Optimal Actuator Location Research Articles

A new optimization framework for piezoelectric actuators location identification

The study addresses piezoelectric actuator placement for active vibration control using an open-access framework that couples ANSYS and Python. It outlines a three-stage procedure: creating a finite element model in ANSYS APDL, using Python to determine the objective function, and applying a genetic algorithm optimization to find optimal actuator locations. Numerical simulations on plates and thin-walled conical structures demonstrate the effectiveness of the approach, showing it efficiently finds optimal placements with minimal search time and energy requirements. The study provides open-access codes for the framework, enhancing its accessibility and reproducibility.

Optimal Actuator Location of the Norm Optimal Controls for Degenerate Parabolic Equations

Optimal Actuator Location of the Norm Optimal Controls for Degenerate Parabolic Equations

Observability inequality of backward stochastic heat equations with Lévy process for measurable sets and its applications

This paper endeavours to directly establish the observability inequality of backward stochastic heat equations involving a Lévy process for measurable sets. As an immediate application, we attain the approximate controllability of forward stochastic heat equations featuring a Lévy process. Subsequently, we embark upon the formulation of a nuanced optimization problem, encompassing both the determination of an optimal actuator location and its associated minimum norm control. This formulation is elegantly cast as a two-person zero-sum game problem. We then proceed to articulate a set of conditions–both sufficient and necessary–required for optimizing the solution through the prism of a Nash equilibrium. At last, we prove that the relaxed optimal solution is an optimal actuator location for the classical problem.

Multi-objective optimization of active control system using population guidance and modified reference-point-based NSGA-II

The optimization of the active control system is pivotal in achieving an acceptable performance level while minimizing control costs. The optimal location of actuators, efficient control force, and adequate vibration reduction are critical objectives in control system optimization. This study introduces a novel optimization algorithm, the Population-Guided and Modified Reference-Point Based Non-Dominated Sorting Genetic Algorithm-II (PMR-NSGA-II), tailored for actuator placement and tuning that incorporates input and output user preference. The analysis focuses on optimizing the vibration control of a 20-story steel frame building. The PMR-NSGA-II could reduce the computational expenses of three objectives optimization by guiding the initial population using prospective population prediction and orienting the search towards a reference point. The pre-calculated input energy distribution guides the determination of the prospective initial population. The reference point, along with the allowable drift and actuator capacity constraints, focuses the search process to efficiently obtain the Pareto fronts with less effort wasted to explore the less preferred areas in the search space. The non-dominated sorting and elitist operators are also employed to fasten the convergence. The structural analysis is conducted via non-linear time history analysis with seven ground motions considered. The PMR-NSGA-II exhibits significant computational efficiency in the active control system optimization. Results demonstrate that PMR-NSGA-II could provide the near-optimal solution closest to the reference point with a smaller population size and a faster convergence rate than the NSGA-II. The computational time per generation of the proposed PMR-NSGA-II is 1.36 to 2.43 times faster than NSGA-II for the seven ground motions analyzed. By applying PMR-NSGA-II, the number of individuals that need to be assessed to reach convergence is reduced by 50 % to 88 % compared to NSGA-II. Ultimately, the near-optimal configurations could significantly reduce the building responses and increase the performance level of the building based on FEMA 356 and ASCE 41 acceptance criteria.

State Observing Method and Active Vibration Control Based on Virtual Sensing

State feedback is mostly used in the active vibration control of structural systems. However, the most challenging problem is to achieve the whole state of the structure. Another issue in active vibration control is that, in many cases, only some particular modes need to be controlled, while the other modes can remain unchanged in order to save on the costs of the control. To solve the above issues, this paper proposes a state-observing method and conducts a non-spillover partial pole placement control using a multistep method. Using the finite element method, the electromechanical coupling equations of motion of the beam are formulated. The reduced finite element model is then obtained by using the system equivalent reduction expansion process method. Introducing the real measurements by sensors and applying the local corresponding principle, the modes of the structural system are corrected, which are then utilized to predict all the degrees of freedom without measuring by sensors. Then, the non-spillover partial pole placement based on the state feedback is conducted using the multistep method. The optimal locations of actuators are derived by the genetic algorithm to control the specific structural modes effectively. The numerical simulations and experimental studies are also carried out.

