scholarly journals Modeling and Analysis of Online Delay of Nonperiodic CAN Message

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Dafang Wang ◽  
Bowen Yang ◽  
Yi Jin ◽  
Ji Qi ◽  
Nannan Li
Keyword(s):  
Mathematical Model ◽  
Queuing Theory ◽  
Online Communication ◽  
Load Ratio ◽  
High Accuracy ◽  
Actual Situation ◽  
Modeling And Analysis ◽  
Experimental Platform ◽  
On Line ◽  
The Mathematical Model

In order to analyze the online communication delay of nonperiodic CAN message, the mathematical model of average on-line delay is established based on M/G/1 queuing theory and an experimental platform is designed to analyze the delay of CAN communication, with which the on-line delays of messages with a different ID are tested at different load ratios. The results show that the model is very close to the actual situation indicating the high accuracy of the model. In the results, for the same message, the average and maximum online delays both increase with the raise of load ratio. At the same load ratio, the maximum on-line delay increases with the decrease of the message priority, and the average on-line delay remains almost unchanged.

Force tracking control of grinding end effector based on backstepping + PID

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Shijie Dai ◽  
Shining Li ◽  
Wenbin Ji ◽  
Zhenlin Sun ◽  
Yufeng Zhao
Keyword(s):  
Mathematical Model ◽  
Linear System ◽  
Control Strategy ◽  
Grinding Force ◽  
Constant Force ◽  
End Effector ◽  
Content Type ◽  
Modeling And Analysis ◽  
The Mathematical Model ◽  
Automobile Wheel

Purpose This study aims to realize the constant force grinding of automobile wheel hub. Design/methodology/approach A force control strategy of backstepping + proportion integration differentiation (PID) is proposed. The grinding end effector is installed on the flange of the robot. The robot controls the position and posture of the grinding end actuator and the grinding end actuator controls the grinding force output. First, the modeling and analysis of the grinding end effector are carried out, and then the backstepping + PID method is adopted to control the grinding end effector to track the expected grinding force. Finally, the feasibility of the proposed method is verified by simulation and experiment. Findings The simulation and experimental results show that the backstepping + PID strategy can track the expected force quickly, and improve the dynamic response performance of the system and the quality of grinding and polishing of automobile wheel hub. Research limitations/implications The mathematical model is based on the pneumatic system and ideal gas, and ignores the influence of friction in the working process of the cylinder, so the mathematical model proposed in this study has certain limitations. A new control strategy is proposed, which is not only used to control the grinding force of automobile wheels, but also promotes the development of industrial control. Social implications The automatic constant force grinding of automobile wheel hub is realized, and the manpower is liberated. Originality/value First, the modeling and analysis of the grinding end effector are carried out, and then the backstepping + PID method is adopted to control the grinding end effector to track the expected grinding force. The nonlinear model of the system is controlled by backstepping method, and in the process, the linear system composed of errors is obtained, and then the linear system is controlled by PID to realize the combination of backstepping and PID control.

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.

scholarly journals Mathematical Modeling and Analysis of Multirobot Cooperative Hunting Behaviors

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yong Song ◽  
Yibin Li ◽  
Caihong Li ◽  
Xin Ma
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Numerical Solutions ◽  
Rate Equations ◽  
Ratio Analysis ◽  
Hunting Behavior ◽  
Modeling And Analysis ◽  
Cooperative Hunting ◽  
Model Equations ◽  
The Mathematical Model

This paper presents a mathematical model of multirobot cooperative hunting behavior. Multiple robots try to search for and surround a prey. When a robot detects a prey it forms a following team. When another “searching” robot detects the same prey, the robots form a new following team. Until four robots have detected the same prey, the prey disappears from the simulation and the robots return to searching for other prey. If a following team fails to be joined by another robot within a certain time limit the team is disbanded and the robots return to searching state. The mathematical model is formulated by a set of rate equations. The evolution of robot collective hunting behaviors represents the transition between different states of robots. The complex collective hunting behavior emerges through local interaction. The paper presents numerical solutions to normalized versions of the model equations and provides both a steady state and a collaboration ratio analysis. The value of the delay time is shown through mathematical modeling to be a strong factor in the performance of the system as well as the relative numbers of the searching robots and the prey.

Research on Mathematical Model and Calibration of Weighing System by Digital Addition

2012 ◽  
Vol 151 ◽  
pp. 101-104
Author(s):  
Chao Fu Zhu ◽  
Shu Jian Ji ◽  
Jin Long Zhao
Keyword(s):  
Mathematical Model ◽  
Calibration Method ◽  
Optimization Method ◽  
Load Cells ◽  
On Line ◽  
The Mathematical Model ◽  
Multiple Load

In practice the method is widely used, by which a gravity is measured using multiple load cells. A weighing system is introduced in this paper, in which a gravity is measured by multiple load cells with digital addition. The mathematical model of weighing system with digital addition is established. Normal calibration method is not suitable for the on-line calibration of weighing system with digital addition. When the mathematical model is given, the accurate on-line calibration of weighing system with digital addition is achieved by using optimization method.

