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 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.

Active vibration control of a polyvinylidene fluoride laminated membrane plate mirror

2019 ◽  
Vol 25 (19-20) ◽  
pp. 2611-2626 ◽  
Author(s):  
Yifan Lu ◽  
Marco Amabili ◽  
Jian Wang ◽  
Fei Yang ◽  
Honghao Yue ◽  
...  
Keyword(s):  
Vibration Control ◽  
Polyvinylidene Fluoride ◽  
Active Vibration Control ◽  
Space Telescopes ◽  
Linear Quadratic ◽  
Sensors And Actuators ◽  
Natural Modes ◽  
Active Vibration ◽  
High Flexibility ◽  
And Control

Lightweight optical mirrors usually play key roles in aerospace and optical structural systems applied to space telescopes, radars, solar collectors, communication antennas, etc. Due to their high flexibility and low damping properties, external excitations such as orbital maneuver may induce unexpected oscillations and thus reduce their working performance. Active vibration control is therefore essential for the lightweight optical mirror systems. In this spirit, a lightweight mirror structronic system with a linear quadratic optimal controller is presented. The mirror is modeled as a membrane plate with pretension and distributed polyvinylidene fluoride sensors and actuators. The sensing sensitivity of the piezoelectric (PVDF) sensors and the modal actuation factor of the PVDF actuators are derived. The state-space equations are established and the feedback control gains between sensing and control signals are obtained. Sensor and actuator of different shape, size, and position are employed to actively control the first four natural modes of the mirror. The influences of mode order, pretension, and the two weighting factors Q and R on the control performance are also investigated. Analytical results in this paper could guide the design and layout of the PZT sensor and actuator on lightweight membrane plate mirrors.

Active Vibration Control of a Doubly Curved Composite Shell Stiffened by Beams Bonded With Discrete Macro Fiber Composite Sensor/Actuator Pairs

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Ali H. Daraji ◽  
Jack M. Hale ◽  
Jianqiao Ye
Keyword(s):  
Vibration Control ◽  
Composite Shell ◽  
Active Vibration Control ◽  
Vibration Reduction ◽  
Piezoelectric Sensor ◽  
Feedback Gain ◽  
Linear Quadratic ◽  
Sensor Actuator ◽  
Active Vibration ◽  
Doubly Curved

Doubly curved stiffened shells are essential parts of many large-scale engineering structures, such as aerospace, automotive and marine structures. Optimization of active vibration reduction has not been properly investigated for this important group of structures. This study develops a placement methodology for such structures under motion base and external force excitations to optimize the locations of discrete piezoelectric sensor/actuator pairs and feedback gain using genetic algorithms for active vibration control. In this study, fitness and objective functions are proposed based on the maximization of sensor output voltage to optimize the locations of discrete sensors collected with actuators to attenuate several vibrations modes. The optimal control feedback gain is determined then based on the minimization of the linear quadratic index. A doubly curved composite shell stiffened by beams and bonded with discrete piezoelectric sensor/actuator pairs is modeled in this paper by first-order shear deformation theory using finite element method and Hamilton's principle. The proposed methodology is implemented first to investigate a cantilever composite shell to optimize four sensor/actuator pairs to attenuate the first six modes of vibration. The placement methodology is applied next to study a complex stiffened composite shell to optimize four sensor/actuator pairs to test the methodology effectiveness. The results of optimal sensor/actuator distribution are validated by convergence study in genetic algorithm program, ANSYS package and vibration reduction using optimal linear quadratic control scheme.

scholarly journals Innovation in Active Vibration Control Strategy of Intelligent Structures

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
A. Moutsopoulou ◽  
G. E. Stavroulakis ◽  
A. Pouliezos
Keyword(s):  
Control Theory ◽  
Vibration Control ◽  
Piezoelectric Materials ◽  
Control Strategies ◽  
Active Vibration Control ◽  
Structural Performance ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
Intelligent Structures ◽  
Active Vibration

Large amplitudes and attenuating vibration periods result in fatigue, instability, and poor structural performance. In light of past approaches in this field, this paper intends to discuss some innovative approaches in vibration control of intelligent structures, particularly in the case of structures with embedded piezoelectric materials. Control strategies are presented, such as the linear quadratic control theory, as well as more advanced theories, such as robust control theory. The paper presents sufficiently a recognizable advance in knowledge of active vibration control in intelligent structures.

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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