Multi-level Optimal Control with Neural Surrogate Models

Optimal actuator and control design is studied as a multi-level optimisation problem, where the actuator design is evaluated based on the performance of the associated optimal closed loop. The evaluation of the optimal closed loop for a given actuator realisation is a computationally demanding task, for which the use of a neural network surrogate is proposed. The use of neural network surrogates to replace the lower level of the optimisation hierarchy enables the use of fast gradient-based and gradient-free consensus-based optimisation methods to determine the optimal actuator design. The effectiveness of the proposed surrogate models and optimisation methods is assessed in a test related to optimal actuator location for heat control.

Optimal Actuator Location for Diffusion Equation with Neumann Boundary Control

This paper is concerned with optimal actuator location for a class of diffusion equations with boundary control. The problem of optimal actuator location based on a linear quadratic cost in case of the worst initial condition is formulated. This leads to a cost involving the operator norm of the Riccati operator. The existence of optimal locations within the uniform operator norm is guaranteed. A Galerkin-based algorithm for approximating the optimal locations, and the convergence of the approximation of the optimal locations is also presented.

Reduction of noise in cold and hot supersonic jets using active flow control guided by a genetic algorithm

This study demonstrates an experimental platform for active jet noise reduction comprising of an automated system that performs a search for the optimal actuator locations and parameters, powered by a genetic algorithm (GA). Sideline noise reduction levels of 7.3 dB were achieved for a cold overexpanded (nozzle pressure ratio, $NPR=2.8$ ) jet, beyond the state-of-the-art for jet noise reduction with air injection. The reduction in noise was achieved at a mass flow rate of 1.4 % of the main jet, requiring no prior knowledge of the flow physics to inform the placement of the actuators. The same actuator pattern was tested in hot conditions (nozzle temperature ratio, $NTR=1.88$ ), achieving 4.7 dB sideline noise reduction. Detailed examination of the solutions obtained unveils some of the mechanisms leveraged by the GA to accomplish these high levels of noise reduction through microphone measurements and schlieren flow visualization. The GA found that actuating at the diverging wall of the convergent–divergent nozzle, where flow is supersonic, is very effective when combined with air injection near the nozzle lip, outside of the nozzle. Although the external actuation is effective at eliminating the screech tone, it is by actuating inside the nozzle at the diverging wall that sufficient disruption of the shock cell train can be achieved in order to reduce the broadband shock-associated noise.

An artificial neural network model for multi-flexoelectric actuation of Plates

ABSTRACT Flexoelectric effect can be used to design actuators to control engineering structures including beams, plates, and shells. Multiple flexoelectric actuators method has the advantage of less stress concentration and better control effect, but the mode-dependent optimal actuator locations could influence the flexoelectric actuation effect significantly. In this work, a neural network model is established to study the optimal combinations of multiple flexoelectric actuators on a rectangular plate. In the physical model, an atomic force microscope (AFM) probe was employed to generate an electric field gradient in the flexoelectric patch, so that flexoelectric control force and moment can be obtained. Multiple flexoelectric actuators on the plate was considered. Case studies showed that the flexoelectricity induced stress mainly concentrate near the probe, the size and shape of the flexoelectric patch have limited effect on the actuation, hence, only the actuator positions were choosing as the input of the ANN model. Using the prediction of the neural network model, the driving effect of a large number of actuators at different positions can be quickly obtained, and the optimal position of the actuator can be analyzed more accurately.

