Multi-Level Linear Flexible Inverted Pendulum Modeling

2014 ◽  
Vol 518 ◽  
pp. 290-296 ◽  
Author(s):  
Tu Xu ◽  
Cui Fang Zhang
Keyword(s):  
Mathematical Model ◽  
Control Algorithm ◽  
Inverted Pendulum ◽  
Dissipation Function ◽  
Second Law ◽  
Control Performance ◽  
Lagrange Equations ◽  
Multi Level ◽  
Newton's Second Law

Linear flexible inverted pendulum is a very good platform for testing control algorithm. A new algorithm will usually be used to control linear inverted pendulum in order to detect its control performance. Before that, you need to know the exact mathematical model of the inverted pendulum. Known modeling of multi-level linear flexible inverted pendulum used Newton's second law, in the case of ignoring the mass obtained, therefore, there are imprecise situation. Here the use of Lagrange equations with dissipation function, consider the quality of the mass of the multi-level linear flexible inverted pendulum modeling to obtain a more accurate mathematical model.

scholarly journals Modeling and Optimal Controller Based on Disturbance Detector for the Stabilization of a Three-link Inverted Pendulum Mobile Robot

Electronics ◽  
2020 ◽  
Vol 9 (11) ◽  
pp. 1821
Author(s):  
Luis Alfonso Jordán-Martínez ◽  
Maricela Guadalupe Figueroa-García ◽  
José Humberto Pérez-Cruz
Keyword(s):  
Mathematical Model ◽  
Mobile Robot ◽  
Nonlinear Model ◽  
Direct Current ◽  
Inverted Pendulum ◽  
Experimental Tests ◽  
Optimal Controller ◽  
Stabilization Problem ◽  
Lagrange Equations ◽  
Direct Measurements

This work presents the realization of a complicated stabilization problem for a three inverted pendulum links-based mobile robot. The actuators of the mobile robot are direct current motors that have tachometer couplings to measure both the position and speed of the wheels and links. Using direct measurements under load and analyzing the deceleration curve, the motor parameters are determined experimentally. A mathematical model of the robot is obtained via the Euler–Lagrange equations. Next, the nonlinear model is linearized and discretized. Based on this discrete LTI model, an optimal controller is designed. The states and disturbances are estimated using a robust detector. Both the controller and detector are implemented in the robot processor. Numerical simulations and experimental tests show a good performance of the controller despite the presence of disturbances.

scholarly journals Laboratory Stand for Simplified Verification of Missile Dynamics for Didactic Purposes

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Adam Rowicki ◽  
Grzegorz Kopecki
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Coordinate System ◽  
Second Law ◽  
Matlab Simulink ◽  
Pi Regulator ◽  
System Parameters ◽  
Proportional Integral ◽  
Roll System ◽  
Newton's Second Law

Abstract The purpose of this study was to describe dynamics of missile based on bibliography, simplify the model to the easiest form, and verify it with the use of a designed laboratory stand. Next, a simple control system of the missile was designed. The stand is prepared for didactic purposes. A mathematical model was derived by applying Newton's second law together with the earth's coordinate system and the base coordinate system. Parameters of the actual rocket model were determined using the created laboratory stand. Synthesis of the rocket roll system was designed using Simulink PID Tuner application (MathWorks, Inc. Natick, Massachusetts, USA). A control system was based on a proportional-integral (PI) regulator. The designed control system was subjected to simulated tests in MATLAB Simulink (MathWorks, Inc. Natick, Massachusetts, USA).

scholarly journals Calculation and simulation of the parachutist's movement from the jump from the aircraft to landing on the ground

2021 ◽  
Author(s):  
Martin Beník ◽  
◽  
Ľubomír Kováčik
Keyword(s):  
Mathematical Model ◽  
Free Fall ◽  
Second Law ◽  
Model Based ◽  
Newton's Second Law ◽  
The Impact

In this article, we focus on the movement of the parachutist from the jump from the plane to the impact on the ground. By creating a mathematical model based on Newton's second law, we create simulations, based on which we can determine whether the movement of a parachutist after jumping from a plane is a "free fall", or whether the action of forces and his position in the air affects the direction of his flight.

scholarly journals Modelling of Classical and Rotary Inverted Pendulum Systems – A Generalized Approach

2013 ◽  
Vol 64 (1) ◽  
pp. 12-19 ◽  
Author(s):  
Slávka Jadlovský ◽  
Ján Sarnovský
Keyword(s):  
Program Implementation ◽  
Inverted Pendulum ◽  
General Procedure ◽  
Simulation Models ◽  
Open Loop ◽  
Dissipation Function ◽  
Lagrange Equations ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Rotary Inverted Pendulum

