Optimum Structural Vibration Control With Bounds on Control Forces

1995 ◽  
Author(s):  
Alexander A. Bolonkin ◽  
Duane E. Veley ◽  
Narendra S. Khot
Keyword(s):  
Control System ◽  
Linear Quadratic Regulator ◽  
Structural Vibration ◽  
Control Force ◽  
Linear Quadratic ◽  
Structural Vibration Control ◽  
Structure Control ◽  
Design Variables ◽  
Control Devices ◽  
Control Forces

Abstract This paper describes an approach for designing a structure-control system based on the linear quadratic regulator (LQR) which suppresses vibrations in structures. Bounds are placed on the control forces to simulate real actuators. The control system is optimized with an objective function of the total weight of the control devices. The design variables are the bounds (which are proportional to the weight of the control devices) on each control force with a constraint on the time to reduce the energy of the vibration to 5% of its initial value. As an example to illustrate the application of an approach, a wing box idealized by rod elements is used. Control systems are designed for this structure using four and eight actuators for several locations.

Diagonal Recurrent Neural Networks for MDOF Structural Vibration Control

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Z. Q. Gu ◽  
S. O. Oyadiji
Keyword(s):  
Vibration Control ◽  
Control Method ◽  
Control Strategies ◽  
Linear Quadratic Regulator ◽  
Pole Placement ◽  
Structural Vibration ◽  
Stability And Convergence ◽  
Northridge Earthquake ◽  
Linear Quadratic ◽  
Structural Vibration Control

In recent years, considerable attention has been paid to the development of theories and applications associated with structural vibration control. Integrating the nonlinear mapping ability with the dynamic evolution capability, diagonal recurrent neural network (DRNN) meets the needs of the demanding control requirements in increasingly complex dynamic systems because of its simple and recurrent architecture. This paper presents numerical studies of multiple degree-of-freedom (MDOF) structural vibration control based on the approach of the backpropagation algorithm to the DRNN control method. The controller’s stability and convergence and comparisons of the DRNN method with conventional control strategies are also examined. The numerical simulations show that the structural vibration responses of linear and nonlinear MDOF structures are reduced by between 78% and 86%, and between 52% and 80%, respectively, when they are subjected to El Centro, Kobe, Hachinohe, and Northridge earthquake processes. The numerical simulation shows that the DRNN method outperforms conventional control strategies, which include linear quadratic regulator (LQR), linear quadratic Gaussian (LQG) (based on the acceleration feedback), and pole placement by between 20% and 30% in the case of linear MDOF structures. For nonlinear MDOF structures, in which the conventional controllers are ineffective, the DRNN controller is still effective. However, the level of reduction of the structural vibration response of nonlinear MDOF structures achievable is reduced by about 20% in comparison to the reductions achievable with linear MDOF structures.

Performance Studies of Linear Quadratic AMD Controller for Civil Engineering

2013 ◽  
Vol 346 ◽  
pp. 95-100
Author(s):  
L. Guenfaf ◽  
S. Allaoua
Keyword(s):  
Dynamic Model ◽  
Performance Studies ◽  
Linear Quadratic Regulator ◽  
Ball Screw ◽  
Structural Vibration ◽  
Practical Implementation ◽  
Linear Quadratic ◽  
Active Mass ◽  
Structural Vibration Control ◽  
Screw Pitch

In this paper a Linear Quadratic Regulator (LQR) with and without actuator dynamic model for an electric-type active mass driver (AMD) system for structural vibration control has been developed. The electric-type active mass driver (AMD) system is composed primarily of an electric servomotor and a ball screw, the electrical AMD system is free from noise problems, oil leakage, and labor-intensive maintenance that commonly are associated with hydraulic AMD systems. The desired stroke amplification of the mass and the power demand of the servomotor can be adjusted via the ball screw pitch, which affects the effectiveness and efficiency of the system. The AMD system performances without and with introduction of the actuators dynamic model are explored. The reductions of the peak responses can reach as high as 65% if the actuator is properly chosen. And the proposed system is recommended for practical implementation.

