New Methodology for Optimal Placement of Piezoelectric Sensor/Actuator Pairs for Active Vibration Control of Flexible Structures

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Ali H. Daraji ◽  
Jack M. Hale ◽  
Jianqiao Ye
Keyword(s):  
Vibration Reduction ◽  
Flexible Structures ◽  
Optimal Solution ◽  
Computational Effort ◽  
Optimization Techniques ◽  
Optimal Placement ◽  
Simplified Approach ◽  
Average Percentage ◽  
Sensor Actuator ◽  
Active Vibration

This paper describes a computationally efficient method to determine optimal locations of sensor/actuator (s/a) pairs for active vibration reduction of a flexible structure. Previous studies have tackled this problem using heuristic optimization techniques achieved with numerous combinations of s/a locations and converging on a suboptimal or optimal solution after multithousands of generations. This is computationally expensive and directly proportional to the number of sensors, actuators, possible locations on structures, and the number of modes required to be suppressed (control variables). The current work takes a simplified approach of modeling a structure with sensors at all locations, subjecting it to external excitation force or structure base excitation in various modes of interest and noting the locations of n sensors giving the largest average percentage sensor effectiveness. The percentage sensor effectiveness is measured by dividing all sensor output voltage over the maximum for each mode using time and frequency domain analysis. The methodology was implemented for dynamically symmetric and asymmetric structures under external force and structure base excitations to find the optimal distribution based on time and frequency responses analysis. It was found that the optimized sensor locations agreed well with the published results for a cantilever plate, while with very much reduced computational effort and higher effectiveness. Furthermore, it was found that collocated s/a pairs placed in these locations offered very effective active vibration reduction for the structure considered.

scholarly journals Linear programming with inequality constraints via entropic perturbation

1996 ◽  
Vol 19 (1) ◽  
pp. 177-184 ◽  
Author(s):  
H.-S. Jacob Tsao ◽  
Shu-Cherng Fang
Keyword(s):  
Linear Inequality ◽  
Optimal Solution ◽  
Path Following ◽  
Inequality Constraints ◽  
Computational Effort ◽  
Optimization Techniques ◽  
Linear Program ◽  
Programming Approach ◽  
Linear Programs ◽  
Dual Program

A dual convex programming approach to solving linear programs with inequality constraints through entropic perturbation is derived. The amount of perturbation required depends on the desired accuracy of the optimum. The dual program contains only non-positivity constraints. Anϵ-optimal solution to the linear program can be obtained effortlessly from the optimal solution of the dual program. Since cross-entropy minimization subject to linear inequality constraints is a special case of the perturbed linear program, the duality result becomes readily applicable. Many standard constrained optimization techniques can be specialized to solve the dual program. Such specializations, made possible by the simplicity of the constraints, significantly reduce the computational effort usually incurred by these methods. Immediate applications of the theory developed include an entropic path-following approach to solving linear semi-infinite programs with an infinite number of inequality constraints and the widely used entropy optimization models with linear inequality and/or equality constraints.

scholarly journals OPTIMAL PLACEMENT AND ACTIVE VIBRATION CONTROL OF COMPOSITE PLATES INTEGRATED PIEZOELECTRIC SENSOR/ACTUATOR PAIRS

2018 ◽  
Vol 56 (1) ◽  
pp. 113 ◽  
Author(s):  
Vu Van Tham ◽  
Tran Huu Quoc ◽  
Tran Minh Tu
Keyword(s):  
Vibration Control ◽  
Degrees Of Freedom ◽  
Active Vibration Control ◽  
Laminated Composite ◽  
Composite Plates ◽  
Piezoelectric Sensor ◽  
Optimal Placement ◽  
Laminated Composite Plates ◽  
Sensor Actuator ◽  
Active Vibration

In this study, a finite element model based on first-order shear deformation theory is presented for optimal placement and active vibration control of laminated composite plates with bonded distributed piezoelectric sensor/actuator pairs. The model employs the nine-node isoparametric rectangular element with 5 degrees of freedom for the mechanical displacements, and 2 electrical degrees of freedom. Genetic algorithm (GA) is applied to maximize the fundamental natural frequencies of plates; and the constant feedback control method is used for the vibration control analysis of piezoelectric laminated composite plates. The results of this study can be used to aid the placement of piezoelectric sensor/actuator pairs of smart composite plates as well as for robust controller design.

