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 Stabilising a cart inverted pendulum with an augmented PID control scheme

2018 ◽  
Vol 197 ◽  
pp. 11013
Author(s):  
Indrazno Siradjuddin ◽  
Zakiyah Amalia ◽  
Budhy Setiawan ◽  
Ferdian Ronilaya ◽  
Erfan Rohadi ◽  
...  
Keyword(s):  
Pid Control ◽  
Control Algorithm ◽  
Inverted Pendulum ◽  
Control Algorithms ◽  
Pendulum System ◽  
Lagrange’S Equation ◽  
System A ◽  
Inverted Pendulum System ◽  
Best Response ◽  
Control Scheme

A cart inverted pendulum is an under actuated system that highly unstable and nonlinear. Therefore, it makes a good problem example which attracts control engineers to validate the developed control algorithms. In this paper, an augmented PID control algorithm is proposed to stabilise a cart inverted pendulum at the desired state. The derivation of a mathematical model of the cart inverted pendulum using Lagrange's equation is discussed in detail. The system dynamics is illustrated to understand better the behaviour of the system. A simulation program has been developed to verify the performance of the proposed control algorithm. The system dynamic behaviours with respect to the variation of the controller parameters are analysed and discussed. Controllers parameters are expressed into two PID gain sets which associated with 2 dynamic states: the cart position (ϰ) and the pendulum angle (θ). It can be concluded from the simulation result that the proposed control algorithm can perform well where acceptable steady errors can be achieved. The best response from the cart inverted pendulum system has been obtained with the value of kPX 190, kDX 50, kIX 5, kPθ 140, kDθ 5, and kIθ 25.

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

Application on Two Degree of Freedom Model Driven PID in Liner First-Order Inverted Pendulum

2013 ◽  
Vol 433-435 ◽  
pp. 1000-1004
Author(s):  
Jing Jing Shi ◽  
Li Xiang Zhang ◽  
Ai Qin Jiang
Keyword(s):  
Control System ◽  
Pid Control ◽  
Inverted Pendulum ◽  
Degree Of Freedom ◽  
Control Technology ◽  
Pendulum System ◽  
First Order ◽  
Model Driven ◽  
Inverted Pendulum System ◽  
Two Degree Of Freedom

The inverted pendulum system is a high order, strong coupling, multi-variable and absolutely unstable nonlinear system. Its optimal control has been the hotspot in the field of study. A new two degree of freedom model driven PID control system is introduced in this paper.It will state the structure of the control technology and design steps.The control technology is applied to control linear inverted pendulum in this paper. The simulation results prove that two degree of freedom model driven PID control system has the feasibility and superiority.

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.

scholarly journals A method to solve the problem of low precision of micro stabilized platform caused by frame coupling - Based on Fuzzy PID

2021 ◽  
Vol 284 ◽  
pp. 04008
Author(s):  
Dongwen Yan
Keyword(s):  
Pid Control ◽  
Control Algorithm ◽  
Fuzzy Controller ◽  
Fuzzy Pid ◽  
Fuzzy Pid Control ◽  
Control Precision ◽  
Position Signal ◽  
High Control ◽  
Stabilized Platform ◽  
Yaw Angle

Aiming at the problem of low control efficiency of small stable platform due to frame coupling, an intelligent control algorithm (fuzzy-PID) combining fuzzy controller with traditional PID is designed. The fuzzy PID controller is added to the position closed loop of the stable platform control system, and the motor position signal is collected and analyzed. Compared with the traditional PID control algorithm, the fuzzy PID control algorithm has the advantages of small overshoot, high control precision and strong anti-interference ability. The simulation test in Simulink environment shows that the overshoot of the system is reduced under the algorithm σ, which can be controlled within 1% and the adjusting time t is controlled within 0.5s, which can realize the stable control of the yaw angle, pitch angle and roll angle of the stabilized platform.

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.

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