Using real interpolation method for adaptive identification of nonlinear inverted pendulum system

<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>

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H2 Sliding Mode Controller Design for Mobile Inverted Pendulum System

Iraqi Journal of Computer Communication Control and System Engineering ◽

10.33103/uot.ijccce.18.2.2 ◽

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.

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Analysis and modeling of an inverted pendulum system

Automation. Modern Techologies ◽

10.36652/0869-4931-2021-75-7-326-330 ◽

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

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Integrated SolidWorks and Simscape platform for the design and control of an inverted pendulum system

Journal of Electrical Engineering ◽

10.2478/jee-2020-0018 ◽

2020 ◽

Vol 71 (2) ◽

pp. 122-126

Author(s):

Ahmed Alkamachi

Keyword(s):

Inverted Pendulum ◽

Controller Design ◽

State Feedback Control ◽

Pendulum System ◽

Inverted Pendulum System ◽

Control Scheme ◽

Implicit System ◽

Physical Elements ◽

And Control ◽

The Mathematical Model

AbstractA single inverted pendulum on a cart (SIPC) is designed and modeled physically using SolidWorks. The model is then exported to the Simulink environment to form a Simscape model for simulation and test purposes. This type of modeling uses a physical grid tactic to model mechanical structures. It requires connection of the physical elements with physical signal converter to define the implicit system dynamics to be modeled. The integration between the SolidWorks and Simscape eliminates the need of deriving the mathematical model and provides a platform for the rapid controller design for the system. State feedback control scheme is proposed, designed, and tuned aiming to maintain the pendulum in the upright place while tracking the desired cart position. Several simulation cases are studied to prove the controller abilities. In order to examine the controller robustness, disturbance rejection and noise attenuation capabilities are also discovered.

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Optimal Design of LQR Controller Based on Improved Artificial Bee Colony Optimization Algorithm

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.971-973.1272 ◽

2014 ◽

Vol 971-973 ◽

pp. 1272-1275 ◽

Cited By ~ 1

Author(s):

Huai De Yang

Keyword(s):

Artificial Bee Colony ◽

Inverted Pendulum ◽

Balance Control ◽

Pendulum System ◽

Artificial Bee Colony Optimization ◽

Bee Colony ◽

Inverted Pendulum System ◽

Lqr Controller ◽

Bee Colony Optimization ◽

The Mathematical Model

The inverted pendulum system is characterized as a typical nonlinear, fast multi-variable, essentially unstable system. It is difficult to control because of its instability .In order to improve balance control, the mathematical model of the single inverted pendulum is established, a LQR controller is designed which is based on improved artificial bee colony. Experiments show that the improved algorithm has better performance than standard artificial bee colony algorithm on convergence and rate balance control to meet the requirements of the single inverted pendulum.

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Intelligent Swing-Up and Robust Stabilization via Tube-based Nonlinear Model Predictive Control for A Rotational Inverted-Pendulum System

Revista Politécnica ◽

10.33333/rp.vol45n1.05 ◽

2020 ◽

Vol 45 (1) ◽

pp. 49-64

Author(s):

Alvaro Prado ◽

Marco Herrera ◽

Oswaldo Menéndez

Keyword(s):

Predictive Control ◽

Nonlinear Model ◽

Closed Loop ◽

Inverted Pendulum ◽

Angular Position ◽

Loop System ◽

Invariant Sets ◽

Closed Loop System ◽

Pendulum System ◽

Inverted Pendulum System

The purpose of this paper is to introduce a new robust nonlinear model-based predictive control scheme applied to a rotational inverted-pendulum system. The rotational pendulum is composed by a mechanical arm attached to a free-motion pendulum (orthogonal to the arm), namely Furuta Pendulum. In principle, a Fuzzy controller enables the robotic arm bar to lift the rotational pendulum through oscillatory swing-up motion up to automatically achieve the upper equilibrium position in a prescribed stabilizing operation range. After the pendulum reaches the operating range, an intelligent control bypass system allows the transition between the swing-up motion controller and a robust predictive controller to maintain the angular position of the pendulum around the upward critical position. To achieve robust performance, a centralized control framework combines a triplet of control actions. The first one compensates for disturbances using the regulation trajectory ?feedforward control. The second control action corrects errors produced by modelling mismatch. The third controller assures robustness on the closed-loop system whilst compensating for deviations of the state trajectories from the nominal ones (i.e, disturbance-free). The control strategy provides robust feasibility despite constraints on the arm bar and pendulum's actuators are met. Such constraints are calculated on-line based on robust positively invariant sets characterised by polytopic sets (tubes). The proposed controller is tested in a series of simulations, and experimentally validated on a high-fidelity simulation environment including a rotational inverted-pendulum built for educational purposes. The results show that robust control performance is strengthened against disturbances of the closed-loop system benchmarked to inherently-robust linear and nonlinear predictive controllers.

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Mathematical Modeling of Five-Link Inverted Cart and Pendulum System

Advanced Numerical Simulations in Mechanical Engineering - Advances in Mechatronics and Mechanical Engineering ◽

10.4018/978-1-5225-3722-9.ch008 ◽

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.

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Modeling and PID Control of Single-Stage Inverted Pendulum System

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.644-650.142 ◽

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.

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

Bulletin of Electrical Engineering and Informatics ◽

10.11591/eei.v9i3.2017 ◽

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.

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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.

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