Optimal Actuator Location Research Articles

Computation of optimal actuator locations for nonlinear controllers in transport-reaction processes

This paper proposes a methodology for the computation of optimal locations of point actuators for nonlinear feedback controllers in transport-reaction processes described by a broad class of quasi-linear parabolic partial differential equations (PDE). Initially, Galerkin's method is employed to derive finite-dimensional approximations of the PDE system which are used for the synthesis of stabilizing nonlinear state feedback controllers via geometric techniques. Then, the optimal location problem is formulated as the one of minimizing a meaningful cost functional that includes penalty on the response of the closed-loop system and the control action and is solved by using standard unconstrained optimization techniques. It is established that the solution to this problem, which is obtained on the basis of the closed-loop finite-dimensional system, is near-optimal for the closed-loop infinite-dimensional system. The proposed methodology is successfully applied to a typical diffusion-reaction process.

Multi-level optimal design of buildings with active control under winds using genetic algorithms

The goal of this paper is to study the complicated optimal design problem of integrating the number of actuators, the configuration of the actuators and the active control algorithms in buildings excited by strong wind force. To do this, the following sequential studies are carried out: (1) Two control algorithms, linear quadratic regulator (LQR) and acceleration feedback control algorithm, are analyzed and used as the control algorithms. (2) The characteristics of the optimal design problem are analyzed in detail by a simulation study. (3) A multi-level optimization model is proposed, and the formulation of sub-optimization problems in each level is presented. (4) To solve the multi-level optimization problem, a multi-level genetic algorithm (MLGA) is proposed. The properties and implementation of MLGA are given and analyzed in detail. Finally, the optimal design model and the corresponding solving algorithm are tested by numerical simulation. The results show that: (1) in the design of actively controlled structures subjected to strong wind excitation, the problem of considering the number of actuators, the position of actuators and the control algorithm simultaneously is of a multi-level design optimization with the properties of non-linearity, discreteness and so on. (2) This kind of optimization problem should be described naturally by the multi-level design model. (3) The multi-level genetic algorithm can solve this complicated problem effectively. (4) The optimal locations of actuators depend on the control approaches.

Simulation of Structure Control and Controller Design Within a Finite Element Code

This paper investigates some aspects of control by using large-order finite element models and low-order controllers for suppression of vibration (active damping), in terms of both controller simulation and design. It is fundamental for understanding interaction in an actively controlled structure to have an accurate model. The basis structure as well as active elements can be modeled with appropriate elements within a finite element (FE) code. It leads to rather complex FE models in particular if 3-D modeling is applied. Optimal sensor and actuator location and collocation are not topics of the current paper. However complex the FE model might be, it always lacks in reality. Moreover, model reduction techniques are necessary to make a controller design feasible. To close the gap between the FE model and reality, experimental modal identification is used to correct the FE model with an updating procedure before putting to use the controller design and simulation. To integrate controller design methods and the simulation of control action into an FE package, appropriate interfaces between structure and controller have to be designed. From the control system designer's point of view, the definition of these interfaces must absolutely take into consideration the nature of the plant and the possible control design methods. The control of mechanical structures will in most cases be a multiple input—multiple output (MIMO) problem. To do all that preliminary work before testing and final tuning on real structure within the FE system is a challenging undertaking, but it can reduce the number of experiments necessary for final design of the controller. And, on the other hand, influences on the controller of change in the structure can be examined. The paper concludes with four examples of different complexity to illustrate methods and tools that can be very helpful in design and testing of structural controllers.

Optimal actuator/sensor location for active noise regulator and tracking control problems

In this paper, we investigate the problem of finding the optimal location of sensors and actuators to achieve reduction of the noise field in an acoustic cavity. We offer two control strategies: the first is based on linear quadratic tracking where the offending noise is tracked, and the second considers the formulation of the harmonic control strategy as a periodic static output feedback control problem. The first method, which is based on full state information, is suitable for optimal location of actuators while the second strategy can extend the results to finding optimal location of sensors as well as actuators. For both methods we consider the optimization of an appropriate quadratic performance criterion with respect to the location of the actuators and/or the sensors. Numerical examples are presented to compare the effectiveness of each control strategy and also the effect of optimal placement of actuators and sensors.

