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.

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

Hybrid Optimization Technique for Enhancing the Stability of Inverted Pendulum System

2021 ◽  
Vol 12 (1) ◽  
pp. 77-97
Author(s):  
M. E. Mousa ◽  
M. A. Ebrahim ◽  
Magdy M. Zaky ◽  
E. M. Saied ◽  
S. A. Kotb
Keyword(s):  
Inverted Pendulum ◽  
Optimization Technique ◽  
Linear Quadratic Regulator ◽  
Variable Structure ◽  
Grey Wolf Optimizer ◽  
Linear Quadratic ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
New Variant ◽  
The Stability

The inverted pendulum system (IPS) is considered the milestone of many robotic-based industries. In this paper, a new variant of variable structure adaptive fuzzy (VSAF) is used with new reduced linear quadratic regulator (RLQR) and feedforward gain for enhancing the stability of IPS. The optimal determining of VSAF parameters as well as Q and R matrices of RLQR are obtained by using a modified grey wolf optimizer with adaptive constants property via particle swarm optimization technique (GWO/PSO-AC). A comparison between the hybrid GWO/PSO-AC and classical GWO/PSO based on multi-objective function is provided to justify the superiority of the proposed technique. The IPS equipped with the hybrid GWO/PSO-AC-based controllers has minimum settling time, rise time, undershoot, and overshoot results for the two system outputs (cart position and pendulum angle). The system is subjected to robustness tests to ensure that the system can cope with small as well as significant disturbances.

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>

scholarly journals Development of Graphical Interface System for Inverted Pendulum Stabilization

2019 ◽  
pp. 150
Author(s):  
Erwin Susanto
Keyword(s):  
Inverted Pendulum ◽  
Control Design ◽  
Mathematic Model ◽  
Graphical Interface ◽  
Control Engineering ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Interface System ◽  
The Stability ◽  
And Control

Currently, most of basic control engineering lectures teach both mathematic model and control of an inverted pendulum to explain stability problems in dynamic systems. The inverted pendulum system is a pendulum controlled with a certain force in order to stand in balance around vertical equilibrium line. Hence this system is a highly unstable system and needs stabilization methods using a  kind of controller. This paper describes how to design a Proportional Derivative Integral (PID) controller via root locus technique to stabilize it and realization of its interface system for monitoring angle trajectory. This visualization is needed to observe the stability and  effectiveness of its mathematic model and control design. Experimental results and analysis show that control design and interface system can be implemented well.

Robust Controller Design for Inverted Pendulum System

2013 ◽  
Vol 631-632 ◽  
pp. 1342-1347
Author(s):  
Xu Cao ◽  
Nian Feng Li ◽  
Hua Xun Zhang
Keyword(s):  
Inverted Pendulum ◽  
Controller Design ◽  
Robust Controller ◽  
Important Indicator ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Lqr Controller ◽  
Coupling Characteristics ◽  
The Stability ◽  
Robust Controller Design

For the high order, unstable, multivariable, nonlinear and strong coupling characteristics, robust stability is an important indicator of inverted pendulum system. In this paper an LQR robust controller of inverter pendulum system is designed. The simulation and the experimental results showed that the stability of the robust LQR controller is better than the original LQR controller. When the system departure counterpoise for all kinds of reasons, it get back equilibrium state without depleting any energy, and approach state of equilibrium of all state component.

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.

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.

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.

Stability of the Controlled Inverted Pendulum With Vertical Oscillations

2007 ◽  
Author(s):  
Chihiro Nakagawa ◽  
Kimihiko Nakano ◽  
Yoshihiro Suda ◽  
Ryuzo Hayashi
Keyword(s):  
Large Scale ◽  
Inverted Pendulum ◽  
Amplitude Ratio ◽  
Mathieu Equation ◽  
Vertical Vibration ◽  
Vibration Exciter ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Vertical Vibrations ◽  
The Stability

These days, inverted pendulum robots, like a two-wheeled robot or vehicle, are seen as a form of dynamically stabilized vehicle. Stability characteristics and moving performances of these vehicles have been studied through many examinations and demonstrations. Considering their practical usage, however, these vehicles travel on rough roads, as well as the flat surface in a laboratory. Therefore it is important to investigate the stability of the dynamically stabilized vehicle under vertical vibration. In this study, the authors investigate the responses of the inverted pendulum, which is stabilized by an optimal controller, to vertical vibrations. With theoretical analysis, numerical simulations and experiments using a large scale vibration exciter, stability to vertical vibration is examined. The results show the system dynamics are governed by the Mathieu equation, thus the amplitude ratio reaches its peak when the frequency of the forced vibration is twice the natural frequency of the controlled inverted pendulum system.

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