Optimal Actuator Location Research Articles

Piezoelectric Actuator Placement Optimization and Active Vibration Control of a Membrane Structure

The placement optimization of piezoelectric actuators and active vibration control of a membrane structure are studied in this paper. The classical linear quadratic regulator controllers are designed to suppress the unwanted vibration. Simulation results indicate that the optimal locations of piezoelectric actuators are affected deeply by the additional mass and stiffness of actuators, the computational efficiency of particle swarm optimizer is higher than that of genetic algorithm for this particular problem, and the control performance of optimally placed actuators is better than that of non-optimally placed actuators.

Optimal actuator location of the minimum norm controls for stochastic heat equations

In this paper, we study the approximate null controllability for the stochastic heat equation with the control acting on a measurable subset, and the optimal actuator location of the minimum norm controls. We formulate a relaxed optimization problem for both actuator location and its corresponding minimum norm control into a two-person zero sum game problem and develop a sufficient and necessary condition for the optimal solution via Nash equilibrium. At last, we prove that the relaxed optimal solution is an optimal actuator location for the classical problem.

Optimal actuator location for electro-active polymer actuated endoscope

This paper deals with optimal actuator location for a medical endoscope controlled by electro-active polymer (EAP). The inner tube of the endoscope is a flexible structure that can be represented by a Timoshenko beam. Actuators are patches of EAP. There is freedom in the choice of EAP actuators location. In this paper, we first propose a port Hamiltonian model of the endoscope. In order to choose the optimal location for the EAP actuators, we consider the linear quadratic (LQ) performance as the optimal performance objective. At last, some numerical simulation results are given based on the real experimental setup parameters.

Vibration suppression of a piezo-equipped cylindrical shell in a broad-band frequency domain

This paper focuses on the dynamic modeling of a cylindrical shell equipped with piezoceramic sensors and actuators, as well as the design of a broad band multi-input and multi-output linear quadratic Gaussian controller for the suppression of vibrations. The optimal locations of actuators are derived by Genetic Algorithm (GA) to effectively control the specific structural modes of the cylinder. The dynamic model is derived based on the Sanders shell theory and the energy approach for both the cylinder and the piezoelectric transducers, all of which reflect the piezoelectric effect. The natural vibration characteristics of the cylindrical shell are investigated both theoretically and experimentally. The theoretical predictions are in good agreement with the experimental results. Then, the broad band multi-input and multi-output linear quadratic Gaussian controller was designed and applied to the test article. An active vibration control experiment is carried out on the cylindrical shell and the digital control system is used to implement the proposed control algorithm. The experimental results show that vibrations of the cylindrical shell can be suppressed by the piezoceramic sensors and actuators along with the proposed controller. The optimal location of the actuators makes the proposed control system more efficient than other configurations.

Optimal Placement of an Actuator for Suppressing Vibrations

Objective: To observe the effect of location of an actuator on the performance of a smart structure based on active vibration control scheme using an optimization criterion which is optimized by employing GA as a meta-heuristic optimization technique. Methods/Analysis: In this work a two degrees of freedom spring-mass-damper system has been considered with a hypothetical actuator placeable at three different locations. Equations of motion derived from free body diagrams are converted into a system of first order ordinary differential equations to get a state space model. Control gains for suppressing transient vibrations are obtained using Linear Quadratic optimal control. For optimal placement of hypothetical actuator, an optimization criterion (performance index) consisting of sum of transient displacements of both the masses is formulated. MATLAB optimization toolbox based Genetic Algorithm (GA) solver is employed to obtain optimal location of an actuator by minimizing the optimization criterion. Findings: It is found that optimal actuator location gives minimum value of performance index. By placing the actuator at 1st location performance index increases by 1.31 times and by placing at 2nd location it increases by 2.87 times the case when actuator is located at optimal location suggested by GA i.e. 3rd location. It is therefore concluded that an optimal location of an actuator plays a vital role in performance of an active vibration control scheme and GA can be easily employed for finding optimal actuator location. Novelty/Improvements: To optimally place an actuator in a typical actively controlled structure a strategy i.e. optimization criterion based on sum of transient vibrations of a smart structure has been suggested. GA can be used to solve this optimization problem.

