Design and Performance Analysis of LQR Controller for Stabilizing Double Inverted Pendulum System

2017 ◽  
Vol 2 (9) ◽  
pp. 1-5
Author(s):  
Ghassan A. Sultan ◽  
Ziyad K. Farej
Keyword(s):  
Inverted Pendulum ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Pendulum System ◽  
Inverted Pendulum Model ◽  
Inverted Pendulum System ◽  
Pendulum Model ◽  
Lqr Controller ◽  
And Performance ◽  
Performance Results

Double inverted pendulum (DIP) is a nonlinear, multivariable and unstable system. The inverted pendulum which continually moves toward an uncontrolled state represents a challenging control problem. The problem is to balance the pendulum vertically upward on a mobile platform that can move in only two directions (left or right) when it is offset from zero stat. The aim is to determine the control strategy that deliver better performance with respect to pendulum's angles and cart's position. A Linear-Quadratic-Regulator (LQR) technique for controlling the linearized system of double inverted pendulum model is presented. Simulation studies conducted in MATLAB environment show that the LQR controller are capable of controlling the multi output double inverted pendulum system. Also better performance results are obtained for controlling heavy driven part DIP system.

scholarly journals USING GENETIC ALGORITHM IN OPTIMIZING THE MATRIX OF LQR CONTROLLER FOR NONLINEAR INVERTED PENDULUM SYSTEM

2019 ◽  
Vol 1 (28) ◽  
pp. 50-55
Author(s):  
Tan Thanh Nguyen
Keyword(s):  
Genetic Algorithm ◽  
Inverted Pendulum ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Pendulum Model ◽  
The Matrix ◽  
Lqr Controller ◽  
Genetic Algorithm Method

In this article, the author used the matlab software to simulate and then compared the results between the classical LQR (Linear Quadratic Regulator) controller and another method to adjust the matrix parameters toward optimization of the LQR controller. It is the GA (Genetic Algorithm) method to optimize the matrix of the LQR controller, and the results have  been verified on the nonlinear pendulum model. The Genetic Algorithm is a modern control algorithm, which is widely applied in research and practice. The main objective of this article is to use the GA algorithm in order to optimize the matrix parameters of LQR controller, whichcontrolled the position and angle of the nonlinear inverted pendulum at the stable balance point. The matlab-based simulating results showed that  the system has operated properly to the requirements and the output response has reached an equilibrium position of about 2.5 seconds.

scholarly journals System design for inverted pendulum using LQR control via IoT

2020 ◽  
Vol 11 ◽  
pp. 12
Author(s):  
Dechrit Maneetham ◽  
Petrus Sutyasadi
Keyword(s):  
Inverted Pendulum ◽  
Control Method ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Lqr Control ◽  
Lqr Controller ◽  
Model Tuning ◽  
And Performance ◽  
Performance Results ◽  
And Control

This research proposes control method to balance and stabilize an inverted pendulum. A robust control was analyzed and adjusted to the model output with real time feedback. The feedback was obtained using state space equation of the feedback controller. A linear quadratic regulator (LQR) model tuning and control was applied to the inverted pendulum using internet of things (IoT). The system's conditions and performance could be monitored and controlled via personal computer (PC) and mobile phone. Finally, the inverted pendulum was able to be controlled using the LQR controller and the IoT communication developed will monitor to check the all conditions and performance results as well as help the inverted pendulum improved various operations of IoT control is discussed.

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.

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.

scholarly journals Design of Linear Quadratic Regulator (LQR) Based on Genetic Algorithm for Inverted Pendulum

MENDEL ◽  
2017 ◽  
Vol 23 (1) ◽  
pp. 149-156
Author(s):  
Tomas Marada ◽  
Radomil Matousek ◽  
Daniel Zuth
Keyword(s):  
Genetic Algorithm ◽  
Control Problem ◽  
Inverted Pendulum ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Optimal Response ◽  
Inverted Pendulum Model ◽  
Horizontal Path ◽  
Automatic Control Theory ◽  
Pendulum Model

One of the crucial problems in the dynamics and automatic control theory is balancing of an invertedpendulum robot by moving a cart along a horizontal path. This task is often used as a benchmark for di erentmethod comparison. In the practical use of the LQR method, the key problem is how to choose weight matricesQ and R correctly. To obtain satisfying results the experiments should be repeated many times with di erentparameters of weight matrices. These LQR parameters can be tuned by a Genetic Algorithm (GA) techniquefor getting better results. In our paper, the LQR parameters weight matrices Q and R which were tuned usingthe Genetic Algorithm. The simulations of the control problem are designed using MATLAB script code andMATLAB Simulink on an inverted pendulum model. The results show that the Genetic Algorithm is suitablefor tuning the parameters to give an optimal response. The control problem of the inverted pendulum was solvedsuccessfully.