Modelling and optimal placement of piezoelectric actuators in isotropic plates using genetic algorithms

Theoretical modelling of the vibration of plate components of a space structure incorporating piezoelectric actuators is presented. The equations governing the dynamics of the plate, relating the strains in the piezoelectric elements to the strain induced in the system, are derived for isotropic plates using the Rayleigh-Ritz method. The developed model was used for a simply supported plate. The results show that the model can predict natural frequencies of the plate very accurately. Two criteria for the optimal placement of piezoelectric actuators were suggested using modal controllability and the controllability Grammian. The model was then used to predict the closed-loop frequency response of the plate for active vibration control studies with optimal locations of actuators successfully obtained using genetic algorithms. Significant vibration suppression was demonstrated using optimal actuator placement algorithm developed.

Control of structure-borne noise of a plate featuring piezoceramic actuators

This paper addresses active structural acoustic control of a flexible plate using piezoelectric actuators. The analytical model of a thin plate with simply supported boundary conditions is derived from Hamilton's principle and a control model represented by the transfer function is obtained. Optimal locations of the piezoelectric actuators are found such that it minimizes the radiated sound power at the farfield. With optimally designed actuators, an controller is designed by using the loop shaping design procedure to achieve robust acoustic control of the proposed system subjected to parameter variations and external disturbances. Control performance and robustness are presented in both frequency and time domains in order to demonstrate the effectiveness of the proposed approach. In addition, the comparison between the proposed robust controller and the conventional adaptive Filtered-x LMS algorithm is undertaken.

A method for the selection of sensor and actuator locations

A new and efficient technique for determining optimal locations of sensors and actuators of intelligent structures is presented. The optimization of sensor and actuator locations is based on the 1st order singular value perturbations of observability and controllability. Using this method the optimal placements of sensors and actuators of the intelligent structurer can be selected. Two numerical examples are given to demonstrate the applications of the method. The impulse responses of structures due to different locations of actuators with the same control law are analyzed in detail.

Shear Control and Analytic Solutions for 2-D Dynamic Smart Beam Theory

Analytic solutions are presented for the boundary control of 2-dimensional dynamic smart beam model with shear actuators on the top and bottom of the beam. By using Fourier Series method, the vibration control, optimal location of actuators, and shape control of smart beam are obtained. Applications are also illustrated.

Determination of Design of Optimal Actuator Location and Configuration Based on Actuator Power Factor

In this paper, a new design algorithm is proposed for optimization of the inducedstrain actuator location and configuration for active vibration control based on an actuator performance index, namely the actuator power factor. The concept of actuator power factor, developed recently by the authors, describes the capability of an integrated induced strain actuator, such as PZT or Terfenol, to transfer the supplied electrical energy into structural mechanical energy (kinetic or potential energy of the mechanical system). A system optimized based on the actuator power factor will guarantee the highest energy efficiency for single frequency and broad-band applications. This paper will also show that a higher energy efficiency corresponds to higher mechanical performance. The approach introduced in this paper is much more convenient to use than the conventional modal domain optimization approach. Furthermore, since the power factor approach can include the electrical parameters from the power system, it will allow a system optimization design including the power electronics and energy consumption. The basic concept of the actuator power factor will be introduced first in this paper. Its utility in the system optimization will be discussed using a PZT actuator-driven simply-supported beam. The optimization of actuator location, length, and thickness will be discussed through numerical examples. This paper will also discuss how to use the actuator energy density and actuator power factor to estimate the dynamic response of a system.

Optimal Sizes and Locations of Piezoelectric Actuators for Curved Panel Sound Sources

Optimal Sizes and Locations of Piezoelectric Actuators for Curved Panel Sound Sources

Actuator placement based on reachable set optimization for expected disturbance

This paper examines the role of the control objective and the control time in determining fuel-optimal actuator placement for structural control. A general theory is developed that can be easily extended to include alternative performance metrics such as energy and timeoptimal control. The performance metric defines a convex admissible control set which leads to a max-min optimization problem expressing optimal location as a function of initial conditions and control time. A solution procedure based on a nested genetic algorithm is presented and applied to an example problem. Results indicate that the optimal placement varies widely as a function of both control time and disturbance location. An approximate fitness function is presented to alleviate the computational burden associated with finding exact solutions. This function is shown to accurately predict the optimal actuator locations for a 6th-order system, and is further demonstrated on a 12th-order system.

