Optimal Weighting Matrices Design for LQR Controller Based on Genetic Algorithm and PSO

2012 ◽  
Vol 433-440 ◽  
pp. 7546-7553 ◽  
Author(s):  
S. Amir Ghoreishi ◽  
Mohammad Ali Nekoui
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problem ◽  
Closed Loop ◽  
Inverted Pendulum ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Swarm Optimization ◽  
Speed Of Response ◽  
Lqr Controller ◽  
Optimal Weighting

In this paper, considering some important indices such as closed-loop pole locations, speed of response and combining them into an objective function an optimization problem is defined in order to select the weighting matrices in Linear Quadratic Regulator (LQR) controller. To solve this optimization problem the Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are utilized and compared. The proposed method is applied to rotational inverted pendulum. Simulation results show the relative superiority of PSO over GA.

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.

Robust stabilization control of a spatial inverted pendulum using integral sliding mode controller

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ishan Chawla ◽  
Vikram Chopra ◽  
Ashish Singla
Keyword(s):  
Inverted Pendulum ◽  
Sliding Mode ◽  
Robust Stabilization ◽  
Linear Quadratic Regulator ◽  
Humanoid Robots ◽  
Sliding Mode Controller ◽  
Linear Quadratic ◽  
Integral Sliding Mode ◽  
Wide Range ◽  
Lqr Controller

AbstractFrom the last few decades, inverted pendulums have become a benchmark problem in dynamics and control theory. Due to their inherit nature of nonlinearity, instability and underactuation, these are widely used to verify and implement emerging control techniques. Moreover, the dynamics of inverted pendulum systems resemble many real-world systems such as segways, humanoid robots etc. In the literature, a wide range of controllers had been tested on this problem, out of which, the most robust being the sliding mode controller while the most optimal being the linear quadratic regulator (LQR) controller. The former has a problem of non-robust reachability phase while the later lacks the property of robustness. To address these issues in both the controllers, this paper presents the novel implementation of integral sliding mode controller (ISMC) for stabilization of a spatial inverted pendulum (SIP), also known as an x-y-z inverted pendulum. The structure has three control inputs and five controlled outputs. Mathematical modeling of the system is done using Euler Lagrange approach. ISMC has an advantage of eliminating non-robust reachability phase along with enhancing the robustness of the nominal controller (LQR Controller). To validate the robustness of ISMC to matched uncertainties, an input disturbance is added to the nonlinear model of the system. Simulation results on two different case studies demonstrate that the proposed controller is more robust as compared to conventional LQR controller. Furthermore, the problem of chattering in the controller is dealt by smoothening the controller inputs to the system with insignificant loss in robustness.

Stabilizing and Swinging-Up the Inverted Pendulum Using PI and PID Controllers Based on Reduced Linear Quadratic Regulator Tuned by PSO

2015 ◽  
Vol 4 (4) ◽  
pp. 52-69 ◽  
Author(s):  
M. E. Mousa ◽  
M. A. Ebrahim ◽  
M. A. Moustafa Hassan
Keyword(s):  
Pid Controller ◽  
Inverted Pendulum ◽  
Research Work ◽  
Linear Quadratic Regulator ◽  
Nonlinear Problems ◽  
Pid Controllers ◽  
Linear Quadratic ◽  
Swarm Optimization ◽  
Feed Forward ◽  
Forward Gain

The inherited instabilities in the Inverted Pendulum (IP) system make it one of the most difficult nonlinear problems in the control theory. In this research work, Proportional –Integral and Derivative (PID) Controller with a feed forward gain is used with Reduced Linear Quadratic Regulator (RLQR) for stabilizing the Cart Position and Swinging-up the Pendulum angle. Tuning the Controllers' gains is achieved by using Particle Swarm Optimization (PSO) Technique. Obtaining the combined PID controllers' gains with a feed forward gain and RLQR is a multi-dimensions control problem. The Proposed Controllers give minimum Settling Time, Rise Time, Undershoot and Over shoot for both the Cart Position and the Pendulum angle. A disturbance with different amplitudes is applied to the system, and the results showed the robustness of the systems based on the tuned controllers. The overall results are promising.

Real-Time Control of a Rotary Inverted Pendulum using Robust LQR-based ANFIS Controller

2018 ◽  
Vol 19 (3-4) ◽  
pp. 379-389 ◽  
Author(s):  
Ishan Chawla ◽  
Ashish Singla
Keyword(s):  
Fuzzy Inference System ◽  
Inverted Pendulum ◽  
Fuzzy Inference ◽  
Sliding Mode ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Inference System ◽  
Wide Range ◽  
Lqr Controller ◽  
Rotary Inverted Pendulum

AbstractFrom the last five decades, inverted pendulum (IP) has been considered as a benchmark problem in the control literature due to its inherit nature of instability, non-linearity and underactuation. Its applicability in wide range of practical systems, demands the need of a robust controller. It is found in the literature that wide range of controllers had been tested on this problem, out of which the most robust being sliding mode controller while the most optimal being linear quadratic regulator (LQR) controller. The former has a problem of discontinuity and chattering, while the latter lacks the property of robustness. To address the robustness issue in LQR controller, this paper proposes a novel robust LQR-based adaptive neural based fuzzy inference system controller, which is a hybrid of LQR and fuzzy inference system. The proposed controller is designed and implemented on rotary inverted pendulum. Further, to validate the robustness of proposed controller to parametric uncertainties, pendulum mass is varied. Simulation and experimental results show that as compared to LQR controller, the proposed controller is robust to variations in pendulum mass and has shown satisfactory performance.

