This article presents in a unified way, the various optimization criteria used by researchers for optimal placement of piezoelectric sensors and actuators on a smart structure. The article discusses optimal placement of piezoelectric sensors and actuators based upon six criteria: (i) maximizing modal forces/moments applied by piezoelectric actuators, (ii) maximizing deflection of the host structure, (iii) minimizing control effort/maximizing energy dissipated, (iv) maximizing degree of controllability, (v) maximizing degree of observability, and (vi) minimizing spill-over effects. Optimal piezoelectric sensor and actuator locations on beam and plate structures for each criterion and modes of interest are presented in a tabular form. This technical review has two objectives: (i) practicing engineers can pick the most suitable philosophy for their end application and (ii) researchers can come to know about potential gaps in this area.

Optimization Criteria for Optimal Placement of Piezoelectric Sensors and Actuators on a Smart Structure: A Technical Review

In active vibration control of smart structures, the actuator and sensor placement is a key point of the control system design. Even the most robust control logics could easily make a structure unstable if the actuators and sensors were not correctly positioned. The objective of this paper is to propose an H2 norm approach for the actuator and sensor placement. Unlike most modal H2 norm actuator and sensor placement methodologies, this work aims not only to maximize the norms of the controlled modes but also to reduce spillover problems by taking into account the residual modes and minimizing their H2 norms. It discusses the optimal actuator and sensor configuration in a finite element model of a square plate fixed on three sides with piezoelectric patch actuators and acceleration sensors. Finally, downstream of the actuator and sensor positioning, IMSC, PPF and NDF controls have been tested and discussed.

http://iopscience.iop.org/article/10.1088/0964-1726/21/12/125016/pdf

An H2 norm approach for the actuator and sensor placement in vibration control of a smart structure

In this research, a piezoelectric actuator was modeled using fuzzy subtractive clustering and neuro-fuzzy networks. In the literature, the use of various modeling techniques (excluding techniques used in this article) and different arrangements of inputs in black box modeling of piezoelectric actuators for the purpose of displacement prediction has been reported. Nowadays, universal approximators are available with proven ability in system modeling; hence, the modeling technique is no longer such a critical issue. Appropriate selection of the inputs to the model is, however, still an unsolved problem, with an absence of comparative studies. While the extremum values of input voltage and/or displacement in each cycle of operation have been used in black box modeling inspired by classical phenomenological methods, some researchers have ignored them. This article focuses on addressing this matter. Despite the fact that classical artificial neural networks, the most popular black box modeling tools, provide no visibility of the internal operation, neuro-fuzzy networks can be converted to fuzzy models. Fuzzy models comprise of fuzzy rules which are formed by a number of fuzzy or linguistic values, and this lets the researcher understand the role of each input in the model in comparison with other inputs, particularly, if fuzzy values (sets) have been selected through subtractive clustering. This unique advantage was employed in this research together with consideration of a few critical but subtle points in model verification which are usually overlooked in black box modeling of piezoelectric actuators.

Fuzzy modeling of a piezoelectric actuator

For the design of smart composite structures, the placement of piezoelectric patch transducers is a very important issue. For sensing and passive vibration damping applications, the electric charge and the generalized electromechanical coupling coefficient are important parameters. This article presents an approximative but efficient method for the calculation of the generalized coupling coefficient using finite element simulation results. A smart composite turbomachine blade serves as a test structure for the new method. The influence of different laminate integration layers, positions, rotation angles, patch size variations and performance benefits of increased allowable strain is tested with the new procedure. The efficient nature of the method allows for parametric placement studies or even exhaustive search to find the global positioning optimum for the structure under investigation. The proposed method is compared to state-of-the-art procedures for the calculation of the generalized electromechanical coupling factor. The 1:5 scale models of full carbon fabric/epoxy blades were manufactured with structurally integrated piezo modules. Two different piezo placement positions inside the blade were investigated experimentally. The coupling coefficient was determined and compared to the calculated values.

Optimum piezoelectric patch positioning

The review presents developments concerning the modelling of vibration control systems with hysteresis. In particular, the review focuses on applications of the Bouc-Wen model that describes accurate hysteretic behaviour in vibration control devices. The review consists of theoretical aspects of the Bouc-Wen model, identification procedures, and applications in vibration control.