Tendon Control System for Active Shape Control of Flexible Space Structures

Large space structures are very flexible and are easily deformed due to any disturbances in the space environment. This paper proposes a tendon control system for the shape control of flexible space structures and presents methods of determining the structural deflections accurately and applying control forces effectively to restore the desired shape. The problem of active shape control consists of: (1) estimating the deformed shape of a flexible structure from multi-point spatially distributed measurement of the structural deflections, and (2) restoring the desired shape by means of control actuators installed on the structure. This paper develops the estimation and control designs using an infinite-dimensional approach, where the necessary finite element truncation and approximation are introduced after solving the estimation problem. The proposed shape estimation algorithm determines the deformed shape of the structure subjected to unknown disturbance forces from multi-point spatially distributed measurement of the structural deflections. Active static control force is determined so that the integrated restoration error may be minimized. The control design is based on the least squares estimation algorithm. This paper also studies the optimal actuator location that minimizes the restoration errors. The method is applied to an experimental tendon control system for a highly flexible beam. The results of numerical simulations are given for demonstrating the feasibility of the present estimation and control method and for investigating the optimal actuator location.

Electro-mechanical impedance modeling of active material systems

An active material system may be generalized as an electro-mechanical network because of the incorporation of actuators (electrically driven) and sensors (that convert mechanical energy into electrical energy). An investigation of the coupled electrical and mechanical aspects of an active material system will help reveal some of its most important characteristics, in particular regarding energy conversion and consumption issues. The research performed in the area of the electro-mechanical impedance (EMI) modeling of active material systems is herein summarized. In this paper, a generic EMI model to describe the electro-mechanical network behavior (time domain and frequency domain) of active material systems will be discussed. The focus of the discussion will be on the methodology and basic components of the EMI modeling technique and its application to assist in the design of efficient active control structures. This paper will first introduce the basic concept of the EMI modeling and its general utility in the area of active material systems. The methodology of the EMI modeling technique will be illustrated using an example of PZT actuator-driven mechanical systems. The basic components of the EMI modeling, including the electro-mechanics of induced strain actuators, the dynamic analysis of active material systems, and the electrical power consumption and requirements, will be discussed. Finally, some applications of the EMI modeling approach, including the determination of the optimal actuator locations, modal analysis using collocated PZT actuator - sensors, and the prediction of radiated acoustic power, will be presented.

Suppression of nonlinear panel flutter at supersonic speeds and elevated temperatures

Coupled structure-electrical nonlinear panel flutter equations of motion are derived using the finite element method for composite panels with embedded piezoelectric layers subjected to thermal loads. The von Karman large-deflection strain-displacement relations, quasisteady first-order piston theory aerodynamics, quasisteady thermal stress theory, and linear piezoelectricity theory are used. Following a modal transformation and reduction, a set of coupled nonlinear modal equations of motion is obtained. By using the linear optimal control design for the linearized modal equations, an optimal shape and location of piezoelectric actuators can be determined. Numerical simulations based on the nonlinear modal equations show that the maximum flutter-free dynamic pressure with the linear optimal control can be increased as high as six times of the critical dynamic pressure. The panel's large-amplitude limit-cycle motions, as well as periodic and chaotic motions at moderate temperatures, are shown to be completely suppressed within the maximum flutter-free dynamic pressure region. Flutter suppression on composite panels with different aspect ratios, boundary conditions, and thermal effects are also studied. The results reveal that piezoelectric actuators are effective in nonlinear panel flutter suppression.

A coupled controls/structures optimization procedure for the design of rotating composite box beams with piezoelectric actuators

An optimization procedure is developed for controls/structures interaction using a multiobjective formulation. A rotating composite cantilever box beam model is presented which includes piezoelectric strain actuators for vibration control. The model is implemented using the finite-element method. Multiple design objectives are efficiently combined using the Kreisselmeier-Steinhauser function approach. Actuator locations and ply stacking sequences are represented by discrete (0,1) variables while structural/control parameters such as box beam dimensions are continuous design variables. A transformation technique is used to formulate the combined continuous/discrete problem as a purely discrete problem. This allows both optimal actuator locations and structural/control parameters to be determined inside a closed loop procedure. A technique based on simulated annealing is used for optimization in conjunction with an approximate analysis procedure to reduce computational effort.

