Optimal Actuator Location Research Articles

The Optimal Location of Piezoelectric Sensor/Actuator Based on Adaptive Genetic Algorithm

This paper considered the optimal placement of collocated piezoelectric actuator-sensor pairs on a thin cantilever plate using a modal-based linear quadratic independent modal space controller. LQR performance was taken as objective for finding the optimal location of sensor–actuator pairs.The discrete optimal sensor and actuator location problem was formulated in the framework of a zero–one optimization problem,which was solved by real-coded adaptive genetic algorithm (AGA). The vibration response of the piezoelectric plate was calculated using the finite element method (FEM).The optimization and vibration control programs were written by FORTRAN language. The results of numrical examples show that the adaptive genetic algorithm based on the minimum of LQR performance for the optimal location of sensors and actuators is feasible and effective.

Optimal actuator location for time and norm optimal control of null controllable heat equation

We consider minimal time and minimal norm of the optimal controls for a multi-dimensional internally controlled heat equation with control domain varying over a class of open sets. Two problems are formulated separately into different types of shape optimization problems over this open set class. The governing equation with any given initial value and admissible control are considered as constraints, and minimal time or minimal norm of the optimal controls is considered as cost for related shape optimization. The solution of the shape optimization leads to the optimal actuator location for optimal controls. The existence of such an optimal location domain for both minimal time and minimal norm controls is presented. A different problem that relates the balance between minimal time and minimal norm controls is also discussed. This study builds a link between optimal control and shape optimization for this multi-dimensional heat equation.

H∞-Optimal Actuator Location

In many control applications, there is freedom to place the actuators. The actuator location should be chosen to optimize certain performance objectives. In this paper, H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -performance with state-feedback is considered. That is, both the controller and the actuator locations are chosen to minimize the effect of disturbances on the output. A framework for calculating H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal actuator locations is developed. Conditions for well-posedness of the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal actuator location problem are presented. Many optimal actuator problems involve systems modelled by partial differential equations and conditions under which approximations yield reliable results are given. A derivative-free optimization algorithm to calculate H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -optimal actuator locations is described. The results are illustrated using several examples.

Optimal locations of piezoelectric actuators and sensors for supersonic flutter control of composite laminated panels

The optimal active flutter control of supersonic composite laminated panels is studied using the distributed piezoelectric actuators/sensors pairs. The supersonic piston theory is used to calculate the unsteady aerodynamic pressure, and Hamilton’s principle with the assumed mode method is employed to develop the equation of motion of the structural system. The controllers are designed by the proportional feedback control method and the linear quadratic Gauss (LQG) algorithm. The optimal locations of the actuator/sensor pairs are determined by the genetic algorithm (GA). The aeroelastic properties of the structural system are mainly analyzed using the frequency-domain method. The time-domain responses of the structure are also computed using the Runge–Kutta method. The influences of ply angle on the flutter bound of the laminated panel with different length–width ratios are analyzed. The optimal design for the locations for different numbers of piezoelectric patches used in the proportional feedback control is carried out through the GA. Meanwhile, the control effects using different numbers of actuator/sensor pairs are investigated. The flutter suppression by the LQG algorithm is also carried out. The control effects using the two different controllers are compared. Numerical simulations show that the optimal locations obtained by the GA can increase the critical flutter aerodynamic pressure significantly, and the LQG algorithm is more effective in flutter suppression for supersonic structures than the proportional feedback controller.

An algorithm for LQ optimal actuator location

The locations of the control hardware are typically a design variable in controller design for distributed parameter systems. In order to obtain the most efficient control system, the locations of control hardware as well as the feedback gain should be optimized. These optimization problems are generally non-convex. In addition, the models for these systems typically have a large number of degrees of freedom. Consequently, existing optimization schemes for optimal actuator placement may be inaccurate or computationally impractical. In this paper, the feedback control is chosen to be an optimal linear quadratic regulator. The optimal actuator location problem is reformulated as a convex optimization problem. A subgradient-based optimization scheme which leads to the global solution of the problem is used to optimize actuator locations. The optimization algorithm is applied to optimize the placement of piezoelectric actuators in vibration control of flexible structures. This method is compared with a genetic algorithm, and is observed to be faster and more accurate. Experiments are performed to verify the efficacy of optimal actuator placement.

