scholarly journals Mathematical Modeling on the Control of Hunting Problems

2021 ◽  
Vol 12 (1) ◽  
pp. 1-8
Author(s):  
Redemtus Heru Tjahjana ◽  
Dhimas Mahardika
Keyword(s):  
Fundamental Problem ◽  
Equation System ◽  
Natural Phenomenon ◽  
Differential Equation System ◽  
Dynamics Model ◽  
Calculation Results ◽  
Successful Control ◽  
Simulation Results ◽  
And Control ◽  
The Pontryagin Maximum Principle

Modeling a natural phenomenon or the action mechanism of a tool is often done in science and technology. Observations through computer simulations cost less relatively. In the research, a bullet control model moving towards the target was explored. The research aimed to try to simulate the trajectory of the bullet that could be controlled in hunting. To model a controlled bullet, the Dubins model was used. Then, the used approach was control theory. The optimal trajectory and control for bullets were designed using the Pontryagin Maximum Principle. The results show that with this principle and the dynamic system of the bullet, a system of differential equations and adjoining is obtained. The fundamental problem arises because the bullet dynamics model in the form of a differential equation system has initial and final requirements. However, the adjoint matching system has no conditions at all. This problem is solved by using numerical methods. In addition, the research proves the convergence of the calculation results with the required results. The track simulation results are also reported at the end of the research to ensure a successful control design. From the simulation results, the presented method with its convergence has successfully solved the problem of bullet control.

The Model of Transfer Robot in Chemical Mechanical Polishing

2013 ◽  
Vol 647 ◽  
pp. 867-874
Author(s):  
Jian Wei Zhao ◽  
Xin Chun Lu ◽  
Yong Yong He
Keyword(s):  
Material Processing ◽  
Chemical Mechanical Polishing ◽  
Lagrange Equation ◽  
Mechanical Polishing ◽  
System Stability ◽  
Dynamics Model ◽  
Strongly Coupled ◽  
Simulation Results ◽  
And Control ◽  
Important Kind

Transfer robot of chemical mechanical polishing (TRCMP) has some joints. For an important kind of special transfer robot, it is used as automatic material processing equipment in the semiconductor manufacture. The TRCMP has nonlinear, strongly coupled, multi-joints and under actuated, and these characteristics brought some difficulties to model and control. A dynamic model of the TRCMP was based on Lagrange equation and Newton dynamics theory. Then linearization of the dynamics model was done and its state-space equations were established. This structure of the model established is very simple, and it can control the TRCMP effectively and easy. Simulation results proved the system stability, and experiment results analyzed verified that the model of TRCMP is valid and rational.

scholarly journals A Contribution to the Mathematical Modeling of the Corona/COVID-19 Pandemic

2020 ◽  
Author(s):  
Günter Bärwolff
Keyword(s):  
Integration Method ◽  
Equation System ◽  
Sir Model ◽  
Good Choice ◽  
Differential Equation System ◽  
Estimation Of Parameters ◽  
Mathematical Methods ◽  
Acceleration Rate ◽  
Johns Hopkins University ◽  
And Control

AbstractThe responsible estimation of parameters is a main issue of mathematical pandemic models. Especially a good choice of β as the number of others that one infected person encounters per unit time (per day) influences the adequateness of the results of the model. For the example of the actual COVID-19 pandemic some aspects of the parameter choice will be discussed. Because of the incompatibility of the data of the Johns-Hopkins-University [3] to the data of the German Robert-Koch-Institut we use the COVID-19 data of the European Centre for Disease Prevention and Control [2] (ECDC) as a base for the parameter estimation. Two different mathematical methods for the data analysis will be discussed in this paper and possible sources of trouble will be shown.Parameters for several countries like UK, USA, Italy, Spain, Germany and China will be estimated and used in W. O. Kermack and A. G. McKendrick’s SIR model[1]. Strategies for the commencing and ending of social and economic shutdown measures are discussed.The numerical solution of the ordinary differential equation system of the modified SIR model is being done with a Runge-Kutta integration method of fourth order [4].At the end the applicability of the SIR model could be shown. Suggestions about appropriate points in time at which to commence with lockdown measures based on the acceleration rate of infections conclude the paper. This paper is an improved sequel of [5].

Model development and control of an auto-refrigerated polystyrene polymerization reactor

2021 ◽  
pp. 014233122110251
Author(s):  
Reyhane Mokhtarname ◽  
Ali Akbar Safavi ◽  
Leonhard Urbas ◽  
Fabienne Salimi ◽  
Mohammad M Zerafat ◽  
...  
Keyword(s):  
Temperature Control ◽  
Model Development ◽  
Heat Removal ◽  
Superior Performance ◽  
Polymerization Process ◽  
Vacuum System ◽  
Control Scheme ◽  
Simulation Results ◽  
And Control ◽  
Operating Plant

