Optimal control design and implementation for the double inverted pendulum system in a graduate control course

2015 ◽  
Author(s):  
Felix Muniz-Rodriguez ◽  
Gerson Beauchamp-Baez ◽  
Gerardo Cruz-Diaz ◽  
Juan Carlos Santos-Ferrer
Keyword(s):  
Optimal Control ◽  
Inverted Pendulum ◽  
Control Design ◽  
Pendulum System ◽  
Design And Implementation ◽  
Inverted Pendulum System

Based on Linear Quadratic Regulator Optimal Control of Single Inverted Pendulum System Co-Simulation of ADAMS and SIMULINK

2011 ◽  
Vol 383-390 ◽  
pp. 7258-7264 ◽  
Author(s):  
Zhao Yang Xu ◽  
Xiao Diao Huang
Keyword(s):  
Optimal Control ◽  
Inverted Pendulum ◽  
Control Design ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Quadratic Optimal Control

In this paper, based on linear quadratic optimal control design the controller of single inverted pendulum system, using the current epidemic method of Co-simulation to play each of the strengths of two software for simulation, Through two methods of the static and dynamic to observe and analyze the quality of feedback controller the based on linear quadratic optimal control.

Nonlinear Optimal Control for the Wheeled Inverted Pendulum System

Robotica ◽  
2019 ◽  
Vol 38 (1) ◽  
pp. 29-47 ◽  
Author(s):  
G. Rigatos ◽  
K. Busawon ◽  
J. Pomares ◽  
M. Abbaszadeh
Keyword(s):  
Optimal Control ◽  
Inverted Pendulum ◽  
Control Method ◽  
Taylor Series Expansion ◽  
Nonlinear Optimal Control ◽  
Algebraic Riccati Equation ◽  
Time Step ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Wheeled Inverted Pendulum

SummaryThe article proposes a nonlinear optimal control method for the model of the wheeled inverted pendulum (WIP). This is a difficult control and robotics problem due to the system’s strong nonlinearities and due to its underactuation. First, the dynamic model of the WIP undergoes approximate linearization around a temporary operating point which is recomputed at each time step of the control method. The linearization procedure makes use of Taylor series expansion and of the computation of the associated Jacobian matrices. For the linearized model of the wheeled pendulum, an optimal (H-infinity) feedback controller is developed. The controller’s gain is computed through the repetitive solution of an algebraic Riccati equation at each iteration of the control algorithm. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, by using the H-infinity Kalman Filter as a robust state estimator, the implementation of a state estimation-based control scheme becomes also possible.

Research of the Inverted Pendulum System Based on the Linear Quadratic Optimal Control

2014 ◽  
Vol 568-570 ◽  
pp. 1104-1107
Author(s):  
Shu Fen Qi ◽  
Huan Huan Liu ◽  
Hong Tao Tian
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Inverted Pendulum ◽  
Balance Control ◽  
Single Stage ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Quadratic Optimal Control

As an ideal experimental method in the study of control theory, inverted pendulum system is an indispensable tool to examine the effects of control strategy. In this paper the corresponding mathematical model and the state space equation are established according to studying the working principle and balance control problem of the single stage linear inverted pendulum system. Using MATLAB solves them and gets the consequences. Finally, the linear quadratic optimal control strategy is used to design the controller of single-stage inverted pendulum system, and a simulation study is carried out. The simulation results show the effectiveness of the most sorrow regulator of the quadratic. And basic rule can be found out between the dynamic response of the inverted pendulum system and weighting matricesandin the LQR.

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.

Optimal Control Theory Research on Inverted Pendulum System

2014 ◽  
Vol 494-495 ◽  
pp. 1118-1121
Author(s):  
Shuo Mei Wu ◽  
Jian Wei Song ◽  
Wen Qing Zhang
Keyword(s):  
Optimal Control ◽  
Inverted Pendulum ◽  
Linear Quadratic Regulator ◽  
Good Control ◽  
Control Effect ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Theory Research

The state space expression can be deduced by establishing the mathematical model of inverted pendulum system. In this paper, linear quadratic regulator (LQR) is used to control the inverted pendulum system, providing better balance between system robustness stability and rapidity. The simulation structure shows that the better the system anti-interference capability is, the shorter its recovery time is. Good control effect can be achieved by applying linear quadratic optimal control in the control of double inverted pendulum balancing system.

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