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.

Control Design of Foreign Fibers Detecting System Paving Mechanism

2013 ◽  
Vol 846-847 ◽  
pp. 228-232
Author(s):  
Hua Qing Wang ◽  
Jian Cheng Yang ◽  
Kai Yang ◽  
Jian Feng Qin ◽  
Ze Xu Zhou ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Control Design ◽  
Line Speed ◽  
On Line ◽  
Working Principle ◽  
The Mathematical Model ◽  
The Relationship

In this paper the working principle of cotton foreign fibers detecting and clearing on line device paving and loosing part is described, and the mathematical model of the relationship between line speed is established, and paving part control system that is suitable for this device has been designed on this basis.

Fault Forecast Technology of Machine Based on Grey Theory for Aero-Engine Product Line

2011 ◽  
Vol 338 ◽  
pp. 718-722 ◽  
Author(s):  
Bing Chen ◽  
Ting Yang ◽  
Jun De Qi
Keyword(s):  
Mathematical Model ◽  
High Accuracy ◽  
Product Line ◽  
Grey Theory ◽  
Mean Time Between Failures ◽  
Time Between Failures ◽  
Aero Engine ◽  
Machine Fault ◽  
The Mathematical Model ◽  
Mean Time

Facing to the dynamic process of machine running, grey theory is introduced to increase the accuracy of forecast on machine fault. Firstly the mathematical model of the machine fault is constructed according to the life cycle of machine. Mean time between failures is defined as a tool to describe the fault on the machine. Moreover the fault is predicted respectively according to amount of data sample. And the produce to build the grey information model is given in this paper in detail. Finally an actual aero-engine casing production line is presented as an example to validate the algorithms in this paper. The results show that the fault forecast based on grey theory has high accuracy.

A NEW DISCRETIZED MODEL IN NONLINEAR KINETIC THEORY—THE SEMICONTINUOUS BOLTZMANN EQUATION

1991 ◽  
Vol 01 (01) ◽  
pp. 113-123 ◽  
Author(s):  
N. BELLOMO ◽  
E. LONGO
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Continuous Dependence ◽  
Modeling And Analysis ◽  
Collision Invariants ◽  
The Mathematical Model ◽  
Nonlinear Kinetic ◽  
Discretized Model

This paper deals with the mathematical modeling and analysis of a new model of the Boltzmann equation with a finite number of velocity moduli, but with a continuous dependence on the velocity directions. The mathematical model is derived in the first part of the paper. Then the analysis of the equilibrium Maxwellian state is dealt with in the second part of the paper with the purpose of showing that the space of collision invariants is the correct one.

Research on Tooth Profile Design of Spur Gears Based on Line of Action

2013 ◽  
Vol 631-632 ◽  
pp. 817-823
Author(s):  
Jian Wang ◽  
Liang Hou ◽  
Shan Ming Luo
Keyword(s):  
Mathematical Model ◽  
Design Method ◽  
Tooth Profile ◽  
Spur Gears ◽  
On Line ◽  
Profile Design ◽  
The Mathematical Model

This paper aims to propose a design method for tooth profiles of spur gears based on given line of action. A simplified derivation of the mathematical model of tooth profiles is introduced according to the meshing theory. Tooth profiles of spur gears, using a parabola as line of action, is established. The result shows that it will be better to control the performances of a gear set by specifying the shape of the line of action rather than specifying tooth profiles of mating gear.

scholarly journals Using real interpolation method for adaptive identification of nonlinear inverted pendulum system

2019 ◽  
Vol 9 (2) ◽  
pp. 1078
Author(s):  
Phu Tran Tin ◽  
Tran Hoang Quang Minh ◽  
Tran Thanh Trang ◽  
Nguyen Quang Dung
Keyword(s):  
Mathematical Model ◽  
Nonlinear Model ◽  
Inverted Pendulum ◽  
Interpolation Method ◽  
High Accuracy ◽  
Real Interpolation ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Real Interpolation Method ◽  
The Mathematical Model

<p>In this paper, we investigate the inverted pendulum system by using real interpolation method (RIM) algorithm. In the first stage, the mathematical model of the inverted pendulum system and the RIM algorithm are presented. After that, the identification of the inverted pendulum system by using the RIM algorithm is proposed. Finally, the comparison of the linear analytical model, RIM model, and nonlinear model is carried out. From the results, it is found that the inverted pendulum system by using RIM algorithm has simplicity, low computer source requirement, high accuracy and adaptiveness in the advantages.</p>

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