scholarly journals Modelado y simulación del péndulo de base móvil

2019 ◽  
pp. 15-22
Author(s):  
Filemón López-Ortega ◽  
Martha Cárdenas-Maciel ◽  
Rogelio Serrano-Zepeda ◽  
Miguel Ángel Lara-Ceballos
Keyword(s):  
Pid Controller ◽  
Angular Displacement ◽  
Equations Of Motion ◽  
Closed Loop System ◽  
Marine Vehicles ◽  
Free Body Diagram ◽  
Free Body ◽  
Physical Laws ◽  
And Control ◽  
Mobile Base

This article describes the simulation and control of a mobile base pendulum (PBM), which consists of a mechanism with two wheels and a vertical cylindrical rod, which can rotate freely on its own axis, then the mobile must move to compensate for the angular displacement of the pendulum. The objective is to develop a mathematical model to simulate the dynamic behavior of the mechanism and thereby develop a Proportional, Integral and Derivative (PID) controller, optimal that manages to maintain this pendulum at a vertical degree in a time ts ≤ 1 second, with an entry angle of ± 10 degrees. The Newton-Euler (NE) methodology was used to determine the dynamic equations of motion, by analyzing the free body diagram and using the physical laws that allow defining the forces acting on the system to achieve the state of equilibrium. These simulations were carried out with the SolidWorks (SimMechanics Link) and Matlab (Simulink) tools, in addition a closed loop system was used to analyze the output signal Y (s) with respect to the input signal U (s). The contributions of this development consist of designing high-precision controllers with the purpose of improving industrial automation processes from the implementation of a control system, in areas such as robotics, marine vehicles, aerospace, to name a few examples.

scholarly journals Modeling and Validation of 2-DOF Rail Vehicle Model Based on Electro–Mechanical Analogy Theory Using Theoretical and Experimental Methods

2018 ◽  
Vol 8 (6) ◽  
pp. 3603-3608
Author(s):  
F. Pehlivan ◽  
C. Mizrak ◽  
I. Esen
Keyword(s):  
Degrees Of Freedom ◽  
Similarity Theory ◽  
Equations Of Motion ◽  
Vehicle Model ◽  
Rail Vehicle ◽  
Free Body Diagram ◽  
Model Transfer ◽  
Simulation Results ◽  
Free Body ◽  
Secondary Suspension

This paper presents theoretical and experimental results on modeling and simulation of two degrees of freedom rail vehicle by using electro-mechanical similarity theory. In this study, the equations of motion were derived using Newton’s second law of motion and then mechanical and equivalent electrical circuits were obtained with the help of a free body diagram. A schema in Simulink allowing analyzing of the behavior of the primary and secondary suspension was created. In order to verify the electrical model, transfer function and schema were developed in Simulink. The simulation results were compared with the experimental data and the comparison showed that the results of the mechanical experiments were close to the simulation results, but the electrical results showed better periodic behavior.

Dynamics of Mechanical Systems and the Generalized Free-Body Diagram—Part II: Imposition of Constraints

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
József Kövecses
Keyword(s):  
Mechanical System ◽  
Configuration Space ◽  
Mechanical Systems ◽  
Constrained Systems ◽  
Simulation Design ◽  
Free Body Diagram ◽  
Free Body ◽  
Dynamics Models ◽  
And Control

In this part of the work we present some applications of the formulation developed in Part I (Kövecses, 2008, “Dynamics of Mechanical Systems and the Generalized Free-Body Diagram—Part I: General Formulation,” ASME J. Appl. Mech., 75(6), p. 061012) for the generalized free-body diagram in configuration space. This involves the specification and imposition of constraint conditions, which were identified as Step 2 of the analysis of a mechanical system in Part I. We will particularly consider bilaterally and unilaterally constrained systems, where constraints are realized via ideal or nonideal interfaces. We also look at the general case where the constraint configuration is possibly redundant. The results represent novel forms of dynamics models for mechanical systems, and can offer the possibility to gain more insight for simulation, design, and control.

