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

Synthesized ADRC for One-Level Inverted Pendulum System through Combination of Separating and Assembling

2014 ◽  
Vol 490-491 ◽  
pp. 794-797
Author(s):  
Wen Ping Li ◽  
Li Qiang Wu
Keyword(s):  
Nonlinear System ◽  
Inverted Pendulum ◽  
Dynamical Decoupling ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Strong Robustness ◽  
Ideal Study ◽  
Simulation Results ◽  
The One ◽  
The Ideal

Inverted pendulum system is the ideal study object of nonlinear system. The ADRC has good estimate for disturbances, strong robustness and using static decoupling instead of dynamical decoupling. The one-level inverted pendulum system can be regarded as composing of the pendulum angel system and the cart position system. The former is faster and the later is slower. The synthesized ADRC for one-level inverted pendulum system is built through combination of separating and assembling to reduce difficulty in optimizing ADRC parameters of the inverted pendulum system. The synthesized controller is simulated by Matlab under different parameters of the inverted pendulum. Simulation results show that the pendulum angle and the cart position are well controlled.

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 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.

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 Qualitative Study of a Well-Stirred Isothermal Reaction Model

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 938
Author(s):  
Barbara Arcet ◽  
Maša Dukarić ◽  
Zhibek Kadyrsizova
Keyword(s):  
Mathematical Model ◽  
Jacobian Matrix ◽  
Temporal Evolution ◽  
Sufficient Conditions ◽  
Reaction System ◽  
Reaction Model ◽  
Dimensional System ◽  
Two Dimensional ◽  
Isothermal Reaction ◽  
Two Dimensional System

We consider a two-dimensional system which is a mathematical model for a temporal evolution of a well-stirred isothermal reaction system. We give sufficient conditions for the existence of purely imaginary eigenvalues of the Jacobian matrix of the system at its fixed points. Moreover, we show that the system admits a supercritical Hopf bifurcation.

LMI-based Multiobjective Integral Sliding Mode Control for Rotary Inverted Pendulum System Under Load Variations

2015 ◽  
Vol 73 (6) ◽  
Author(s):  
Fairus, M. A. ◽  
Mohamed, Z. ◽  
Ahmad, M. N. ◽  
Loi, W. S.
Keyword(s):  
Nonlinear System ◽  
Inverted Pendulum ◽  
Sliding Mode ◽  
Space Representation ◽  
Linear Matrix ◽  
Pendulum System ◽  
Integral Sliding Mode ◽  
State Space Representation ◽  
Inverted Pendulum System ◽  
Rotary Inverted Pendulum

This paper presents a multiobjective integral sliding mode controller (ISMC) for a rotary inverted pendulum system under the influence of varying load. Firstly, the nonlinear system is approximated to facilitate the desired control design via extended linearization and deterministic approach. By using both of these techniques, the nonlinear system is formulated into a nonlinear state-space representation where the uncertainties are retained in the model. Next, the design objectives are formulated into linear matrix inequalities (LMI) which are then solved efficiently through convex optimization algorithms. With proper selection variables, numbers of the decision variables for LMIs are reduced. Hence, it will reduce the numerical burden and believes the calculated values more viable in practice. Finally, simulation works are conducted and comparison is made between the proposed controller, such as normal ISMC and LQR. The simulation results illustrate the effectiveness of the proposed controller and the performance is evaluated through integral of absolute-value error (IAE) performance index. 

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.

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