Dynamic model development and control of an existing operating industrial continuous bulk free radical styrene polymerization process are carried out to evaluate the performance of auto-refrigerated CSTRs (continuous stirred tank reactors). One of the most difficult tasks in polymerization processes is to control the high viscosity reactor contents and heat removal. In this study, temperature control of an auto-refrigerated CSTR is carried out using an alternative control scheme which makes use of a vacuum system connected to the condenser and has not been addressed in the literature (i.e. to the best of our knowledge). The developed model is then verified using some experimental data of the real operating plant. To show the heat removal potential of this control scheme, a common control strategy used in some previous studies is also simulated. Simulation results show a faster dynamics and superior performance of the first control scheme which is already implemented in our operating plant. Besides, a nonlinear model predictive control (NMPC) is developed for the polymerization process under study to provide a better temperature control while satisfying the input/output and the heat exchanger capacity constraints on the heat removal. Then, a comparison has been also made with the conventional proportional-integral (PI) controller utilizing some common tuning rules. Some robustness and stability analyses of the control schemes investigated are also provided through some simulations. Simulation results clearly show the superiority of the NMPC strategy from all aspects.

scholarly journals A modular framework to generate robust biped locomotion: from planning to control

2021 ◽  
Vol 3 (9) ◽  
Author(s):  
Mohammadreza Kasaei ◽  
Ali Ahmadi ◽  
Nuno Lau ◽  
Artur Pereira
Keyword(s):  
Numerical Simulations ◽  
Predictive Control ◽  
Biped Locomotion ◽  
Input Output ◽  
Dynamics Model ◽  
Biped Robots ◽  
The Core ◽  
Simulation Results ◽  
Reference Trajectories ◽  
Modular Framework

AbstractBiped robots are inherently unstable because of their complex kinematics as well as dynamics. Despite many research efforts in developing biped locomotion, the performance of biped locomotion is still far from the expectations. This paper proposes a model-based framework to generate stable biped locomotion. The core of this framework is an abstract dynamics model which is composed of three masses to consider the dynamics of stance leg, torso, and swing leg for minimizing the tracking problems. According to this dynamics model, we propose a modular walking reference trajectories planner which takes into account obstacles to plan all the references. Moreover, this dynamics model is used to formulate the controller as a Model Predictive Control (MPC) scheme which can consider some constraints in the states of the system, inputs, outputs, and also mixed input-output. The performance and the robustness of the proposed framework are validated by performing several numerical simulations using MATLAB. Moreover, the framework is deployed on a simulated torque-controlled humanoid to verify its performance and robustness. The simulation results show that the proposed framework is capable of generating biped locomotion robustly.

scholarly journals Transient Dynamics in the Random Growth and Reset Model

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 306
Author(s):  
Tamás S. Biró ◽  
Lehel Csillag ◽  
Zoltán Néda
Keyword(s):  
Differential Equation ◽  
Mean Field ◽  
Equation System ◽  
Transient Dynamics ◽  
Type Model ◽  
Discrete Version ◽  
Differential Equation System ◽  
Practical Applications ◽  
Random Growth ◽  
Recursive Integration

A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics.

Study on Engine Kinematics and Dynamics Simulation Based on COSMOSMotion

2012 ◽  
Vol 503-504 ◽  
pp. 731-734
Author(s):  
Xiao Xu Liu ◽  
Min Chen ◽  
Ai Hua Tang
Keyword(s):  
Virtual Prototype ◽  
Dynamics Simulation ◽  
Kinematics And Dynamics ◽  
Engine Model ◽  
Kinematics Simulation ◽  
Simulation Based ◽  
Calculation Results ◽  
Simulation Results ◽  
Dynamics Simulations

The engine model with 4 cylinders is built by SolidWorks, the kinematics and dynamics simulations of the engine virtual prototype are done by COSMOSMotion, the results of kinematics simulation are checked, there are very small errors between the simulation results and the calculation results according to formulas. The mainly results of dynamics simulation are given. The simulation result consists with the parameters of the engine.

A multigroup model for cholera dynamics and control

2015 ◽  
Vol 09 (01) ◽  
pp. 1650001 ◽  
Author(s):  
Drew Posny ◽  
Chairat Modnak ◽  
Jin Wang
Keyword(s):  
Reproduction Number ◽  
Vaccination Strategy ◽  
Sharp Threshold ◽  
Indirect Transmission ◽  
Dynamics And Control ◽  
Simulation Results ◽  
Transmission Pathways ◽  
And Control ◽  
Control Study ◽  
The Basic Reproduction Number

We propose a general multigroup model for cholera dynamics that involves both direct and indirect transmission pathways and that incorporates spatial heterogeneity. Under biologically feasible conditions, we show that the basic reproduction number R0 remains a sharp threshold for cholera dynamics in multigroup settings. We verify the analysis by numerical simulation results. We also perform an optimal control study to explore optimal vaccination strategy for cholera outbreaks.

scholarly journals Kinematic Analysis of Three-Wire-Driven Parallel (TWDP) Robot

2011 ◽  
Vol 2-3 ◽  
pp. 302-307 ◽  
Author(s):  
Tao Yu ◽  
Qing Kai Han
Keyword(s):  
Static Analysis ◽  
Parallel Robot ◽  
Analytical Models ◽  
Kinematics Analysis ◽  
Mechanism Model ◽  
Good Movement ◽  
Dynamics And Control ◽  
Movement Stability ◽  
Simulation Results ◽  
And Control

In the paper, a novel new gravity-constrained (GC) three-wire-driven (TWD) parallel robot is proposed. With its mechanism model, three typical kinematics analytical models, including horizontal up-down motion, pitching motion and heeling motion and their corresponding simulations are given in detail. In static analysis, the change of tensions in the wires is calculated based on previous kinematics analysis. The simulation results show the robot has good movement stability. The paper can provide useful materials to study of dynamics and control on wire-driven robot.

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