Stability of the Controlled Inverted Pendulum With Vertical Oscillations

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.

Download Full-text

Hybrid Optimization Technique for Enhancing the Stability of Inverted Pendulum System

International Journal of Swarm Intelligence Research ◽

10.4018/ijsir.2021010105 ◽

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.

Download Full-text

Fuzzy Control of an Inverted Pendulum

Volume 6: 16th Computers in Engineering Conference ◽

10.1115/96-detc/cie-1441 ◽

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.

Download Full-text

Development of Graphical Interface System for Inverted Pendulum Stabilization

Lontar Komputer Jurnal Ilmiah Teknologi Informasi ◽

10.24843/lkjiti.2019.v10.i03.p03 ◽

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.

Download Full-text

Robust Controller Design for Inverted Pendulum System

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.631-632.1342 ◽

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.

Download Full-text

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

Energies ◽

10.3390/en13195215 ◽

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.

Download Full-text