Robust eigenstructure assignment using the genetic algorithm and constrained state feedback

1997 ◽  
Vol 211 (1) ◽  
pp. 53-61 ◽  
Author(s):  
T Clarke ◽  
R Davies
Keyword(s):  
Genetic Algorithm ◽  
State Feedback ◽  
Linear Quadratic Regulator ◽  
Eigenstructure Assignment ◽  
Dynamic Feedback ◽  
Linear Quadratic ◽  
Stability Margins ◽  
Lateral Dynamics ◽  
Genetic Algorithm Approach ◽  
Handling Quality

This paper describes a robust eigenstructure assignment methodology for a constrained state feedback problem. The method, which is based upon the linear quadratic regulator and involves the minimization, via the genetic algorithm, of a multiobjective cost function, is applied to L1011 Tristar aircraft lateral dynamics. The design example generates a fixed-gain state feedback solution which shows independent phase margins of 51· in each channel, while exhibiting an eigenstructure close to that desired, lying well within specified handling quality requirements. If two states are made unavailable for feedback, the robustness properties are seriously eroded. When a dynamic feedback compensator is then used, there is a substantial recovery of the robustness. It is concluded that the genetic algorithm approach described here is easy to use and generates good multivariable stability margins.

A Genetic Algorithm Convergence and Models for Eigenstructure Assignment via Linear Quadratic Regulator (LQR)

2008 ◽  
Vol 6 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Joao Viana Fonseca ◽  
Ivanildo Silva Abreu ◽  
Patricia Helena Moraes Rego ◽  
Marlon de Paulo Melo Wolff ◽  
Orlando Fonseca Silva
Keyword(s):  
Genetic Algorithm ◽  
Linear Quadratic Regulator ◽  
Eigenstructure Assignment ◽  
Linear Quadratic ◽  
Algorithm Convergence

scholarly journals Terrain-Perception-Free Quadrupedal Spinning Locomotion on Versatile Terrains: Modeling, Analysis, and Experimental Validation

2021 ◽  
Vol 8 ◽  
Author(s):  
Hongwu Zhu ◽  
Dong Wang ◽  
Nathan Boyd ◽  
Ziyi Zhou ◽  
Lecheng Ruan ◽  
...  
Keyword(s):  
Motion Tracking ◽  
Center Of Mass ◽  
Kinematic Model ◽  
Linear Quadratic Regulator ◽  
Small Scale ◽  
Small Range ◽  
Linear Quadratic ◽  
Stability Margins ◽  
Uneven Terrain ◽  
Quadruped Robots

Dynamic quadrupedal locomotion over rough terrains reveals remarkable progress over the last few decades. Small-scale quadruped robots are adequately flexible and adaptable to traverse uneven terrains along the sagittal direction, such as slopes and stairs. To accomplish autonomous locomotion navigation in complex environments, spinning is a fundamental yet indispensable functionality for legged robots. However, spinning behaviors of quadruped robots on uneven terrain often exhibit position drifts. Motivated by this problem, this study presents an algorithmic method to enable accurate spinning motions over uneven terrain and constrain the spinning radius of the center of mass (CoM) to be bounded within a small range to minimize the drift risks. A modified spherical foot kinematics representation is proposed to improve the foot kinematic model and rolling dynamics of the quadruped during locomotion. A CoM planner is proposed to generate a stable spinning motion based on projected stability margins. Accurate motion tracking is accomplished with linear quadratic regulator (LQR) to bind the position drift during the spinning movement. Experiments are conducted on a small-scale quadruped robot and the effectiveness of the proposed method is verified on versatile terrains including flat ground, stairs, and slopes.

scholarly journals Optimization of the linear quadratic regulator (LQR) control quarter car suspension system using genetic algorithm

2016 ◽  
Vol 36 (1) ◽  
pp. 23-30 ◽  
Author(s):  
Mahesh Nagarkar ◽  
G. J. Vikhe Patil
Keyword(s):  
Genetic Algorithm ◽  
Linear Quadratic Regulator ◽  
Suspension System ◽  
Optimization Approach ◽  
Multi Objective Optimization ◽  
Linear Quadratic ◽  
Multi Objective ◽  
Weighting Matrix ◽  
Car Suspension ◽  
Quarter Car

<p>In this paper, a genetic algorithm (GA) based in an optimization approach is presented in order to search the optimum weighting matrix parameters of a linear quadratic regulator (LQR). A Macpherson strut quarter car suspension system is implemented for ride control application. Initially, the GA is implemented with the objective of minimizing root mean square (RMS) controller force. For single objective optimization, RMS controller force is reduced by 20.42% with slight increase in RMS sprung mass acceleration. Trade-off is observed between controller force and sprung mass acceleration. Further, an analysis is extended to multi-objective optimization with objectives such as minimization of RMS controller force and RMS sprung mass acceleration and minimization of RMS controller force, RMS sprung mass acceleration and suspension space deflection. For multi-objective optimization, Pareto-front gives flexibility in order to choose the optimum solution as per designer’s need.</p>

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 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.

New genetic algorithm for structural active control by considering the effect of time delay

2020 ◽  
pp. 107754632093346
Author(s):  
Ali Banaei ◽  
Javad Alamatian
Keyword(s):  
Genetic Algorithm ◽  
Time Delay ◽  
Active Control ◽  
Control Method ◽  
Control Process ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
The Common ◽  
New Generation ◽  
Active Control Method

This study focuses on a new active control method by improving specification of a well-known intelligent numerical search method, that is the genetic algorithm. The proposed scheme modifies the specifications of the common genetic algorithm by using two strategies. First, a new constrained objective function is proposed. Then, a procedure is designed for evaluating and reducing time delay in control process. These procedures lead to a new generation of the genetic algorithm, which is more reliable. For verifying the efficiency of the proposed method, vibrations of several structures are controlled, and results are compared with other well-known methods such as the common genetic algorithm, linear quadratic regulator, and equivalent critical damping. Numerical results clearly prove the accuracy and efficiency of the proposed control process in comparison with other methods.

Sign in / Sign up

Export Citation Format

Share Document