the discharge pressure; (2) the larger the starting force of spring in control valve or the smaller the effective area of evacuated bellows, the larger the suction pressure at preset control point; and the larger the starting force of spring in control valve and the smaller the maximum opening of ball valve, the more quickly the crankcase pressure changes and the smaller mass flow rate of control valve; the slope ratio of crankcase pressure to suction pressure cannot be influenced by the starting force of spring in control valve but can be influenced by the effective area of evacuated bellows; (3) the transition time of the crankcase pressure is about 1 s and can be neglected when working condition changes.

Small-Signal Equivalent Circuit Modeling and Controller Design of DC/DC Converter Based on Matlab

2014 ◽  
Vol 1070-1072 ◽  
pp. 1586-1591
Author(s):  
Xiao Long Xiao ◽  
Xiao Jun Lu ◽  
Jian Wei Yi ◽  
Xiao Hua Ding
Keyword(s):  
Mathematical Model ◽  
Control Strategy ◽  
Model Building ◽  
Controller Design ◽  
Dynamic Performance ◽  
Feedback System ◽  
Small Signal ◽  
Loop Feedback ◽  
And Control ◽  
The Mathematical Model

The model-building of DC/DC converter is the key to design the control of system. It is important to study DC/DC converter stability and dynamic performance. A small-signal model of buck/boost circuit was built by average state-space. By analyzing the transfer function of buck/boost circuit, a voltage closed-loop feedback system was designed. Building system of simulation circuit in the Matlab, the result of simulation shows the system has a good static and dynamic performance. It verifies the rationality of the mathematical model and control strategy. It verifies the rationality of the mathematical model and control strategy.

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