scholarly journals State-Space Modeling and Active Vibration Control of Smart Flexible Cantilever Beam with the Use of Finite Element Method

2020 ◽  
Vol 10 (6) ◽  
pp. 6549-6556
Author(s):  
K. G. Aktas ◽  
I. Esen
Keyword(s):  
Finite Element ◽  
Vibration Control ◽  
State Space ◽  
Cantilever Beam ◽  
Active Vibration Control ◽  
Sensors And Actuators ◽  
Sensor Actuator ◽  
Lqr Controller ◽  
Smart Beam ◽  
Active Vibration

The aim of this study is to design a Linear Quadratic Regulator (LQR) controller for the active vibration control of a smart flexible cantilever beam. The mathematical model of the smart beam was created on the basis of the Euler-Bernoulli beam theory and the piezoelectric theory. State-space and finite element models used in the LQR controller design were developed. In the finite element model of the smart beam containing piezoelectric sensors and actuators, the beam was divided into ten finite elements. Each element had two nodes and two degrees of freedom were defined for each node, transverse displacement, and rotation. Two Piezoelectric ceramic lead Zirconate Titanate (PZT) patches were affixed to the upper and lower surfaces of the beam element as pairs of sensors and actuators. The location of the piezoelectric sensor and actuator pair changed and they were consecutively placed on the fixed part, the middle part, and the free end of the beam. In each case, the design of the LQR controller was made considering the first three dominant vibratory modes of the beam. The effect of the position of the sensor-actuator pair on the beam on the vibration damping capability of the controller was investigated. The best damping performance was found when the sensor-actuator pair was placed at the fixed end.

Determination of State Space Matrices for Active Vibration Control Using ANSYS Finite Element Package

2012 ◽  
Author(s):  
A. H. Daraji ◽  
J. M. Hale
Keyword(s):  
Finite Element ◽  
Vibration Control ◽  
State Space ◽  
Active Vibration Control ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
Sensors And Actuators ◽  
Sensor Actuator ◽  
Finite Element Package ◽  
Active Vibration

This paper concerns optimal placement of discrete piezoelectric sensors and actuators for active vibration control, using a genetic algorithm based on minimization of linear quadratic index as an objective function. A new method is developed to get state space matrices for simple and complex structures with bonded sensors and actuators, using the ANSYS finite element package taking into account piezoelectric mass, stiffness and electromechanical coupling effects. The state space matrices for smart structures are highly important in active vibration control for the optimisation of sensor and actuator locations and investigation of open and closed loop system control response, both using simulation and experimentally. As an example, a flexible flat plate with bonded sensor/actuator pairs is represented in ANSYS using three dimensional SOLID45 elements for the passive structure and SOLID5 for the piezoelectric elements, from which the necessary state space matrices are obtained. To test the results, the plate is mounted as a cantilever and two sensor/actuator pairs are located at the optimal locations. These are used to attenuate the first six modes of vibration using active vibration reduction based on a classical and optimal linear quadratic control scheme. The plate is subject to forced vibration at the first, second and third natural frequencies and represented in ANSYS using a proportional derivative controller and compared with a Matlab model based on ANSYS state space matrices using linear quadratic control. It is shown that the ANSYS state space matrices describe the system efficiently and correctly.

scholarly journals Active Vibration Control of Cantilever Beam by Using Optimal LQR Controller

2018 ◽  
Vol 24 (11) ◽  
pp. 1
Author(s):  
Hadeer Abd UL-Qader Mohammed ◽  
Hatem Rahem Wasmi
Keyword(s):  
Vibration Control ◽  
Cantilever Beam ◽  
Experimental Work ◽  
Active Vibration Control ◽  
Actuation Voltage ◽  
Smart Structure ◽  
Control Gain ◽  
Lqr Controller ◽  
Smart Beam ◽  
Active Vibration

Many of mechanical systems are exposed to undesired vibrations, so designing an active vibration control (AVC) system is important in engineering decisions to reduce this vibration. Smart structure technology is used for vibration reduction. Therefore, the cantilever beam is embedded by a piezoelectric (PZT) as an actuator. The optimal LQR controller is designed that reduce the vibration of the smart beam by using a PZT element.   In this study the main part is to change the length of the aluminum cantilever beam, so keep the control gains, the excitation, the actuation voltage, and mechanical properties of the aluminum beam for each length of the smart cantilever beam and observe the behavior and effect of changing the length of the smart cantilever beam. A cantilever beam with piezoelectric is modeled in Mechanical APDL ANSYS version 15.0 and verified this by using experimental work. The AVC was tested on a smart beam under different control gains in experimental work and chose the best control gain depending on FEM results for each length of the smart beam. The response of the smart beam is noticed to be different for every length and the reduction percentage for settling time was different for every length.  

Optimal Placement of Piezoelectric Sensors and Actuators for Controlled Flexible Linkage Mechanisms

2005 ◽  
Vol 128 (2) ◽  
pp. 256-260 ◽  
Author(s):  
Xianmin Zhang ◽  
Arthur G. Erdman
Keyword(s):  
Vibration Control ◽  
Simulation Analysis ◽  
Active Vibration Control ◽  
Optimal Placement ◽  
Control Effect ◽  
Sensors And Actuators ◽  
Piezoelectric Sensors And Actuators ◽  
Active Vibration ◽  
Flexible Mechanism ◽  
Flexible Linkage

The optimal placement of sensors and actuators in active vibration control of flexible linkage mechanisms is studied. First, the vibration control model of the flexible mechanism is introduced. Second, based on the concept of the controllability and the observability of the controlled subsystem and the residual subsystem, the optimal model is developed aiming at the maximization of the controllability and the observability of the controlled modes and minimization of those of the residual modes. Finally, a numerical example is presented, which shows that the proposed method is feasible. Simulation analysis shows that to achieve the same control effect, the control system is easier to realize if the sensors and actuators are located in the optimal positions.

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