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.

scholarly journals H2 Sliding Mode Controller Design for Mobile Inverted Pendulum System

2018 ◽  
pp. 17-29
Keyword(s):  
Mathematical Model ◽  
Inverted Pendulum ◽  
Controller Design ◽  
Sliding Mode ◽  
Upright Position ◽  
Sliding Mode Controller ◽  
Pendulum System ◽  
System Parameters ◽  
Inverted Pendulum System ◽  
The Mathematical Model

The design of an H2 sliding mode controller for a mobile inverted pendulum system is proposed in this paper. This controller is conducted to stabilize the mobile inverted pendulum in the upright position and drive the system to a desired position. Lagrangian approach is used to develop the mathematical model of the system. The H2 controller is combined with the sliding mode control to give a better performance compared to the case of using each of the above controllers alone. The results show that the proposed controller can stabilize the system and drive the output to a given desired input. Furthermore, variations in system parameters and disturbance are considered to illustrate the robustness of the proposed controller.

Analysis and modeling of an inverted pendulum system

2021 ◽  
Author(s):  
Keyword(s):  
Mathematical Model ◽  
Nonlinear System ◽  
Inverted Pendulum ◽  
System Analysis ◽  
Dimensional System ◽  
Two Dimensional ◽  
System Operation ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Two Dimensional System

A nonlinear system, which consists of an inverted pendulum mounted on a cart with an electric drive, is considered. A mathematical model is created, its analysis and modeling of the investigated two-dimensional system operation is carried out. Keywords mathematical model; inverted pendulum; system analysis; state space

Fuzzy Control of an Inverted Pendulum

1996 ◽  
Author(s):  
Tuna Balkan ◽  
Mehmet Emin Ari
Keyword(s):  
Inverted Pendulum ◽  
Fuzzy Controller ◽  
Angular Position ◽  
Upright Position ◽  
Control Signal ◽  
Position Measurement ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
And Performance ◽  
The Stability

Abstract An inverted pendulum system has been designed and constructed as a physical model of inherently unstable mechanical systems. The vertical upright position of a pendulum is controlled by changing the horizontal position of a cart to which the pendulum is hinged. The stability of the system has been investigated when a fuzzy controller is used to produce the control signal, while making a single measurement. It has been shown that by using simple fuzzy rules to allow real time computation with a single angular position measurement, the system can not be made absolutely stable. However, the stability and performance of the system have been considerably improved by shrinking the membership functions of angular position, computed angular velocity and control signal when inverted pendulum is very close to the vertical upright position.

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>

Modelling and Simulation of Spherical Inverted Pendulum Based on LQR Control with SimMechanics

2013 ◽  
Vol 391 ◽  
pp. 163-167 ◽  
Author(s):  
M. Fajar ◽  
S.S. Douglas ◽  
J.B. Gomm
Keyword(s):  
Time Domain ◽  
Control Strategy ◽  
Inverted Pendulum ◽  
Multibody System ◽  
Equations Of Motion ◽  
Pendulum System ◽  
Lqr Control ◽  
Inverted Pendulum System ◽  
Lqr Controller ◽  
Feedback Method

This paper describes how to simulate the spherical inverted pendulum, a dynamics of multibody system, with SimMechanics. The control strategy used is based on the LQR feedback method for the stabilisation of the spherical inverted pendulum system. Simulation study has been done in Simulink environment shows that LQR controller is capable to control multi input and multi output of spherical inverted pendulum system successfully. The result shows that LQR control strategy gives satisfactory response that is presented in time domain with the details analysis. The use of SimMechanics for simulation of spherical inverted pendulum has some advantages i.e. not need to derive equations of motion, available visualisation tools, fast and easy design

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 Linear quadratic regulator and pole placement for stabilizing a cart inverted pendulum system

2020 ◽  
Vol 9 (3) ◽  
pp. 914-923
Author(s):  
Mila Fauziyah ◽  
Zakiyah Amalia ◽  
Indrazno Siradjuddin ◽  
Denda Dewatama ◽  
Rendi Pambudi Wicaksono ◽  
...  
Keyword(s):  
Mathematical Model ◽  
System Performance ◽  
Inverted Pendulum ◽  
Linear Quadratic Regulator ◽  
Pole Placement ◽  
Underactuated System ◽  
Mechanical Transmission ◽  
Linear Quadratic ◽  
Pendulum System ◽  
Inverted Pendulum System

