scholarly journals State Space Based Linear Controller Design for the Inverted Pendulum

2019 ◽  
Vol 12 (2) ◽  
pp. 130-147 ◽  
Author(s):  
Miklós Kuczmann
Keyword(s):  
State Space ◽  
Inverted Pendulum ◽  
Controller Design ◽  
Pole Placement ◽  
Space Representation ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Pendulum System ◽  
Linear Controller ◽  
Inverted Pendulum System

In a previous survey paper the detailed PID controller design to stabilize the inclination angle as well as the horizontal movement of an inverted pendulum system has been presented. In this paper the linear controller design based on the state space representation is shown step by step. Pendulum model is based on EulerLagrange modeling, and the nonlinear state space model is linearized in the unstable upward position, finally pole placement by Ackermann formula and Bass–Gura equation, moreover linear quadratic optimal control are presented. The pendulum has been inserted into a virtual reality laboratory, which is suitable to use in model based control teaching.

scholarly journals Multibody Modeling and Balance Control of a Reaction Wheel Inverted Pendulum Using LQR Controller

2021 ◽  
Vol 1 (1) ◽  
pp. 84-89
Author(s):  
Ümit Önen ◽  
Abdullah Çakan
Keyword(s):  
State Space ◽  
Inverted Pendulum ◽  
Balance Control ◽  
Space Representation ◽  
Reaction Wheel ◽  
Linear Quadratic ◽  
Pendulum System ◽  
State Space Representation ◽  
Inverted Pendulum System ◽  
Lqr Controller

In this study, modeling and LQR control of a reaction wheel inverted pendulum system is described. The reaction wheel inverted pendulum model is created by using a 3D CAD platform and exported to Simscape Multibody. The multibody model is linearized to derive a state-space representation. A LQR (Linear-quadratic regulator) controller is designed and applied for balance control of the pendulum. The results show that deriving a state-space representation from multibody is an easy and effective way to model dynamic systems and balance control of the reaction wheel inverted pendulum is successfully achieved by LQR controller. Results are given in the form of graphics.

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.

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.

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.

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.

Robust Stabilizing Controller Design for Inverted Pendulum System

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Hazem I. Ali
Keyword(s):  
Steady State ◽  
Time Domain ◽  
State Feedback ◽  
Inverted Pendulum ◽  
Controller Design ◽  
H Infinity ◽  
Pendulum System ◽  
Stabilizing Controller ◽  
Inverted Pendulum System ◽  
System Uncertainties

In this paper the design of robust stabilizing state feedback controller for inverted pendulum system is presented. The Ant Colony Optimization (ACO) method is used to tune the state feedback gains subject to different proposed cost functions comprise of H-infinity constraints and time domain specifications. The steady state and dynamic characteristics of the proposed controller are investigated by simulations and experiments. The results show the effectiveness of the proposed controller which offers a satisfactory robustness and a desirable time response specifications. Finally, the robustness of the controller is tested in the presence of system uncertainties and disturbance.

scholarly journals Design of hybrid sliding mode controller based on fireworks algorithm for nonlinear inverted pendulum systems

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668427 ◽  
Author(s):  
Te-Jen Su ◽  
Shih-Ming Wang ◽  
Tsung-Ying Li ◽  
Sung-Tsun Shih ◽  
Van-Manh Hoang
Keyword(s):  
Inverted Pendulum ◽  
Sliding Mode ◽  
Linear Quadratic Regulator ◽  
Sliding Mode Controller ◽  
Proportional Integral Derivative ◽  
Linear Quadratic ◽  
Pendulum System ◽  
Fireworks Algorithm ◽  
Simulation Process ◽  
Inverted Pendulum System

The objective of this article is to optimize parameters of a hybrid sliding mode controller based on fireworks algorithm for a nonlinear inverted pendulum system. The proposed controller is a combination of two modified types of the classical sliding mode controller, namely, baseline sliding mode controller and fast output sampling discrete sliding mode controller. The simulation process is carried out with MATLAB/Simulink. The results are compared with a published hybrid method using proportional–integral–derivative and linear quadratic regulator controllers. The simulation results show a better performance of the proposed controller.

Hybrid Optimization Technique for Enhancing the Stability of Inverted Pendulum System

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.

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