/pdf/modelling-of-hysteresis-in-vibration-control-systems-by-1ikk3fiqwj.pdf

Modelling of Hysteresis in Vibration Control Systems by means of the Bouc-Wen Model

This paper demonstrates an active vibration control system of flexible structures by using piezoelectric sensors and actuators. A set of vibration control equations, sensing equations and actuating equations are derived through using the modal theory for piezoelectric flexible structures, then the model is converted into the state space form. With recent developments in sensors/actuators technologies, many researchers have concentrated on control methods for suppressing vibration of the structures using smart materials such as piezoelectric transducers (PZT). In this paper, two piezoelectric patches are collocated on both sides of the same position of the structure which used as modal sensors and actuators, and the optimal location of them is ascertained by the function of displacement deflection, a LQR controller is designed based on the independent mode space control techniques to suppress the vibration of the system. Finally, the paper takes a piezoelectric cantilever beam as an example, and gives the control simulation results which demonstrate the effectiveness of the method in this paper.

A LQR Controller Design for Active Vibration Control of Flexible Structures

Considerable attentions have been devoted recently to active vibration control using intelligent materials as sensors/actuators. This paper presents results on active control schemes for vibration suppression of flexible cantilever beam with bonded piezoelectric sensors and actuators. State equations which the generalized modal coordinates as variables are built.With the piezoelectric elements are surface-bonded near the same position to the fixed end of flexible cantilever beam, two active vibration control methods such as Linear Quadratic Gauss (LQG) optimal control and robust H∞ control are investigated. Finally, the simulation results are given to demonstrate the effectiveness of the control method in this paper, compared with the LQG control method, robust H control has strong robustness to modal parameters variation, and it has a good closed-loop dynamic performance, can suppress the vibration better at the circumstance of the system with uncertainty factors.

Active Vibration Control of Flexible Structures Using Piezoelectric Materials

H robust active control strategy of the vibration system for the flexible cantilever beam. The model of the system is built by the application of ANSYS software, and then the vibration model is gained by the modal analysis. Finally, by analyzing the model uncertainty of the system existed and choosing the appropriate weighting function, a robust controller is designed based on the ∞ H mixed sensitivity analysis method. The simulation results show that both the dynamics and robustness of the vibration system are effectively improved.

Robust Active Vibration Control of Flexible

Piezoelectric materials are finding increasing applications in active vibration control of flexible structures. The active vibration control for the laminated plane bonded with piezoelectric sensors and actuators is researched in this paper. A set of vibration control equations, sensing equations and actuating equations are derived through using the modal theory for piezoelectric flexible structures, then the model is converted into the state space form. A LQR controller is designed based on the independent mode space control techniques. Finally, the paper takes a piezoelectric cantilever beam as an example, and the simulation results demonstrate the controller is able to suppress efficiently the flexible structure's vibration with piezoelectric sensors and actuators.

The Design of LQR Controller Based on Independent Mode Space for Active Vibration Control

The piezoelectric smart structure is a force-electric coupling structure, and piezoelectric patches can not be patched ideally, so it is difficult to build the accurate mathematical model of piezoelectric smart structure. The traditional vibration control methods depend on the structural mathematical model, and the control result is unsatisfactory. Considering this problem, this paper introduces the nonlinear generalized predictive control algorithm based on neural network predictive model into piezoelectric smart structure. Because of the difficulties of building the mathematical model and extracting dynamic data from experiment, the finite element software (ANSYS) is employed to analyze and obtain the dynamic response data of piezoelectric smart structure through modal analysis and transient analysis. Neural network predictive model of structure is built through off-line training on the basis of the data. The nonlinear generalized predictive control based on neural network has a better ability to solve complex nonlinear problem. Then the author introduces the Neural Network Based System Identification Toolbox (NNSYSID) and Neural Network Based Control System Design Toolkit (NNCTRL), which are two special toolboxes for designing neural network control system and can save lots of time for designers who can commit themselves to sixty-four-dollar question. At last, the author shows the method through a case. A cantilever beam which surface is boned piezoelectric patches used for sensor and actuator respectively is analyzed by ANSYS and controled by the neural network predictive control algorithm on the platform of NNSYSID and NNCTRL. This is a simple and effective method for designers to solve the vibration control problem of piezoelectric smart structure.Copyright © 2008 by ASME

Ercheng Wang

Papers

A LQR Controller Design for Active Vibration Control of Flexible Structures

Active Vibration Control of Flexible Structures Using Piezoelectric Materials

Robust Active Vibration Control of Flexible

The Design of LQR Controller Based on Independent Mode Space for Active Vibration Control

Neural Network Predictive Control for Piezoelectric Smart Structures