Optimal vibration control of smart composite beams with optimal size and location of piezoelectric sensing and actuation

Control performances of smart structures depend on the size and location of the piezoelectric actuators and sensors as well as on the applied control algorithm. This article presents optimal vibration control of a thin-walled composite beam by using the fuzzy optimization strategy based on the particle swarm optimization algorithm. The optimization of the size and location of the conventionally collocated piezoelectric actuators and sensors, and optimization of the controller parameters are performed separately. The optimization criteria for optimal size and location of piezoelectric actuators and sensors are based on eigenvalues of the controllability Grammian matrix. The optimization procedure implies constraint of the original dynamic properties change and limitation of the beam mass increase. The particle swarm optimization-based linear quadratic regulator has been implemented for optimal vibration control in order to maximize the modal closed-loop damping ratios and minimize the control voltages required for actuation while keeping them below breakdown voltage for the used piezoelectric actuator. A pseudo-goal function, derived from the fuzzy set theory, gives an expression for global objective functions eliminating the use of weighting coefficients and penalty functions. The problem is formulated using the finite element method based on the third-order shear deformation theory. Several numerical examples are presented for the cantilever beam.

Optimal actuation in vibration control

The paper addresses the problem of finding the optimal location of actuators and their relative gain so that the control effort in an actively controlled vibrating system is minimized. In technical terms the problem is finding the optimal input vector of unit norm that minimizes the norm of the control gain vector. This problem is addressed in the context of the active natural frequency modification problem associated with resonance avoidance in undamped systems, and in the context of the single-input-multi-output pole assignment problem for second order systems.

Optimal sensor and actuator location for unstable systems

Accurate and reliable process measurements play a key role in the success of process control. In addition to selecting the instrumentation hardware, it is important to determine which variables should be measured in a process. Therefore it is important to study techniques for placing sensors on the processes. Dually the problem of placing actuators on the processes is equally important. In this paper, the problem of determining optimal sensor and actuator locations for the linear systems is addressed. The problem of the sensor locations is viewed as the problem of maximizing the output energy generated by a given state and for the actuator locations is viewed as the problem of minimizing the input energy required to reach a given state. Such design problems occur in many applications, and therefore have been studied extensively. Unfortunately, the results in this context, which have been proposed so far, only support stable systems. However, in industrial practices it is often the case that the system, which is needed to be controlled, is not stable. The method which is proposed in this paper is a general method in the sense that it supports both stable and unstable systems. The technique is successfully used for determining the optimal sensor locations of the linearized Continuous Stirred-Tank Reactor unstable model.

Genetic algorithm based LQR vibration wireless control of laminated plate using photostrictive actuators

A photostrictive type of opto-electromechanical actuator activated by high-energy lights can introduce actuation and control effects without hard-wired connections. This paper addresses the controllability aspect in wireless vibration control of plate structures via photostrictive actuators. A modal force index, which has taken into account the mode number, the spatial distribution, and the dimension of the actuator, is chosen as an objective function to determine the optimal locations of photostrictive actuators. A linear methodology is proposed in this paper and the vibration equation is written in the standard state-space form. A binary-coded GA based combined optimal placement and LQR (linear quadratic regulator) control scheme has been incorporated, which maximizes the modal force index, the closed loop damping and minimizes input light intensity to the actuators. In the present method only three weighting factors have been used to search optimal Q and R matrices using GA, which reduces chromosome length and hence minimizes computational time. Numerical results demonstrate that the use of strategically positioned actuator patches can effectively control the fundamental modes that dominate the structural vibration.

Optimization of actuator placement in a truss-cored sandwich plate with independentmodal space control

The determination of optimal locations of actuators is an important issue in the field ofvibration control in structures. In this paper, a practical method for the optimal actuatorplacement in a truss-cored sandwich plate based on independent modal space control(IMSC) is proposed. It is shown that the modal strain energy (MSE) alone isnot enough to determine the actuator locations since the system may becomeuncontrollable, especially when the structure is symmetrical. Moreover, it is found that thecontrollability can be measured through the singular values of the input matrix. Thereforethe singular values of the input matrix together with the modal strain energymay serve as an effective optimization index for actuator placement. Numericalexamples are presented to show that the maximal actuator force can be significantlyreduced after the optimization in order to achieve an equal modal control force.