Design and Analysis of Linear Quadratic Regulator for a Non-Linear Positioning System

2015 ◽  
Vol 761 ◽  
pp. 227-232 ◽  
Author(s):  
Tang Teng Fong ◽  
Zamberi Jamaludin ◽  
Ahmad Yusairi Bani Hashim ◽  
Muhamad Arfauz A. Rahman
Keyword(s):  
Physical System ◽  
Inverted Pendulum ◽  
Linear Quadratic Regulator ◽  
Upright Position ◽  
System Model ◽  
Optimum Control ◽  
Control Vector ◽  
Linear Quadratic ◽  
Non Linear ◽  
Lqr Controller

The control of rotary inverted pendulum is a case of classical robust controller design of non-linear system applications. In the control system design, a precise system model is a pre-requisite for an enhanced and optimum control performance. This paper describes the dynamic system model of an inverted pendulum system. The mathematical model was derived, linearized at the upright equilibrium points and validated using non-linear least square frequency domain identification approach based on measured frequency response function of the physical system. Besides that, a linear quadratic regulator (LQR) controller was designed as the balancing controller for the pendulum. An extensive analysis was performed on the effect of the weighting parameter Q on the static time of arm, balance time of pendulum, oscillation, as well as, response of arm and pendulum, in order to determine the optimum state-feedback control vector, K. Furthermore, the optimum control vector was successfully applied and validated on the physical system to stabilize the pendulum in its upright position. In the experimental validation, the LQR controller was able to keep the pendulum in its upright position even in the presence of external disturbance forces.

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 Modeling, Simulation, and Optimal Control for Two-Wheeled Self-Balancing Robot

2017 ◽  
Vol 7 (4) ◽  
pp. 2008 ◽  
Author(s):  
Modestus Oliver Asali ◽  
Ferry Hadary ◽  
Bomo Wibowo Sanjaya
Keyword(s):  
Mathematical Model ◽  
Inverted Pendulum ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Modeling Simulation ◽  
Mathematic Modeling ◽  
Lqr Controller ◽  
Output System ◽  
Balancing Robot ◽  
Cart Model

Two-wheeled self-balancing robot is a popular model in control system experiments which is more widely known as inverted pendulum and cart model. This is a multi-input and multi-output system which is theoretical and has been applied in many systems in daily use. Anyway, most research just focus on balancing this model through try-on experiments or by using simple form of mathematical model. There were still few researches that focus on complete mathematic modeling and designing a mathematical model based controller for such system. This paper analyzed mathematical model of the system. Then, the authors successfully applied a Linear Quadratic Regulator (LQR) controller for this system. This controller was tested with different case of system condition. Controlling results was proved to work well and tested on different case of system condition through simulation on matlab/Simulink program.

scholarly journals Performance Comparisons Of Hybrid Fuzzy-LQR And Hybrid PID-LQR Controllers On Stabilizing Double Rotary Inverted Pendulum

2020 ◽  
Vol 1 (2) ◽  
pp. 71-80
Author(s):  
Jamilu Kamilu Adamu ◽  
Mukhtar Fatihu Hamza ◽  
Abdulbasid Ismail Isa
Keyword(s):  
Inverted Pendulum ◽  
Fuzzy Logic Controller ◽  
Linear Quadratic Regulator ◽  
State Feedback Control ◽  
Linear Quadratic ◽  
Trajectory Tracking Control ◽  
Stabilization Control ◽  
Full State Feedback ◽  
Lqr Controller ◽  
Rotary Inverted Pendulum

Double Rotary Inverted Pendulum (DRIP) is a member of the mechanical under-actuated system which is unstable and nonlinear. The DRIP has been widely used for testing different control algorithms in both simulation and experiments. The DRIP control objectives include Stabilization control, Swing-up control and trajectory tracking control. In this research, we present the design of an intelligent controller called “hybrid Fuzzy-LQR controller” for the DRIP system. Fuzzy logic controller (FLC) is combined with a Linear Quadratic Regulator (LQR). The LQR is included to improve the performance based on full state feedback control. The FLC is used to accommodate nonlinearity based on its IF-THEN rules. The proposed controller was compared with the Hybrid PID-LQR controller. Simulation results indicate that the proposed hybrid Fuzzy-LQR controllers demonstrate a better performance compared with the hybrid PID-LQR controller especially in the presence of disturbances.

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.

A PSO-Based LQR Controller for Accelerator PWM Power Supply

2012 ◽  
Vol 490-495 ◽  
pp. 71-75 ◽  
Author(s):  
Xian Qiang Zeng ◽  
Lan Jing ◽  
Ze En Yao ◽  
Yu Hui Guo
Keyword(s):  
Particle Swarm Optimization ◽  
Dynamic Behavior ◽  
Power Supply ◽  
Fitness Function ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Swarm Optimization ◽  
Weighting Matrix ◽  
Lqr Controller ◽  
Better Than

In this paper the method of Linear Quadratic Regulator (LQR) is employed for controlling accelerator PWM power supply, and improving its dynamic functioning. A method based on the Particle Swarm Optimization is proposed to optimize the weighting matrix Q and R. In order to control the dynamic behavior of the power supply, the fitness function of PSO is acquired considering the needs of the power properties. The results of simulation proved that the proposed method was much better than simple LQR method and LQR-GA method, and the performance of the power supply was improved dramatically.

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