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.

Identification and Model Predictive Position Control of Two Wheeled Inverted Pendulum Mobile Robot

2015 ◽  
Vol 73 (6) ◽  
Author(s):  
Amir A. Bature ◽  
Salinda Buyamin ◽  
Mohamad N. Ahmad ◽  
Mustapha Muhammad ◽  
Auwalu A. Muhammad
Keyword(s):  
Mathematical Model ◽  
System Identification ◽  
Mobile Robot ◽  
Inverted Pendulum ◽  
Position Control ◽  
Superior Performance ◽  
System A ◽  
Wheeled Inverted Pendulum ◽  
Simulation Results ◽  
Real Plant

In order to predict and analyse the behaviour of a real system, a simulated model is needed. The more accurate the model the better the response is when dealing with the real plant. This paper presents a model predictive position control of a Two Wheeled Inverted Pendulum robot. The model was developed by system identification using a grey box technique. Simulation results show superior performance of the gains computed using the grey box model as compared to common linearized mathematical model. 

scholarly journals Modelling of Dynamics of a Wheeled Mobile Robot with Mecanum Wheels with the use of Lagrange Equations of the Second Kind

2017 ◽  
Vol 22 (1) ◽  
pp. 81-99 ◽  
Author(s):  
Z. Hendzel ◽  
Ł. Rykała
Keyword(s):  
Mathematical Model ◽  
Kinetic Energy ◽  
Mobile Robot ◽  
Mobile Robots ◽  
Equations Of Motion ◽  
Wheeled Mobile Robot ◽  
Dynamic Equations ◽  
Lagrange Equations ◽  
Wheeled Mobile Robots ◽  
New Type

Abstract The work presents the dynamic equations of motion of a wheeled mobile robot with mecanum wheels derived with the use of Lagrange equations of the second kind. Mecanum wheels are a new type of wheels used in wheeled mobile robots and they consist of freely rotating rollers attached to the circumference of the wheels. In order to derive dynamic equations of motion of a wheeled mobile robot, the kinetic energy of the system is determined, as well as the generalised forces affecting the system. The resulting mathematical model of a wheeled mobile robot was generated with the use of Maple V software. The results of a solution of inverse and forward problems of dynamics of the discussed object are also published.

A Method for Attitude Control Based on a Mathematical Model for an Inverted Pendulum-Type Mobile Robot

2016 ◽  
Vol 6 (1) ◽  
pp. 198
Author(s):  
Jin-Ho Yoon ◽  
Myung-Jin Chung
Keyword(s):  
Mathematical Model ◽  
Mobile Robot ◽  
Attitude Control ◽  
Pid Controller ◽  
Inverted Pendulum ◽  
Control Method ◽  
State Space Model ◽  
Initial State ◽  
Estimated Parameters ◽  
Linear Elements

A method for attitude control based on a mathematical model for an inverted pendulum-type mobile robot was proposed. The inverted pendulum-type mobile robot was designed and the mathematical modeling was conducted. The parameters of the mobile robot were estimated and the state-space model of mobile robot was obtained by the substitution of the estimated parameters into the mathematical model. The transfer function of the mobile robot is applied to generate the root-locus diagram used for the estimation of the gains of the PID controller. The attitude control method including a PID controller, non-linear elements, and integral saturation prevention was designed and simulated. The experiment was conducted by applying the method to the mobile robot. In the attitude control experiment, the performance of attitude recovery from ±12° tilted initial state with a settling time of 0.98s and a percent overshoot of 40.1% was obtained. Furthermore, the attitude maintaining robustness against disturbance was verified.

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>

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 A Method for Attitude Control Based on a Mathematical Model for an Inverted Pendulum-Type Mobile Robot

2016 ◽  
Vol 6 (1) ◽  
pp. 198
Author(s):  
Jin-Ho Yoon ◽  
Myung-Jin Chung
Keyword(s):  
Mathematical Model ◽  
Mobile Robot ◽  
Attitude Control ◽  
Pid Controller ◽  
Inverted Pendulum ◽  
Control Method ◽  
State Space Model ◽  
Initial State ◽  
Estimated Parameters ◽  
Linear Elements

A method for attitude control based on a mathematical model for an inverted pendulum-type mobile robot was proposed. The inverted pendulum-type mobile robot was designed and the mathematical modeling was conducted. The parameters of the mobile robot were estimated and the state-space model of mobile robot was obtained by the substitution of the estimated parameters into the mathematical model. The transfer function of the mobile robot is applied to generate the root-locus diagram used for the estimation of the gains of the PID controller. The attitude control method including a PID controller, non-linear elements, and integral saturation prevention was designed and simulated. The experiment was conducted by applying the method to the mobile robot. In the attitude control experiment, the performance of attitude recovery from ±12° tilted initial state with a settling time of 0.98s and a percent overshoot of 40.1% was obtained. Furthermore, the attitude maintaining robustness against disturbance was verified.

scholarly journals A Multivariable Adaptive Control Approach for Stabilization of a Cart-Type Double Inverted Pendulum