scholarly journals Linear Quadratic Gaussian Regulator for the Nonlinear Observer-Based Control of a Dynamic Base Inverted Pendulum

2021 ◽  
Vol 13 (3) ◽  
pp. 79-90
Author(s):  
K. Z. MIRZA
Keyword(s):  
Inverted Pendulum ◽  
Control Mechanism ◽  
Linear Quadratic Regulator ◽  
Nonlinear Observer ◽  
Linear Control ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
The Given

The inverted pendulum is a non-linear control problem permanently tending towards instability. The main aim of this study is to design a controller capable enough to work within the given conditions while also keeping the pendulum erect given the impulsive movement of the cart to which it is joint via a hinge. The first half of the paper presents the mathematical modelling of the dynamic system, together with the design of a linear quadratic regulator (LQR). This paper also discusses a novel adaptive control mechanism employing a Kalman filter for the mobile inverted pendulum system (MIPS). In the second half of the paper, a Gaussian Quadratic Linear Controller (LQG) is adapted to improve on previous deficiencies. The simulation is done through Simulink and results show that both controllers are capable of managing the multiple output model. However, data from simulations clearly showed that an LQG controller is a better choice.

scholarly journals Effect of reduced gravity on the preferred walk-run transition speed.

1997 ◽  
Vol 200 (4) ◽  
pp. 821-826 ◽  
Author(s):  
R Kram ◽  
A Domingo ◽  
D P Ferris
Keyword(s):  
Froude Number ◽  
Inverted Pendulum ◽  
Center Of Mass ◽  
Reduced Gravity ◽  
Leg Length ◽  
Pendulum System ◽  
Transition Speed ◽  
Inverted Pendulum Model ◽  
Inverted Pendulum System ◽  
Pendulum Model

We investigated the effect of reduced gravity on the human walk-run gait transition speed and interpreted the results using an inverted-pendulum mechanical model. We simulated reduced gravity using an apparatus that applied a nearly constant upward force at the center of mass, and the subjects walked and ran on a motorized treadmill. In the inverted pendulum model for walking, gravity provides the centripetal force needed to keep the pendulum in contact with the ground. The ratio of the centripetal and gravitational forces (mv2/L)/(mg) reduces to the dimensionless Froude number (v2/gL). Applying this model to a walking human, m is body mass, v is forward velocity, L is leg length and g is gravity. In normal gravity, humans and other bipeds with different leg lengths all choose to switch from a walk to a run at different absolute speeds but at approximately the same Froude number (0.5). We found that, at lower levels of gravity, the walk-run transition occurred at progressively slower absolute speeds but at approximately the same Froude number. This supports the hypothesis that the walk-run transition is triggered by the dynamics of an inverted-pendulum system.

scholarly journals Improved Artificial Bee Colony Algorithm and Its Application in LQR Controller Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Haiquan Wang ◽  
Lei Liao ◽  
Dongyun Wang ◽  
Shengjun Wen ◽  
Mingcong Deng
Keyword(s):  
Artificial Bee Colony ◽  
Linear Quadratic Regulator ◽  
Food Sources ◽  
Linear Quadratic ◽  
Pendulum System ◽  
Abc Algorithm ◽  
Bee Colony ◽  
Inverted Pendulum System ◽  
Fitness Value ◽  
Lqr Controller

In order to get the optimal performance of controller and improve the design efficiency, artificial bee colony (ABC) algorithm as a metaheuristic approach which is inspired by the collective foraging behavior of honey bee swarms is considered for optimal linear quadratic regulator (LQR) design in this paper. Furthermore, for accelerating the convergence speed and enhancing the diversities of population of the traditional ABC algorithm, improved solution searching approach is proposed creatively. The proposed approach refers to the procedure of differential mutation in differential evolutionary (DE) algorithm and produces uniform distributed food sources in employed bee phase to avoid local optimal solution. Meanwhile, during the onlooker bees searching stage where the solution search area has been narrowed by employed bees, new solutions are generated around the solution with higher fitness value to keep the fitness values increasing monotonously. The improved ABC algorithm is applied to the optimization of LQR controller for the circular-rail double inverted pendulum system, and the simulation results show the effect on the proposed optimization problem.

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