Optimal actuator location of minimum norm controls for heat equation with general controlled domain

In this paper, we study optimal actuator location of the minimum norm controls for a multi-dimensional heat equation with control defined in the space L2(Ω×(0,T)). The actuator domain is time-varying in the sense that it is only required to have a prescribed Lebesgue measure for any moment. We select an optimal actuator location so that the optimal control takes its minimal norm over all possible actuator domains. We build a framework of finding the Nash equilibrium so that we can develop a sufficient and necessary condition to characterize the optimal relaxed solutions for both actuator location and corresponding optimal control of the open-loop system. The existence and uniqueness of the optimal classical solutions are therefore concluded. As a result, we synthesize both optimal actuator location and corresponding optimal control into a time-varying feedbacks.

Operator theoretic framework for optimal placement of sensors and actuators for control of nonequilibrium dynamics

In this paper, we present a novel operator theoretic framework for optimal placement of actuators and sensors in nonlinear systems. The problem is motivated by its application to control of nonequilibrium dynamics in the form of temperature in building systems and control of oil spill in oceanographic flow. The controlled evolution of a passive scalar field, modeling the temperature distribution or density of oil dispersant, is governed by a linear advection partial differential equation (PDE) with spatially located actuators and sensors. Spatial locations of actuators and sensors are optimized to maximize the controllability and observability regions of the linear advection PDE. Linear transfer Perron–Frobenius and Koopman operators, associated with the advective velocity field, are used to provide an analytical characterization for the controllable and observable spaces of the advection PDE. Set-oriented numerical methods are proposed for the finite dimensional approximation of the linear transfer operators. The finite dimensional approximation is shown to introduce weaker notion of controllability and observability, referred to as coarse controllability and observability. The finite dimensional approximation is used to formulate the optimization problem for the optimal placement of sensors and actuators. The optimal placement problem is a combinatorial optimization problem. However, the positivity property of the linear transfer operator is exploited to provide an exact solution to the optimal placement problem using greedy algorithm. Application of the framework is demonstrated for the placement of sensors in a building system for the detection of contaminants and for optimal release of dispersant location for control of contaminant in a Double Gyre velocity field. Simulation results reveal interesting connections between the optimal location of actuators and sensors, maximizing the controllability and observability regions respectively, and the coherent structures in the fluid flow.

Hybrid vibration absorber with detached design for global vibration control

A new hybrid vibration absorber, with detached passive and active parts, is designed, analyzed and tested. This is an alternative approach in case the traditional bundled hybrid vibration absorber with collocated active and passive control elements cannot be applied. In fixed-free structures like buildings and towers, a passive dynamic vibration absorber is very popular for vibration control at or near the free ends. Active control may be introduced to improve performance, but space or weight may be limited in some applications. It may not be practical to attach an actuator near the passive part. The new approach provides more flexibility to retrofit a passive dynamic vibration absorber into a high performance hybrid vibration absorber by installing the actuator at a more suitable location than collocated with the passive part. The proposed hybrid vibration absorber is based on the pole-placement control strategy. Its controller is able to deal with a possible nonminimum-phase secondary path caused by noncollocated actuator sensors. This feature does not exist in a bundled hybrid vibration absorber with collocated actuator sensors. The performance of the new hybrid vibration absorber is analyzed in this study. Experimental and simulation results are used to verify the theoretical results and demonstrate the excellent performance of the new hybrid vibration absorber for vibration control at multiple points. A bundled hybrid vibration absorber with collocated passive and active elements is compared with the proposed hybrid vibration absorber with detached control elements, using experimental and simulation results. It was found that the vibration attenuation performance of the proposed hybrid vibration absorber can be better than the traditional bundled hybrid vibration absorber. The optimal actuator location, which is not necessarily the coupling point of the passive resonator, can be selected numerically by a proposed procedure. One could miss a better solution for vibration control if he/she only uses the bundled hybrid vibration absorber without considering the detached hybrid vibration absorber as a possible alternative.

Estimating parameters with pre-specified accuracies in distributed parameter systems using optimal experiment design

ABSTRACTEstimation of physical parameters in dynamical systems driven by linear partial differential equations is an important problem. In this paper, we introduce the least costly experiment design framework for these systems. It enables parameter estimation with an accuracy that is specified by the experimenter prior to the identification experiment, while at the same time minimising the cost of the experiment. We show how to adapt the classical framework for these systems and take into account scaling and stability issues. We also introduce a progressive subdivision algorithm that further generalises the experiment design framework in the sense that it returns the lowest cost by finding the optimal input signal, and optimal sensor and actuator locations. Our methodology is then applied to a relevant problem in heat transfer studies: estimation of conductivity and diffusivity parameters in front-face experiments. We find good correspondence between numerical and theoretical results.