Mathematical Modeling of Five-Link Inverted Cart and Pendulum System

2018 ◽  
pp. 140-155
Author(s):  
Ashwani Kharola
Keyword(s):  
Mathematical Model ◽  
Inverted Pendulum ◽  
Equations Of Motion ◽  
Upright Position ◽  
Pendulum System ◽  
Free Body Diagram ◽  
Simulink Model ◽  
Inverted Pendulum System ◽  
Design Structure ◽  
Free Body

This chapter describes a mathematical model and design structure of five-link inverted pendulum on cart. The system comprises of five rigid pendulums or links mounted on a mutable cart. The objective is to control all the five links at vertical upright position when cart is stationary at particular location. The study considered free-body-diagram (FBD) analysis of proposed system and applied Newton's second law of motion for deriving a mathematical model of proposed system. The derived governing equations of motion can be further used by researchers for developing a Matlab-Simulink model of five-link inverted pendulum system. The developed model can be further used for deriving equations of motions for n-link cart and pendulum system. Researchers can further apply various control techniques for control of proposed system.

A Robust Controller of Multi DOF-Cooperating Planar Robotic Manipulators Using a Tuned PID Approach

2014 ◽  
Author(s):  
Dhafar Al-Ani ◽  
Hamed H. Afshari ◽  
Saeid Habibi
Keyword(s):  
Pid Controller ◽  
Equations Of Motion ◽  
Robotic Manipulators ◽  
Robust Controller ◽  
Contact State ◽  
Practical Applications ◽  
Design Values ◽  
End Effectors ◽  
And Control ◽  
The Impact

Usually, a dynamic system with impact conditions is an interesting problem with practical applications in the fields of dynamics, vibrations, and control. One difficulty in controlling robotics (i.e., a multi DOF two-cooperating or two-link planar) is the subject to impact between the end-effectors of manipulators is that the dynamics (i.e., equations of motion) are different when the system status changes suddenly from a non-contact state to a contact state. In this paper, a Tuned PID controller with different design scenarios is developed to regulate the states of two dynamic systems that collide. Further, in this work, three types of errors are used to compare among different cases that are; (1) the steady state error, (2) the root mean square error, and (3) the final value error. The results of the Tuned PID controller are compared to those obtained by a classical PID controller. The PID controller is tuned using the Ziegler–Nicholas approach. The simulation results of the robotic manipulators confirmed the theoretical effectiveness of the proposed controller, based on MATLAB/Simulink. Unlike the classical PID results (i.e., the impact-induced force is found to be 2.0 N), the Tuned PID controller successfully determined the impact-induced force as same as the desired force (i.e., 0.6 N). Moreover, the Tuned PID satisfied all other desired design values.

Control of processing at multi-tool two-support setup

2020 ◽  
pp. 67-73
Author(s):  
N.D. YUsubov ◽  
G.M. Abbasova
Keyword(s):  
Degrees Of Freedom ◽  
Factor Model ◽  
Angular Displacement ◽  
Factor Models ◽  
Technological System ◽  
Displacement Control ◽  
Model Accuracy ◽  
Six Degrees Of Freedom ◽  
Angular Displacements ◽  
And Control

The accuracy of two-tool machining on automatic lathes is analyzed. Full-factor models of distortions and scattering fields of the performed dimensions, taking into account the flexibility of the technological system on six degrees of freedom, i. e. angular displacements in the technological system, were used in the research. Possibilities of design and control of two-tool adjustment are considered. Keywords turning processing, cutting mode, two-tool setup, full-factor model, accuracy, angular displacement, control, calculation [email protected]

scholarly journals Design, Construction, and Control for an Underwater Vehicle Type Sepiida

Robotica ◽  
2020 ◽  
pp. 1-18
Author(s):  
M. Garcia ◽  
P. Castillo ◽  
E. Campos ◽  
R. Lozano
Keyword(s):  
Embedded System ◽  
Closed Loop ◽  
Underwater Vehicle ◽  
Mathematical Representation ◽  
Closed Loop System ◽  
Vehicle Type ◽  
Mathematical Equations ◽  
And Control ◽  
Design Construction

SUMMARY A novel underwater vehicle configuration with an operating principle as the Sepiida animal is presented and developed in this paper. The mathematical equations describing the movements of the vehicle are obtained using the Newton–Euler approach. An analysis of the dynamic model is done for control purposes. A prototype and its embedded system are developed for validating analytically and experimentally the proposed mathematical representation. A real-time characterization of one mass is done to relate the pitch angle with the radio of displacement of the mass. In addition, first validation of the closed-loop system is done using a linear controller.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

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