The Effects of Symmetry on Optimal Transducer Location for Active Vibration Control

2012 ◽  
Author(s):  
A. H. Daraji ◽  
J. M. Hale
Keyword(s):  
Genetic Algorithm ◽  
Finite Element ◽  
Boundary Conditions ◽  
Electromechanical Coupling ◽  
Piezoelectric Sensor ◽  
Optimal Placement ◽  
Sensors And Actuators ◽  
Sensor Actuator ◽  
Modes Of Vibration ◽  
Active Vibration

In this article, the global optimal configuration of sensors and actuators has been investigated for active vibration reduction of plates with symmetrical and asymmetrical geometries and boundary conditions. An isotropic plate element stiffened by beam elements on its edges and with piezoelectric sensor/actuator pairs bonded to its surfaces is modeled, using Hamilton’s principle and the finite element method taking into account piezoelectric mass, stiffness and electromechanical coupling effects. The modeling is based on Mindlin-Reissner plate and Timoshenko beam theories. Optimization is obtained by means of a genetic algorithm using minimization of linear quadratic index is taken as an objective function. The program is written in Matlab m-code and incorporates results from an ANSYS finite element model of the basic structure to take the effects of the first six modes of vibration collectively. The plates with different boundary conditions and geometries are represented by the ANSYS package using two dimensional shell63 elements and three dimensional soild45 elements for the passive structure, and solid5 elements for the active piezoelectric components. The first six modes of vibration are validated experimentally. The genetic algorithm is used to obtain optimal placement of eight and ten piezoelectric sensor/actuator pairs to suppress the first six modes of vibration, investigating the effects of plate boundary conditions and geometry on the optimal distribution of piezoelectric actuators. It is shown that structures with symmetrical geometries and boundary conditions have optimal transducer locations distributed with the same axes of symmetry.

Actuator Selection for Vibration Control With Control Energy Constraints

1997 ◽  
Author(s):  
Hitoshi Doki ◽  
Kazuhiko Hiramoto ◽  
Jun Kaido ◽  
Robert E. Skelton
Keyword(s):  
Total Energy ◽  
Vibration Control ◽  
Dynamic Range ◽  
Active Vibration Control ◽  
Optimal Placement ◽  
Control Effort ◽  
Design Algorithm ◽  
Sensor Actuator ◽  
Energy Constraints ◽  
Active Vibration

Abstract This paper deals with a sensor/actuator placement problem in design of active vibration control systems for flexible structures. This problem is formulated as a minimization problem of the total energy which is defined as a sum of a kinetic and strain energy in a controlled structure with a constraint of control effort. The inequality constraint on the variance of the closed-loop control effort is adopted to represent the capacity (dynamic range) of the actuator. Using a design algorithm which iteratively tunes the weighting matrix of the quadratic performance index in the LQG problem, the controller which meets these specifications can be synthesized. The optimal location of the sensor/actuator is determined by calculating the total energy for each candidate under several energy constraints of the control effort. The optimal placement of the sensor/actuator depends on the control energy constraint. Simulations and experiments for a cantilevered beam are conducted. These results of the optimization can be used as a guide to the design of active vibration control system.

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 Classes of Strongly Stabilizing Bandpass Controllers for Flexible Structures

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Alberto Cavallo ◽  
Giuseppe De Maria ◽  
Ciro Natale ◽  
Salvatore Pirozzi
Keyword(s):  
Control Strategies ◽  
Vibration Reduction ◽  
Flexible Structures ◽  
Linear Matrix ◽  
Design Strategies ◽  
Control Laws ◽  
Practical Applications ◽  
Strong Stabilization ◽  
Inequality Technique ◽  
Active Vibration

This paper proposes different design strategies of robust controllers for high-order plants. The design is tailored on the structure of the equations resulting from modeling flexible structures by using modal coordinates. Moreover, the control laws have some characteristics which make them specially suited for active vibration reduction, such as strong stabilization property and bandpass frequency shape. The approach is also targeted the case of more sensors than actuators, which is very frequent in practical applications. Indeed, actuators are often rather heavy and bulky, while small and light sensors may be placed more freely. In such cases, sensors can be usefully placed in the locations where the primary force fields act on the structure, so as to provide the controller with a direct information on the disturbance effects in terms of structural vibrations. Eventually, this approach may lead to uncolocated control strategies. The design problem is here solved by resorting to a Linear Matrix Inequality technique, which allows also to select the performance weights based on different design requirements, for example, a suitable bandpass frequency shape. Experimental results are presented for a vibration reduction problem of a stiffened aeronautical panel controlled by piezoelectric actuators.

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