Determination of Design of Optimal Actuator Location and Configuration Based on Actuator Power Factor

In this paper, a new design algorithm is proposed for optimization of the inducedstrain actuator location and configuration for active vibration control based on an actuator performance index, namely the actuator power factor. The concept of actuator power factor, developed recently by the authors, describes the capability of an integrated induced strain actuator, such as PZT or Terfenol, to transfer the supplied electrical energy into structural mechanical energy (kinetic or potential energy of the mechanical system). A system optimized based on the actuator power factor will guarantee the highest energy efficiency for single frequency and broad-band applications. This paper will also show that a higher energy efficiency corresponds to higher mechnical performance. The approach introduced in this paper is much more convenient to use than the conventional modal domain optimization approach. Furthermore, since the power factor approach can include the electrical parameters from the power system, it will allow a system optimization design including the power electronics and energy consumption. The basic concept of the actuator power factor will be introduced first in this paper. Its utility in the system optimization will be discussed using a PZT actuator-driven simply-supported beam. The optimization of actuator location, length, and thickness will be discussed through numerical examples. This paper will also discuss how to use the actuator energy density and actuator power factor to estimate the dynamic response of a system.

Suppression of nonlinear panel flutter with piezoelectric actuators using finite element method

An optimal control design is presented to actively suppress large-amplitude, limit-cycle flutter motions of rectangular isotropic plates at supersonic speeds using piezoelectric actuators. The nonlinear panel flutter equations based on the finite element method are derived for isotropic plates with piezoelectric layers subjected to aerodynamic and thermal loads. A model reduction is performed to the finite element system equations of motion for the control design and the time domain simulation. An optimal controller is developed based on the linearized modal equations, and the norms of the feedback control gain are employed to provide the optimal shape and location of the piezoelectric actuators. Numerical simulations based on the reduced nonlinear panel flutter model show that the critical dynamic pressure can be increased three to four times by the piezoelectric actuation. Within the increased critical dynamic pressure, the limit-cycle motions can be completely suppressed. The results demonstrate that piezoelectric materials are effective in panel flutter suppression.

Experimental Verification of Optimal Actuator Location and Configuration Based on Actuator Power Factor

The actuator power factor is defined as the ratio of the total dissipative mechanical power of a PZT actuator to the total supplied electrical power to the PZT actuator. If measured experimentally, it can be used to optimize the actuator location and configuration for complex structures. The concept of actuator power factor is based on the ability of an integrated induced strain actuator such as a PZT to transfer supplied electrical energy into structural mechanical energy. For a given structure such as a beam or a plate, the location and configuration of an actuator will directly influence the authority of the actuator towards driving the structure. Presented in this paper are the experimental as well as the theoretical results for the case of a cantilever beam as a proof-of-concept of this technique. The design of a fixture which allows for the relocation of a PZT patch which can be used for both actuation and sensing is presented as well. For the experimental case, the electromechanical PZT admittance was measured by an HP 4194A impedance analyzer for the power factor analysis. The experimental and the theoretical power factor results were subsequently compared and showed good qualitative similarities over the frequency range analyzed. This initial comparison between the experimental and the theoretical power factor results will be used to analyze the capabilities and limitations of the actuator power factor algorithm as a tool for determining the optimal configuration and location for a PZT actuator for simple as well as complex structural vibration control applications.

Actuator placement in lumped parameter systems subjected to disturbance

This paper is intended to report preliminary results in the area of actuator placement in a lumped parameter system subjected to a disturbance at a known location. A criterion has been established relating the optimal actuator position to the location of the disturbance. Linear time invariant lumped parameter models were chosen to investigate the effect of control actuator locations. The results of the simulations show that the optimal actuator location is the one closest to the source of the unknown disturbance. This work suggests placing the actuator as close as possible to the source of the known disturbance.

Optimal Placement of Piezoelectric Actuators for Active Structural Acoustic Control

This paper presents a general formulation of the optimization problem for the place ment and sizing of piezoelectric actuators in adaptive LMS control systems. The selection of objec tive function, design variables and physical constraints are separately discussed. A case study for the optimal placement of multiple fixed size piezoelectric actuators in sound radiation control is pre sented. A solution strategy is proposed to calculate the applied voltages to piezoelectric actuators with the use of linear quadratic optimal control theory which is to simulate the LMS feedforward control algorithm. The location of piezoelectric actuators is then determined by minimizing the ob jective function, which is defined as the sum of the mean square sound pressure measured by a number of error microphones. The optimal location of piezoelectric actuators for sound radiation control is determined and shown to be dependent on the excitation frequency. Particularly, the opti mal placement of multiple piezoelectric actuators for on-resonance and off-resonance excitation is presented. The results show that the optimally located piezoelectric actuators perform far better sound radiation control than arbitrarily selected ones. This work leads to a design methodology for adaptive or intelligent material systems with highly integrated actuators and sensors. The optimiza tion procedure also leads to a reduction in the number of control transducers.