制御性指標に基づくスマート構造のアクチュエータ配置最適化

This paper proposes an easy-to-use optimization method of actuator location on smart structure evaluating controllability and modal strain energy. Generally, the location of the actuator greatly affects the control performance. In this paper, the controllability Gramian is used as a objective function for PZT actuator location, and it's obtained from a state space equation derived from FE model. Additionally, the modal strain energy obtained from FE model is evaluated as an indicator of optimal actuator location. Particle swarm optimization is used as the algorithm of the optimization. In this paper, an active vibration control system using H-infinity control theory is used to suppress the vibration, and vibration control experiments using the optimized actuator locations are carried out, and the results are argued. As the result, the control system using the optimized actuator location shows high control performance for easy method. From these results, the proposed optimization method is easily and effectively used for suppressing the vibration of the structure.

Observability Inequality of Backward Stochastic Heat Equations for Measurable Sets and Its Applications

This paper aims to provide directly the observability inequality of backward stochastic heat equations for measurable sets. As an immediate application, the null controllability of the forward heat equations is obtained. Moreover, an interesting relaxed optimal actuator location problem is formulated, and the existence of its solution is proved. Finally, the solution is characterized by a Nash equilibrium of the associated game problem.

Optimum control system for earthquake-excited building structures with minimal number of actuators and sensors

For vibration control of civil structures, especially large civil structures, one of the important issues is how to place a minimal number of actuators and sensors at their respective optimal locations to achieve the predetermined control performance. In this paper, a methodology is presented for the determination of the minimal number and optimal location of actuators and sensors for vibration control of building structures under earthquake excitation. In the proposed methodology, the number and location of the actuators are first determined in terms of the sequence of performance index increments and the predetermined control performance. A multi-scale response reconstruction method is then extended to the controlled building structure for the determination of the minimal number and optimal placement of sensors with the objective that the reconstructed structural responses can be used as feedbacks for the vibration control while the predetermined control performance can be maintained. The feasibility and accuracy of the proposed methodology are finally investigated numerically through a 20-story shear building structure under the El-Centro ground excitation and the Kobe ground excitation. The numerical results show that with the limited number of sensors and actuators at their optimal locations, the predetermined control performance of the building structure can be achieved.

Comparison of actuator placement criteria for control of structures

The performance of a controlled system depends on the location of the control actuator, in addition to the controller itself. Thus actuator placement is part of controller design for these systems. In this paper, a number of different actuator placement criteria are compared in the context of controlling vibrations on a simply supported beam. Maximizing a measure of the controllability is very common actuator placement criteria. It is shown here that this approach yields predictions that depend on the order of the model used for the calculations. Furthermore, this criteria does not always lead to locations that also minimize the control objective. The control objectives considered here are the minimization of linear-quadratic, H2 and H∞ costs. The effect of different weights in the linear-quadratic, H2 and H∞ cost functions on the optimal actuator location is also examined. The control signal is calculated for a number of different cases. Linear-quadratic, H2 or H∞ optimal location of the actuator typically leads to better performance with control effort comparable to that at sub-optimal points.

Modeling and optimal design for static shape control of smart reflector using simulated annealing algorithm

This article presents a finite element formulation for static shape control and optimal design of smart reflector with distributed piezoelectric actuators. The finite element model is developed based on the higher-order shear deformation theory where the displacement field in the model accounts for a parabolic distribution of the shear strain, and the shear correction factor is not involved. The Hamilton variational principle is used to formulate the governing equation of the system. A four-node element with seven mechanical degrees of freedom for each node and one electrical potential degree of freedom for each piezoelectric actuator element is used in the finite element formulation. The optimization model for finding the optimal control voltages is derived, and the control voltages can be determined using Lagrange multipliers. The optimal design of actuator locations using simulated annealing algorithm is also investigated. Finally, numerical examples are given to demonstrate the effectiveness of the present model and optimization scheme. The obtained results show that the use of piezoelectric actuators for static shape control of smart reflector can greatly improve the root mean square error, and the optimal location of actuators can be determined effectively using simulated annealing algorithm.