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
I. Hassanzadeh ◽  
A. Nejadfard ◽  
M. Zadi
Keyword(s):  
Steady State ◽  
Nonlinear Model ◽  
Degrees Of Freedom ◽  
Inverted Pendulum ◽  
Feedback Gain ◽  
Practical Implementation ◽  
Model Parameters ◽  
Lagrange Equations ◽  
Control Approach ◽  
Input Structure

This paper considers the design and practical implementation of linear-based controllers for a cart-type double inverted pendulum (DIPC). A constitution of two linked pendulums placed on a sliding cart, presenting a three Degrees of Freedom and single controlling input structure. The controller objective is to keep both pendulums in an up-up unstable equilibrium point. Modeling is based on the Euler-Lagrange equations, and the resulted nonlinear model is linearized around up-up position. First, the LQR method is used to stabilize DIPC by a feedback gain matrix in order to minimize a quadratic cost function. Without using an observer to estimate the unmeasured states, in the next step we make use of LQG controller which combines the Kalman-Bucy filter estimation and LQR feedback control to obtain a better steady-state performance, but poor robustness. Eventually, to overcome the unknown nonlinear model parameters, an adaptive controller is designed. This controller is based on Model Reference Adaptive System (MRAS) method, which uses the Lyapunov function to eliminate the defined state error. This controller improves both the steady-state and disturbance responses.

Mathematical Model Based Attitude Control of Inverted Pendulum Type Mobile Robot

2015 ◽  
Vol 789-790 ◽  
pp. 700-704
Author(s):  
Jin Ho Yoon ◽  
Ah Do Ko ◽  
Kil Hwan Choi ◽  
Hyoung Bae Park ◽  
Myung Jin Chung
Keyword(s):  
Mathematical Model ◽  
Mobile Robot ◽  
Attitude Control ◽  
Pid Controller ◽  
Inverted Pendulum ◽  
Control Method ◽  
State Space Model ◽  
Estimated Parameters ◽  
The Mathematical Model ◽  
Robot Platform

In this paper, attitude control method based on mathematical model for inverted pendulum type mobile robot was proposed. After the inverted pendulum type mobile robot platform was designed, a mathematical modeling was performed. Also, the motor parameters and the mechanism parameters were estimated, and then the estimated parameters were substituted into the mathematical model to obtain the state-space model of mobile robot platform. Using this, a PID controller was designed, and simulations were performed. Also, the experiments were performed after applying it to the mobile robot platform. The simulation and experimental results were obtained similarly, and attitude control performance was excellent.

scholarly journals Comprehensive Parameters Identification and Dynamic Model Validation of Interior-Mount Line-Start Permanent Magnet Synchronous Motors

Machines ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 4 ◽  
Author(s):  
Luqman S. Maraaba ◽  
Zakariya M. Al-Hamouz ◽  
Abdulaziz S. Milhem ◽  
Ssennoga Twaha
Keyword(s):  
Mathematical Model ◽  
Permanent Magnet ◽  
High Efficiency ◽  
Experimental Tests ◽  
Induction Machines ◽  
Test Methods ◽  
Operating Conditions ◽  
Test Method ◽  
Permanent Magnet Synchronous Motors ◽  
Synchronous Motors

The application of line-start permanent magnet synchronous motors (LSPMSMs) is rapidly spreading due to their advantages of high efficiency, high operational power factor, being self-starting, rendering them as highly needed in many applications in recent years. Although there have been standard methods for the identification of parameters of synchronous and induction machines, most of them do not apply to LSPMSMs. This paper presents a study and analysis of different parameter identification methods for interior mount LSPMSM. Experimental tests have been performed in the laboratory on a 1-hp interior mount LSPMSM. The measurements have been validated by investigating the performance of the machine under different operating conditions using a developed qd0 mathematical model and an experimental setup. The dynamic and steady-state performance analyses have been performed using the determined parameters. It is found that the experimental results are close to the mathematical model results, confirming the accuracy of the studied test methods. Therefore, the output of this study will help in selecting the proper test method for LSPMSM.

scholarly journals Passive Measurement of Three Optical Beacon Coordinates Using a Simultaneous Method

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5235
Author(s):  
Jiri Nemecek ◽  
Martin Polasek
Keyword(s):  
Mathematical Model ◽  
Relative Position ◽  
Experimental Tests ◽  
Image Sensor ◽  
Geometric Parameters ◽  
Light Sources ◽  
Feature Points ◽  
Passive Measurement ◽  
The Mathematical Model ◽  
Physical Principles

Among other things, passive methods based on the processing of images of feature points or beacons captured by an image sensor are used to measure the relative position of objects. At least two cameras usually have to be used to obtain the required information, or the cameras are combined with other sensors working on different physical principles. This paper describes the principle of passively measuring three position coordinates of an optical beacon using a simultaneous method and presents the results of corresponding experimental tests. The beacon is represented by an artificial geometric structure, consisting of several semiconductor light sources. The sources are suitably arranged to allow, all from one camera, passive measurement of the distance, two position angles, the azimuth, and the beacon elevation. The mathematical model of this method consists of working equations containing measured coordinates, geometric parameters of the beacon, and geometric parameters of the beacon image captured by the camera. All the results of these experimental tests are presented.

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