Smart Choice and Location of Sensors and Actuators for Aeroelastic Object Motion Control

AbstractNew results of application of the sensor system optimization method developed by the authors had been achieved in the solving of the dual problem of optimal choice and location of actuators in the control system of aeroelastic object. This method initially was proposed to optimize the sensor choice and position of measuring system appropriate for the estimation of the aerospace vehicle motion parameters and the elastic components of this motion. The accuracy of the estimation of these parameters determines the anticipated error in the conformation of controlled variables of state-space vector to the preset values. The control system consists of the estimator and the regulator with time variable parameters optimal for the chosen quadric performance index and the stochastic models of noises and disturbances. The maximal admissible dispersions of the controlled variables estimation errors and time-average magnitudes of the chosen criterions are assumed as limitations for a Linear Matrix Inequalities (LMI) based sensors system optimization problem using a specified goal function related with the number, type and accuracy of sensors. The single set of LMIs defining requirements for estimate accuracy, control quality and consumption by minimizing the goal function had been formed for considered LQG control system consisting of an observer and controller to determine the required number, parameters, and location of sensors and actuators.

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

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.

A screw theory basis for quantitative and graphical design tools that define layout of actuators to minimize parasitic errors in parallel flexure systems

Abstract In this paper we introduce a visual approach for placing actuators within multi-axis parallel flexure systems such that position and orientation errors are minimized. A stiffness matrix, which links twists and wrenches, is used to generate geometric shapes that guide designers in selecting optimal actuator locations and orientations. The geometric shapes, called actuation spaces, enable designers to (i) visualize the regions wherein actuators should be placed so as to minimize errors, (ii) guide designers in selecting these actuators to maximize the decoupling of actuator inputs, and (iii) determine actuator forces and displacements for actuating specific degrees of freedom. These new principles, the means to practice them, and a comparison of theory verses measured behavior, are demonstrated within a case study.

An impedance approach to the design of optimal actuator location for acoustic responsesynthesis

We present a method for optimization of the location of the induced-strain actuator foracoustic response synthesis, based on the impedance technique. A dynamic model thatcouples the actuator impedance, the host structure impedance and the acoustic impedanceis developed and then utilized to determine the optimal location of the actuator. Theactuator power factor concept describes the transfer efficiency of the supplied electricalenergy into the host structure. This work is based on the power factor and provides analternative to the traditional optimization methods for determining where to bondthe actuator. For an intelligent structure which is usually bonded with multipleactuators, a modified impedance model including the mass effect resulting fromthe actuators themselves is also proposed. Numerical examples are presented toshow the influence of the mass effect on the power factor and to illustrate how toimplement this method to design the optimal location of the actuator for acousticsynthesis.

Optimal design of piezolaminated structures using B-spline strip finite element models

A package of B-spline finite strip models is developed for the linear analysis of piezolaminated plates and shells. This package is associated to a global optimization technique in order to enhance the performance of these types of structures, subjected to various types of objective functions and/or constraints, with discrete and continuous design variables. The models considered are based on a higher-order displacement field and one can apply them to the static, free vibration and buckling analyses of laminated adaptive structures with arbitrary lay-ups, loading and boundary conditions. Genetic algorithms, with either binary or floating point encoding of design variables, were considered to find optimal locations of piezoelectric actuators as well as to determine the best voltages applied to them in order to obtain a desired structure shape. These models provide an overall economy of computing effort for static and vibration problems.