A novel stable deviation quantum-behaved particle swarm optimization to optimal piezoelectric actuator and sensor location for active vibration control

In this article, a novel stable deviation quantum-behaved particle swarm optimization for solving global optimization problem is presented. The proposed stable deviation quantum-behaved particle swarm optimization algorithm uses interpolation and stable deviation function. The method of recombination operator is employed to generate a new solution vector in the search space. Therefore, the chance of fast converging can be improved. The performance of the proposed stable deviation quantum-behaved particle swarm optimization algorithm is compared with a quantum-behaved particle swarm optimization and a quantum-behaved particle swarm optimization with quadratic interpolation recombination operator, which is an advanced variant of quantum-behaved particle swarm optimization. Finally, the proposed stable deviation quantum-behaved particle swarm optimization algorithm is applied to constrained optimal piezoelectric actuator and sensor location for active vibration control of a simply supported plate under the different periodic loads.

Optimal location of piezoelectric actuators for active vibration control of thin axially functionally graded beams

Up to now, optimal location for active control studies concern principally multilayers or homogeneous structures. In the case of functionally graded materials, very few papers exist and they only concern cross section variations. In this way, this paper deals with the optimization of piezoelectric actuators locations on axially functionally graded beams for active vibration control. For this kind of structures, the free vibration problem is more complicated as the governing equations have variable coefficients. Here, the eigenproblem is solved using Fredholm integral equations. The optimal locations of actuators are determined using an optimization criterion, ensuring good controllability of each eigenmode of the structure. The linear quadratic regulator, including a state observer, is used for active control simulations. Two numerical examples are presented for two kinds of boundary conditions.

Comparison of Formulas Obtained for Analytical and LQ Idea Approaches to Determine the Optimal Actuator Location in Active Multimodal Beam Vibration Reduction

Abstract In this paper an active multimodal beam vibration reduction via one actuator is considered. The optimal actuator distribution is analyzed with two methods: an exact mathematical principles and the LQ problem idea. It turned out that the same mathematical expressions are derived. Thus, these methods are equivalent.

Using $\BBH_{2}$-Control Performance Metrics for the Optimal Actuator Location of Distributed Parameter Systems

This paper is concerned with the use of $\BBH_{2}$ -control performance metrics in finding optimal actuator locations for a class of infinite-dimensional systems. Conditions that guarantee convergence of the optimal actuator location for the finite-dimensional representation of the infinite-dimensional system to the optimal actuator location of the original infinite-dimensional system are provided. Minimizing an $\BBH_{2}$ -performance index, parameterized by the possible actuator locations and disturbance functions, leads to optimal locations that in addition to enhanced performance, also provide robustness with respect to the spatial distribution of disturbances. Numerical studies for a cantilever beam and a diffusion problem are used to demonstrate the effects of the spatial distribution of disturbances on the optimal actuator location. The effect of the diffusivity parameter on the best actuator locations is also considered.

Precision Microscopic Actuations of Parabolic Cylindrical Shell Reflectors

An open parabolic cylindrical shell panel plays a key role in radial signal collection, reflection, and/or transmission applied to radar antennas, space reflectors, solar collectors, etc. Active vibration control can suppress unexpected fluctuation and maintain its precision surface and operations. This study aims to investigate the distributed active actuation behavior of adaptive open parabolic cylindrical shell panels using piezoelectric actuator patches. Dynamic equations of parabolic cylindrical shells laminated with piezoelectric actuator patches are presented first. Then, the actuator induced modal control force is defined based on a newly derived mode shape function. As the actuator area varies due to the curvature change, the normalized actuation effectiveness (i.e., modal control force per unit actuator area) is further evaluated. When the actuator area shrinks to infinitesimal, the expression of microscopic local modal control force is obtained to predict the spatial microscopic actuation behavior on parabolic cylindrical shells. The total control force and its three components exhibit distinct characteristics with respect to shell geometries, modes, and actuator properties. Analyzes suggest that the control force contributed by the membrane force component dominates the total actuation effect. The bending-contributed component increases with the corresponding mode number, while the membrane-contributed component decreases. Actuation effectiveness of two shell geometries, from shallow to deep, and actuator sizes are evaluated. Analysis of optimal actuator locations reveals that actuators placed at the maximal shell curvature are more effective and maximize the control effects.

Optimal sensor and actuator locations in linear distributed parameter systems

A constructive method is developed to obtain optimal sensor and actuator locations for inverse optimal state estimation and control of a class of linear distributed parameter systems (DPSs). Given the inverse optimal state estimators and controllers for linear DPSs developed by the rst author recently, it is shown that the performance index for optimal locations of sensors and actuators is the trace of the solution of the Bernoulli partial dierential equations (PDEs), which are the optimal state estimation and control gain matrices. Thus, the optimal locations are designed so as to minimize the trace of the solution of the Bernoulli partial dierential equations.