The system of a cart inverted pendulum has many problems such as  nonlinearity, complexity, unstable, and underactuated system. It makes this system be a benchmark for testing many control algorithm. This paper  presents a comparison between 2 conventional control methods consist of a linear quadratic regulator (LQR) and pole placement. The comparison  indicated by the most optimal steps and results in the system performance  that obtained from each method for stabilizing a cart inverted pendulum system. A mathematical model of DC motor and mechanical transmission are included in a mathematical model to minimize the realtime implementation problem. From the simulation, the obtained system performance shows that each method has its advantages, and the desired pendulum angle and cart position reached.

scholarly journals Dynamic Response of an Inverted Pendulum System in Water under Parametric Excitations for Energy Harvesting: A Conceptual Approach

Energies ◽  
2020 ◽  
Vol 13 (19) ◽  
pp. 5215
Author(s):  
Saqib Hasnain ◽  
Karam Dad Kallu ◽  
Muhammad Haq Nawaz ◽  
Naseem Abbas ◽  
Catalin Iulin Pruncu
Keyword(s):  
Mathematical Model ◽  
Energy Harvesting ◽  
Dynamic Response ◽  
Parametric Excitation ◽  
Stability Region ◽  
Inverted Pendulum ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Underwater Environment ◽  
The Stability

In this paper, we have investigated the dynamic response, vibration control technique, and upright stability of an inverted pendulum system in an underwater environment in view point of a conceptual future wave energy harvesting system. The pendulum system is subjected to a parametrically excited input (used as a water wave) at its pivot point in the vertical direction for stabilization purposes. For the first time, a mathematical model for investigating the underwater dynamic response of an inverted pendulum system has been developed, considering the effect of hydrodynamic forces (like the drag force and the buoyancy force) acting on the system. The mathematical model of the system has been derived by applying the standard Lagrange equation. To obtain the approximate solution of the system, the averaging technique has been utilized. An open loop parametric excitation technique has been applied to stabilize the pendulum system at its upright unstable equilibrium position. Both (like the lower and the upper) stability borders have been shown for the responses of both pendulum systems in vacuum and water (viscously damped). Furthermore, stability regions for both cases are clearly drawn and analyzed. The results are illustrated through numerical simulations. Numerical simulation results concluded that: (i) The application of the parametric excitation control method in this article successfully stabilizes the newly developed system model in an underwater environment, (ii) there is a significant increase in the excitation amplitude in the stability region for the system in water versus in vacuum, and (iii) the stability region for the system in vacuum is wider than that in water.

scholarly journals Robust Full State Feedback Controller Design Using H∞ for Inverted Pendulum System

2018 ◽  
pp. 39-48
Keyword(s):  
State Feedback ◽  
Inverted Pendulum ◽  
Controller Design ◽  
Upright Position ◽  
Feedback Controller ◽  
Pendulum System ◽  
Integral Term ◽  
Inverted Pendulum System ◽  
Full State ◽  
Full State Feedback

This paper presents the design of a full state feedback H∞ controller to an inverted pendulum system. The nonlinear and linearized models of the system are obtained. The main goal of the proposed controller is to maintain the pendulum in the upright position and achieve a desirable tracking for the cart position. To achieve desirable tracking properties an integral term is added. The robustness of the proposed controller is examined when a 20% variation in the parameters of system is considered.

Predictor-network-based MRACS for inverted pendulum system.

1991 ◽  
Vol 111 (3) ◽  
pp. 221-229 ◽  
Author(s):  
Motomiki Uchida ◽  
Yukihiro Toyoda ◽  
Yoshikuni Akiyama ◽  
Kazushi Nakano ◽  
Hideo Nakamura
Keyword(s):  
Inverted Pendulum ◽  
Pendulum System ◽  
Inverted Pendulum System
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