Microscopic control actions for distributed LaSMP patches laminated on paraboloidal thin shells

Paraboloidal shells are widely used for antennas, reflectors, optical mirrors, etc. LaSMP is a novel light-actuated shape memory polymer (LaSMP) with dynamic Young’s modulus which can act as actuators. This study focuses on the microscopic control actions and distributed control effectiveness of LaSMP patches laminated on a paraboloidal thin shell. With the light-induced strain model, the dynamic governing equations of paraboloidal structures laminated with LaSMP patches are established. Based on an assumed mode shape function for the simply-supported paraboloidal thin shell, the total control force and its contributing components resulting from bending control moments and membrane control forces in the meridional/circumferential directions are defined respectively. In case studies, distributed control actions of two kinds of paraboloidal thin shells with different geometrical parameters, i.e. deep and shallow, are evaluated. The distributed control forces, components, normalized control forces, as well as the effects of shell and LaSMP thickness are evaluated for the first three natural modes by varying laminated LaSMP patch locations in the meridional direction. The results suggest: (a) the magnitude of control actions and normalized control actions are affected by the actuation location and vibration modes; (b) the moment-induced control actions dominate the total control forces; (c) there are optimal LaSMP actuator locations on the simply-supported paraboloidal thin shell with the maximal control actions per unit area for each natural mode; and (d) the control forces increase with the increasing of LaSMP thickness and decreasing of shell thickness.

A modified fuzzy-tuned artificial bee algorithm to optimal location of piezoelectric actuators and sensors for active vibration control of isotropic rectangular plates

In this study, an efficient modified artificial bee colony algorithm is presented to find the optimal location of piezoelectric actuators and sensors for active vibration control of plates. An artificial bee algorithm is a population-based approach utilized to search for the optimal solution using swarm intelligence. There are two searching steps in the proposed algorithm, i.e., the random and the local search. These two search types present the main processes of the algorithm, known as exploration and exploitation. Making a balance between these two processes is important in obtaining the best solution. Therefore, a new technique is proposed herein to keep a balance between exploration and exploitation. In this technique, a fuzzy system is utilized as the parameter tuner in the improved artificial bee colony algorithm for providing the balance between global search and local search. Consequently, the solution of the algorithm approaches the optimal object. The presented algorithm is utilized to determine the optimal placement of piezoelectric sensors and actuators on an isotropic rectangular plate. Ensuring good observability and controllability is considered as the optimization criterion. Also, residual modes are considered to limit the spillover effect. The obtained results indicate the superiority of the proposed approach.

Software-in-the-loop optimization of actuator and sensor placement for a smart piezoelectric funnel-shaped inlet of a magnetic resonance imaging tomograph

Performance of smart piezoelectric structures strongly depends on placement of integrated piezoelectric actuators and sensors, which may be implemented in the form of thin film layers on the structure surface or embedded within the structure. In both cases actuator and sensor placement plays an important role, since after applying they remain permanently integrated with structure. In this paper the optimization procedure for piezoelectric structures with curved surfaces is proposed based on the Software-in-the-Loop (SiL) methodology and balanced modal order reduction in combination with H2 and H∞ norms used in placement indices. The optimization procedure is a global one, since it seeks for optima across the entire domain of the structure. A special challenge is tackling the problem of curved surfaces. This problem is solved in this work for a funnel shaped structure – inlet of the magnetic resonance imaging tomopraph. A thorough mesh convergence study with respect to the eigenfrequency analysis is performed in order to obtain a reliable numeric finite element model for further optimization purposes. Material parameter optimization is performed as well. Based on placement indices optimal placement study is performed under consideration of several eigenmodes of interest. The optimization is performed for individual modes as well as for simultaneous consideration of multiple modes. The SiL approach with recurrent communication in each iteration of the optimization between the numerical simulation FE software and optimization tool designed in Python is implemented through the evaluation of the placement indices for candidate locations over the entire curved surface of the structure. Depending on support conditions, optimal locations of piezoelectric actuators and sensors are proposed.