Fuzzy neural network control algorithm for asymmetric building structure with active tuned mass damper

2020 ◽  
Vol 26 (21-22) ◽  
pp. 2037-2049
Author(s):  
Xiao Yan ◽  
Zhao-Dong Xu ◽  
Qing-Xuan Shi
Keyword(s):  
Neural Network ◽  
Control System ◽  
Fuzzy Neural Network ◽  
Linear Quadratic Regulator ◽  
Tuned Mass Damper ◽  
Linear Quadratic ◽  
Mass Damper ◽  
Fuzzy Neural ◽  
Neural Network Algorithm ◽  
Damper Control

Asymmetric structures experience torsional effects when subjected to seismic excitation. The resulting rotation will further aggravate the damage of the structure. A mathematical model is developed to study the translation and rotation response of the structure during seismic excitation. The motion equations of the structures which cover the translation and rotation are obtained by the theoretical derivations and calculations. Through the simulated computation, the translation and rotation response of the structure with the uncontrolled system, the tuned mass damper control system, and active tuned mass damper control system using linear quadratic regulator algorithm are compared to verify the effectiveness of the proposed active control system. In addition, the linear quadratic regulator and fuzzy neural network algorithm are used to the active tuned mass damper control system as a contrast group to study the response of the structure with different active control method. It can be concluded that the structure response has a significant reduction by using active tuned mass damper control system. Furthermore, it can be also found that fuzzy neural network algorithm can replace the linear quadratic regulator algorithm in an active control system. Because fuzzy neural network algorithm can control the process on an uncertain mathematical model, it has more potential in practical applications than the linear quadratic regulator control method.

scholarly journals Satellite Attitude Control System Design Taking into Account the Fuel Slosh and Flexible Dynamics

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Alain G. de Souza ◽  
Luiz C. G. de Souza
Keyword(s):  
Control System ◽  
Attitude Control ◽  
Center Of Mass ◽  
Rigid Motion ◽  
Linear Quadratic Regulator ◽  
Comparative Investigation ◽  
Attitude Control System ◽  
Linear Quadratic ◽  
Deformable Structure ◽  
Fuel Slosh

The design of the spacecraft Attitude Control System (ACS) becomes more complex when the spacecraft has different type of components like, flexible solar panels, antennas, mechanical manipulators and tanks with fuel. The interaction between the fuel slosh motion, the panel’s flexible motion and the satellite rigid motion during translational and/or rotational manoeuvre can change the spacecraft center of mass position damaging the ACS pointing accuracy. This type of problem can be considered as a Fluid-Structure Interaction (FSI) where some movable or deformable structure interacts with an internal fluid. This paper develops a mathematical model for a rigid-flexible satellite with tank with fuel. The slosh dynamics is modelled using a common pendulum model and it is considered to be unactuated. The control inputs are defined by a transverse body fixed force and a moment about the centre of mass. A comparative investigation designing the satellite ACS by the Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) methods is done. One has obtained a significant improvement in the satellite ACS performance and robustness of what has been done previously, since it controls the rigid-flexible satellite and the fuel slosh motion, simultaneously.

scholarly journals The linear quadratic regular algorithm-based control system of the direct current motor

2019 ◽  
Vol 10 (2) ◽  
pp. 768
Author(s):  
Trong-Thang Nguyen
Keyword(s):  
Control System ◽  
Direct Current ◽  
State Space Model ◽  
Linear Quadratic Regulator ◽  
Response Speed ◽  
Dc Motor ◽  
Linear Quadratic ◽  
Lqr Controller ◽  
Mathematical Equations ◽  
Feed Forward Controller

<span>This research aims to propose an optimal controller for controlling the speed of the Direct Current (DC) motor. Based on the mathematical equations of DC Motor, the author builds the equations of the state space model and builds the linear quadratic regulator (LQR) controller to minimize the error between the set speed and the response speed of DC motor. The results of the proposed controller are compared with the traditional controllers as the PID, the feed-forward controller. The simulation results show that the quality of the control system in the case of LQR controller is much higher than the traditional controllers. The response speed always follows the set speed with the short conversion time, there isn't overshoot. The response speed is almost unaffected when the torque impact on the shaft is changed.</span>

Linear Quadratic Regulator Method in Vision-Based Laser Beam Tracking for a Mobile Target Robot

Robotica ◽  
2020 ◽  
pp. 1-11
Author(s):  
Yun Ling ◽  
Jian Wu ◽  
Weiping Zhou ◽  
Yubiao Wang ◽  
Changcheng Wu
Keyword(s):  
Control System ◽  
Laser Beam ◽  
Tracking Control ◽  
Error Control ◽  
Linear Quadratic Regulator ◽  
Lyapunov Theory ◽  
State Function ◽  
Linear Quadratic ◽  
Mobile Target ◽  
Beam Tracking

SUMMARY This paper proposes a novel laser beam tracking mechanism for a mobile target robot that is used in shooting ranges. Compared with other traditional tracking mechanisms and modules, the proposed laser beam tracking mechanism is more flexible and low cost in use. The mechanical design and the working principle of the tracking module are illustrated, and the complete control system of the mobile target robot is introduced in detail. The tracking control includes two main steps: localizing the mobile target robot with regards to the position of the laser beam and tracking the laser beam by the linear quadratic regulator (LQR). First of all, the state function of the control system is built for this tracking system; second, the control law is deduced according to the discretized state function; lastly, the stability of the control method is proved by the Lyapunov theory. The experimental results demonstrate that the Hue, Saturation, Value feature-extracting method is robust and is qualified to be used for localization in the laser beam tracking control. It is verified through experiments that the LQR method is of better performance than the conventional Proportional Derivative control in the aspect of converge time, lateral error control, and distance error control.