The purpose of this paper is to present the design and program implementation of a general procedure which yields the mathematical model for a classical or rotary inverted pendulum system with an arbitrary number of pendulum links. Lagrange equations of the second kind with an integrated Rayleigh dissipation function are employed in model design, and the energetic balance relations, derived for the base and all pendulum links in a generalized (n-link) classical and rotary inverted pendulum system, are implemented in form of symbolic MATLAB functions and a MATLAB GUI application. The validity and accuracy of motion equations generated by the application are demonstrated by evaluating the open-loop responses of simulation models of classical double and rotary single inverted pendulum.

Modeling and PID Control of Single-Stage Inverted Pendulum System

2014 ◽  
Vol 644-650 ◽  
pp. 142-145
Author(s):  
Yu Qiang Jin ◽  
Jun Wei Lei ◽  
Di Liu
Keyword(s):  
Mathematical Model ◽  
Dynamic Model ◽  
Pid Control ◽  
Control Algorithm ◽  
Inverted Pendulum ◽  
Good Stability ◽  
Pendulum System ◽  
Control Precision ◽  
Inverted Pendulum System ◽  
High Control

The dynamic model is obtained based on researching the structure of single inverted pendulum system in this paper. Mathematical model of inverted pendulum that is close to the working point is deduced by linearization. A PID control algorithm is put forward by analyzing the factor of influencing inverted pendulum stability. The effectiveness of proposed algorithm is verified by simulation. This algorithm has the features of high control precision and good stability.

scholarly journals SIMULATION OF PELLET DRYING PROCESS FROM APATITE-NEPHELINE ORES WASTES

2020 ◽  
Vol 55 ◽  
pp. 109-115
Author(s):  
Vladimir I. Bobkov ◽  
◽  
Мaxim I. Dli ◽  
Alexander S. Fedulov ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Moisture Transfer ◽  
Electric Energy ◽  
Drying Process ◽  
Increase Energy Efficiency ◽  
Multi Scale ◽  
Multi Level ◽  
Account Heat ◽  
Negative Phenomena

The paper presents a multi-scale mathematical model of a complex multi-level drying process of lumped man-made wastes of apatite-nepheline ores. It takes into account heat-technological peculiarities of the burning conveyor machine, intensity of internal moisture transfer in the shell, negative phenomena of over-wetting of separate horizons of the moving dense multilayer mass of pellets and heat carrier gas. This makes it possible to increase energy efficiency by intensifying heat-mass exchanging multi-layer drying processes. An essential dependence of efficiency of using heat and electric energy from organization of thermal and aerodynamic mode of thermal treatment of pellets from wastes of apatite-nepheline ores on quality of obtained pellets is revealed. According to numerous computational experiments on the developed simulation model, it is shown that when drying a moving multilayer mass of pellets in the drying zone of the burning conveyor machine, moisture is redistributed along the height of the multilayer mass, as a result of which in certain areas the pellets are over-watered.

scholarly journals KELAYAKAN MEDIA ANIMASI HUKUM NEWTON II TENTANG GERAK PADA BIDANG MIRING DAN KATROL DI SMA KABUPATEN ACEH BESAR

2018 ◽  
Vol 1 (1) ◽  
pp. 64-72
Author(s):  
Muslina Muslina ◽  
Abdul Halim ◽  
Ibnu Khaldun
Keyword(s):  
School Districts ◽  
Second Law ◽  
Test Results ◽  
Media Design ◽  
R And D ◽  
Teachers And Students ◽  
The Media ◽  
Newton's Second Law ◽  
Beta Testing