Optimal location and geometry of sensors and actuators for active vibration control of smart composite beams

ABSTRACT This work investigates the problem of optimal placement and geometry of piezoelectric sensors and actuators (S/A) to improve active vibration control performance of smart laminated beam. Theoretical formulation is based on efficient layer-wise finite element model along with an optimal control theory. Control theory is implemented in state space format considering a reduced order model. A laminated beam with collocated piezoelectric S/A placed at the top and bottom surfaces has been considered. A series of simulation based on Taguchi design of experiment has been carried out to determine the optimal placement and geometry of the S/A to achieve best control performance that is maximum modal active damping ratio /minimum settling time with minimum actuator voltage. A multi-criteria optimisation has been performed using Proximity Indexed Value (PIV) integrated with entropy methods. Further, the analysis of mean (ANOM) and analysis of variance (ANOVA) are performed to identify the most significant input parameter based on their percentage contribution. For the smart cantilever beam considered in the analysis, the location of the S/A is the most significant having maximum percentage contribution (35.69%) followed by its length (33.04%) and thickness (24.55%).

Data-driven selection of actuators for optimal control of airfoil separation

We present a systematic approach for determining the optimal actuator location for separation control from input-output response data, gathered from numerical simulations or physical experiments. The Eigensystem Realization Algorithm is used to extract state-space descriptions from the response data associated with a candidate set of actuator locations. These system realizations are then used to determine the actuator location among the set that can drive the system output to an arbitrary value with minimal control effort. The solution of the corresponding minimum energy optimal control problem is evaluated by computing the generalized output controllability Gramian. We use the method to analyze high-fidelity numerical simulation data of the lift and separation-angle responses to a pulse of localized body-force actuation from six distinct locations on the upper surface of a NACA 65(1)-412 airfoil. We find that the optimal location for controlling lift is different from the optimal location for controlling separation angle. In order to explain the physical mechanisms underlying these differences, we conduct controllability analyses of the flowfield by leveraging the dynamic mode decomposition with control algorithm. These modal analyses of flowfield response data reveal that excitation of coherent structures in the wake benefit lift control; whereas, excitation of coherent structures in the shear layer benefit separation-angle control.

Analysis of Novel Morphing Trailing Edge Flap Actuated by Multistable Laminates

This paper presents an analysis of a novel morphing trailing edge flap design for a wind turbine rotor blade with embedded multistable composite plates. Morphing trailing edge devices are promising candidates for reducing loads in variable wind conditions and turbulent flows as well as capable of changing the shape rapidly. The application of multistable laminates allows large deformations with modest actuation demand, without the need for a continuous supply of energy. They can undergo snap-through with the help of Macro Fiber Composites actuator patches. A rectangular multistable plate is designed with the optimal location of actuators, aiming at two-way snap-through without the loss of bistability. A multi-objective derivative-free optimization scheme is used to minimize the snap-through voltages and maximize the out-of-plane displacements. The designed multistable plates with actuators are embedded at a suitable location of the morphing trailing edge flap. As the multistable plates snap, the flap deflects to a new position. The mechanism of the new morphing concept is simulated and analyzed with finite element tools.

Closed-form H-infinity optimal control for a class of infinite-dimensional systems

H-infinity optimal control and estimation are addressed for a class of systems governed by partial differential equations with bounded input and output operators. Diffusion equations are an important example in this class. Explicit formulas for the optimal state feedback controller as well as the optimal state estimator are given. Unlike traditional methods for H-infinity synthesis, no iteration is needed to obtain the optimal solution. Moreover, the optimal performance for both the state feedback and state estimation problems are explicitly calculated. This is shown to be useful for problems of H-infinity optimal actuator and sensor location. Furthermore, the results can be used in testing and bench-marking of general purpose algorithms for H-infinity synthesis. The results also apply to finite-dimensional systems.