A Controllability-Based TO Approach for the Piezoelectric Actuator Design Considering Multimodal Vibration Control

2020 ◽  
pp. 2043009
Author(s):  
Juliano F. Gonçalves ◽  
Emílio C. N. Silva ◽  
Daniel M. De Leon ◽  
Eduardo A. Perondi
Keyword(s):  
Vibration Control ◽  
Active Vibration Control ◽  
Optimization Procedure ◽  
Linear Quadratic Regulator ◽  
Time Interval ◽  
Control Performance ◽  
Linear Quadratic ◽  
Main Work ◽  
Design Variables ◽  
Material Interpolation

This paper addresses the design problem of piezoelectric actuators for multimodal active vibration control. The design process is carried out by a topology optimization procedure which aims at maximizing a control performance index written in terms of the controllability Gramian, which is a measure that describes the ability of the actuator to move the structure from an initial condition to a desired final state in a finite time interval. The main work contribution is that independent sets of design variables are associated with each modal controllability index, then the multi-objective problem can be split into independent single-objective problems. Thus, no weighting factors are required to be tuned to give each vibration mode a suitable relevance in the optimization problem. A material interpolation scheme based on the Solid Isotropic Material with Penalization (SIMP) and the Piezoelectric Material with Penalization (PEMAP) models is employed to consider the different sets of design variables and the sensitivity analysis is carried out analytically. Numerical examples are presented by considering the design and vibration control for a cantilever beam and a beam fixed at both ends to show the efficacy of the proposed formulation. The control performance of the optimized actuators is analyzed using a Linear-Quadratic Regulator (LQR) simulation.

scholarly journals Swing Vibration Control of Suspended Structure Using Active Rotary Inertia Driver System: Parametric Analysis and Experimental Verification

2019 ◽  
Vol 9 (15) ◽  
pp. 3144 ◽  
Author(s):  
Chunwei Zhang ◽  
Hao Wang
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Vibration Control ◽  
Parametric Analysis ◽  
Linear Quadratic Regulator ◽  
Shaking Table ◽  
Rotary Inertia ◽  
System Control ◽  
Linear Quadratic ◽  
Control Effectiveness

The Active Rotary Inertia Driver (ARID) system is a novel vibration control system that can effectively mitigate the swing vibration of suspended structures. Parametric analysis is carried out using Simulink based on the mathematical model and the effectiveness is further validated by a series of experiments. Firstly, the active controller is designed based on the system mathematical model and the LQR (linear quadratic regulator) algorithm. Next, the parametric analysis is carried out using Simulink to study the key parameters such as the coefficient of the control algorithm, the rotary inertia ratio. Lastly, the ARID system control effectiveness and the parametric analysis results are further validated by the shaking table experiments. The effectiveness and robustness of the ARID system are well verified. The dynamic characteristics of this system are further studied, and the conclusions of this paper provide a theoretical basis for further development of such unique control system.

On Selection of Control Parameters for H∞ Output Feedback

2005 ◽  
Author(s):  
Chang-Ching Chang ◽  
Chi-Chang Lin
Keyword(s):  
Control System ◽  
Feedback Control ◽  
Output Feedback ◽  
Delay Time ◽  
Output Feedback Control ◽  
Feedback Gain ◽  
Control Force ◽  
Control Parameters ◽  
Structural Responses ◽  
Control Forces

In this paper, an H∞ direct output feedback control algorithm through minimizing the entropy, a performance index measuring the tradeoff between H∞ optimality and H2 optimality, is employed to design the control system in reducing structural responses due to dynamic loads such as earthquakes. The control forces are obtained from the multiplication of direct output measurements by a pre-calculated time-invariant feedback gain matrix. To achieve optimal control performance, the strategy to select both control parameters γ and α is extensively investigated. The decrease of γ or increase of α results in better control effectiveness, but larger control force requirement. For a single degree-of-freedom (SDOF) damped structure, exact solutions of output feedback gains and control parameters are derived. It can be proved analytically that the LQR control is a special case of the proposed H∞ control. Direct velocity feedback control is effective in reducing structural responses with very small number of sensors and controllers compared with the DOFs of the structure. In active control of a real structure, control force execution time delay cannot be avoided. Relatively small delay time not only can render the control ineffective, but also may cause system instability. In this study, explicit formulas to calculate maximum allowable delay time and critical control parameters are derived for the design of a stable control system. Some solutions are also proposed to increase the maximum allowable delay time.

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