Abstrak. Penelitian ini dilakukan untuk mengembangkan media animasi hukum Newton II tentang gerak pada bidang miring dan katrol, mendeskripsikan kelayakan media animasi hukum Newton II yang dikembangkan baik dari segi kualitas, validitas, berdasarkan masukan para ahli, meminta tanggapan guru dan siswa terhadap media sehingga layak digunakan dalam pembelajaran fisika. Penelitian dilakukan di tiga sekolah kabupaten Aceh Besar (SMAN Modal Bangsa, SMAN 1 Montasik,  dan SMAN 1 Krueng Barona Jaya) menggunakan metode penelitian reasearch and development (R and D) dengan model pengembangan ADDIE.  Hasil pengujian alfa test  menunjukkan bahwa media animasi hukum Newton II tentang gerak pada bidang miring dan katrol sangat baik/layak digunakan sebagai media dari segi validitas. Penilaian kualitas media  dari aspek perangkat lunak, desain pembelajaran, desain media dan aspek komunikasi  secara keseluruhan menunjukkan bahwa media mempunyai kriteria sangat baik dan layak digunakan. Pengujian beta testing yang didasarkan pada hasil uji/tanggapan pengguna oleh guru dan siswa secara keseluruhan memberikan respon positif terhadap media, sehingga media animasi hukum Newton II yang dikembangkan memiliki kriteria sangat baik. Dari hasil penelitian  didapat bahwa kualitas media animasi yang dikembangkan memenuhi kriteria sangat baik dan layak digunakan sebagai media yang menunjang proses pembelajaran fisika. Kata Kunci : Media, Animasi, Katrol, Bidang Miring,Alfa test, Beta TestAbstract. This research was conducted to develop animation media Newton's second law of motion on an incline and pulley, describes eligibility animation media Newton's second law developed both in terms of quality, validity based on the input of experts, asking for a response of teachers and students to the media so it's worth used in learning physics. The study was conducted in three school districts of Aceh Besar (SMAN Modal Bangsa, SMAN 1 Montasik and SMAN 1 Krueng Barona Jaya) using research methods reasearch and development (R and D) with ADDIE development model. The test results showed that the alpha test animation media Newton's second law of motion on an incline and pulley very good / decent used as a medium in terms of validity. Quality assessment of aspects of the software media, instructional design, media design and communication aspects of the overall show that the media has a very good criteria and fit for use. Testing beta testing based on the test results / user feedback by teachers and students as a whole give a positive response to the media, so the media animation Newton's second law which has developed criteria very well. The result is that the quality of animation media which meet the criteria developed very well and fit for use as a media that support the learning process of physics.Keywords: Media, Animation, Pulleys, Field Leaning, Alpha Test, Beta Test

Multifactor mathematical model of criticality of welding process of products from aluminum- magnesium alloys

2020 ◽  
pp. 12-18
Author(s):  
F.A. Urazbahtin ◽  
A.YU. Urazbahtina
Keyword(s):  
Mathematical Model ◽  
Magnesium Alloy ◽  
Magnesium Alloys ◽  
Welding Process ◽  
Welding Equipment ◽  
Equipment Operation ◽  
Aluminum Magnesium Alloys ◽  
Aluminum Magnesium Alloy ◽  
Welding Materials

A multifactor mathematical model of the welding process of products from aluminum-magnesium alloys, consisting of 71 indicators that assess the quality of the weld, the welding process, costs, equipment operation and quality of the welded material. The model can be used to control and optimize the welding process of products from aluminum-magnesium alloys. Keywords welding, products, aluminum-magnesium alloy, indicators, process parameters, welding equipment, welding materials, electrode sharpening, lining [email protected]

Network analysis models – the secret for success

2004 ◽  
Vol 4 (5-6) ◽  
pp. 383-388
Author(s):  
D.M. Rogers
Keyword(s):  
Mathematical Model ◽  
Field Data ◽  
Essential Element ◽  
Distribution Networks ◽  
Automatic Calibration ◽  
Supply And Distribution ◽  
The World ◽  
Optimum Approach ◽  
Analysis Models

Water is a fundamental necessity of life. Yet water supply and distribution networks the world over are old and lacking in adequate maintenance. Consequently they often leak as much water as they deliver and provide an unacceptable quality of service to the customer. In certain parts of the world, water is available only for a few hours of the day. The solution is to build a mathematical model to simulate the operation of the real network in all of its key elements and apply it to optimise its operation. To be of value, the results of the model must be compared with field data. This process is known as calibration and is an essential element in the construction of an accurate model. This paper outlines the optimum approach to building and calibrating a mathematical model and how it can be applied to automatic calibration systems.

Numerical Simulation on Mold Electromagnetic Eccentric Stirring and Central Segregation of Round Bloom

2013 ◽  
Vol 652-654 ◽  
pp. 2450-2454
Author(s):  
Zhi Hong Zhang ◽  
Guo Guang Cheng
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Electromagnetic Stirring ◽  
Center Line ◽  
Central Segregation

The paper describes multi-section round bloom casting using external MEMS, equipped with max section D600mm and min D280mm mold, the center line of D280mm mold not coincident with the axis of stirrer coils. it is exist eccentric electromagnetic stirring of mold which section less than max D600mm, a mathematical model of MEMS has been established, the index of central segregation of D280mm macrostructure had decreased less than 1.12 by optimized parameters of electromagnetic stirring and SEN immerse depth, in the end, the quality of round bloom had improved.

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