Placement of Multiple Piezo Patch Sensors and Actuators for a Cantilever Beam to Maximize Frequencies and Frequency Gaps

Active vibration control is implemented using multiple piezoelectric actuators and sensors bonded to the top and bottom surfaces of a cantilever beam. The control is exercised using closed-loop displacement feedback. The objective of the study is to determine the optimal locations of patch actuators and sensors such that the fundamental frequency or the frequency gap between higher frequencies of the beam is maximized. Maximizing the fundamental frequency is useful to avoid resonance when the excitation frequency is less than the fundamental frequency. Alternatively, the excitation frequency can also be placed in between two higher order frequencies and the difference between the two higher order frequencies can be maximized. In the present study the fundamental frequency and the frequency gaps between the higher order frequencies are investigated with respect to actuator and sensor locations with a view towards determining their optimal locations for largest frequency gaps. The locations of the piezo patches to maximize first, second and third frequencies are also given. The differential equation governing the vibrations of a feedback controlled beam/piezo patch system is solved using an integral equation approach. The numerical results are given for various patch combinations and the optimal locations of the actuators and the sensors are determined. It is observed that the optimal locations of the piezo patches depend on the specific frequency gap as well as the patch configurations.

Robust detection and accommodation of incipient component and actuator faults in nonlinear distributed processes

AbstractA class of nonlinear distributed processes with component and actuator faults is presented. An adaptive detection observer with a time varying threshold is proposed that provides additional robustness with respect to false declarations of faults and minimizes the fault detection time. Additionally, an adaptive diagnostic observer is proposed that is subsequently utilized in an automated control reconfiguration scheme that accommodates the component and actuator faults. An integrated optimal actuator location and fault accommodation scheme is provided in which the actuator locations are chosen in order to provide additional robustness with respect to actuator and component faults. Simulation studies of the Kuramoto‐Sivashinsky nonlinear partial differential equation are included to demonstrate the proposed fault detection and accommodation scheme. © 2008 American Institute of Chemical Engineers AIChE J, 2008

The optimal placement of actuator and sensor for active noise control of sound–structureinteraction systems

This paper presents new objective functions and a practical method for finding the optimalplacement of actuator and sensor for a sound–structure interaction system. The developedmethod for optimal actuator and sensor positioning is based on an energy-based approachand model uncertainty. The optimal actuator and sensor location obtained is used toconstruct a feedback controller using a minimax LQG control design method for reducingacoustic potential energy caused by structure-borne sound inside the acoustic cavity. Theexperimental demonstration of the novel method presented in this paper attenuatesstructural vibration up to 17 dB over the entire frequency range of interest and theassociated noise up to 10 dB without explicit knowledge of the acoustic model.

The optimal location of piezoelectric actuators and sensors for vibration control ofplates

This paper considers the optimal placement of collocated piezoelectric actuator–sensorpairs on a thin plate using a model-based linear quadratic regulator (LQR) controller. LQRperformance is taken as objective for finding the optimal location of sensor–actuator pairs. Theproblem is formulated using the finite element method (FEM) as multi-input–multi-output(MIMO) model control. The discrete optimal sensor and actuator location problem isformulated in the framework of a zero–one optimization problem. A genetic algorithm (GA)is used to solve the zero–one optimization problem. Different classical control strategieslike direct proportional feedback, constant-gain negative velocity feedback andthe LQR optimal control scheme are applied to study the control effectiveness.

Optimal placement of actuators for active vibration control of seismic excited tall buildings using a multiple start guided neighbourhood search (MSGNS) algorithm

Active control devices can be implemented on seismically excited high rise buildings using appropriate active control theory, to reduce structural responses to a desired level. Certain locations of the structure are advantageous for placement of actuators in the sense that these locations effectively reduce the structural responses. Hence, optimal placement of actuators at discrete locations is an important problem that will have significant impact on control of civil structures like high rise buildings, bridges, etc. This optimal placement problem leads to a combinatorial optimisation and is difficult to solve. This paper presents a multi-start meta-heuristic algorithm called multiple start guided neighbourhood search (MSGNS) algorithm, which makes use of the good features of guided local searches like simulated annealing (SA) and tabu search (TS). Four distinct design criteria which influence the active control design are considered in this paper to study the optimal actuator placement problem. The sensitivities of the four optimisation criteria with respect to different earthquake records are explored. Further, in this paper, we deviate from the usual practice of using shear building models (or simple lumped mass model) in active control research for finding optimal actuator locations. Instead, we use detailed finite element models and demonstrate through numerical examples their effectiveness in arriving at the optimal actuator locations. Finally, the superior performance of the proposed MSGNS algorithm over popular meta-heuristic algorithms like GA, SA and TS is demonstrated through numerical experiments.