Graph-based determination of structural controllability and observability for pressure and temperature dynamics during steam-assisted gravity drainage operation

Steam assisted gravity drainage (SAGD), which is used for the in-situ extraction and recovery of oil sands bitumen, is represented by a distributed parameter system (DPS). The problem of sensor placement and the control of steam chamber growth and oil production, respectively, require analysis of the observability and controllability of the system. In this type of system, parametric sensitivity is traditionally used in lieu of observability, and controllability has not been explored rigorously. In this work, we analyze the pressure and temperature fields of a SAGD model based on detailed reservoir simulations and present a data-driven technique to assess the structural controllability and observability of the system, with a view to determine optimal locations of actuators and sensors. An agglomerative hierarchical clustering technique is used to obtain a spanning tree of the clusters which is partitioned based on an objective function to arrive at a set of spatially contiguous clusters that display similar pressure/temperature dynamics. A Granger causality measure is used to create the linkage amongst the clusters to build a digraph model of the data. The driver nodes of the graph identify locations for actuation which provide full control over the graph, and the root strongly connected components indicate sensor locations which ensure structural observability over the entire graph. We demonstrate the method using data generated from SAGD simulations using the CMG-STARS simulator, identify the sensor and actuator locations required for complete structural observability and controllability of the system, and also provide a method of assessment of partial actuation and in-sensor ranges.

Towards a generic optimal co-design of hardware architecture and control configuration for interacting subsystems

In plants consisting of multiple interacting subsystems, the decision on how to optimally select and place actuators and sensors and the accompanying question on how to control the overall plant is a challenging task. Since there is no theoretical framework describing the impact of sensor and actuator placement on performance, an optimization method exploring the possible configurations is introduced in this paper to find a trade-off between implementation cost and achievable performance.Moreover, a novel model-based procedure is presented to simultaneously co-design the optimal number, type and location of actuators and sensors and to determine the corresponding optimal control architecture and accompanying control parameters. This paper adds the optimization of the control architecture to the current state-of-the-art. As an optimization output, a Pareto front is presented, providing insights on the optimal total plant performance related to the hardware and control design implementation cost.The proposed algorithm is not focused on one particular application or a specific optimization problem, but is instead a generally applicable method and can be applied to a wide range of applications (e.g., mechatronic, electrical, thermal). In this paper, the co-design approach is validated on a mechanical setup.

Active vibration control of smart composite plates using optimized self-tuning fuzzy logic controller with optimization of placement, sizing and orientation of PFRC actuators

This paper deals with optimization of the sizing, location and orientation of the piezo-fiber reinforced composite (PFRC) actuators and active vibration control of the smart composite plates using particle-swarm optimized self-tuning fuzzy logic controller. The optimization criteria for optimal sizing, location and orientation of the PFRC actuators is based on the Gramian controllability matrix and the optimization process is performed by involving the limitation of the plates masses increase. Optimal configurations of five PFRC actuators for active vibration control of the first six modes of cantilever symmetric ((90°/0°/90°/0°)S), antisymmetric cross-ply ((90°/0°/90°/0°/90°/0°/90°/0°)) and antisymmetric angle-ply ((45°/-45°/45°/-45°/45°/-45°/45°/-45°)) composite plates are found using the particle swarm optimization. The detailed analysis of influences of the PFRC layer orientation and position (top or bottom side of composite plates), as well as bending-extension coupling of antisymmetric laminates on controllabilities is also performed. The experimental study is performed in order to validate this behavior on controllabilities of antisymmetric laminates. The particle swarm-optimized self-tuning fuzzy logic controller (FLC) adapted for the multiple-input multiple-output (MIMO) control is implemented for active vibration suppression of the plates. The membership functions as well as output matrices are optimized using the particle swarm optimization. The Mamdani and the zero-order Takagi–Sugeno–Kang fuzzy inference methods are employed and their performances are examined and compared. In order to represent the efficiency of the proposed controller, results obtained using the proposed particle swarm optimized self-tuning FLC are compared with the corresponding results in the case of the linear quadratic regulator (LQR) optimal control strategy.

Optimal Actuator Design for Nonlinear Partial Differential Equations

Abstract For systems modeled by partial differential equations, the location and shape of the actuators can be regarded as a design variable and included as part of the controller synthesis procedure. Optimal actuator location is a special case of optimal design. For linear partial differential equations (PDEs), the existence of an optimal actuator location for a number of cost functions has been established. However, many dynamics are affected by nonlinearities and linearization of the PDE can neglect some important aspects of the model. This paper describes recent results establishing conditions for existence of optimal actuator design and control for important classes of nonlinear PDEs.