Optimal Placement Of Actuators Research Articles

Security‐aware optimal actuator placement in vehicle platooning

AbstractVehicle platooning, as a large class of cyber‐physical systems, is prone to be under the risk of cyber attacks. One (or more) external intelligent intruder(s) might attack one (or more) of the vehicles participating in a platoon. This paper proposes a general approach to find an optimal actuator placement strategy according to the Stackelberg game between the attacker and the defender. The game payoff is the energy needed by the attacker to steer the consensus follower–leader dynamics of the system towards his desired direction. The attacker tries to minimize this energy while the defender attempts to maximize it. Thus, based on the defined game and its optimal equilibrium point, the defender(s) selects optimal actuator placement action to face the attacker(s). Both cases of single attacker–single defender and multiple attackers–multiple defenders cases are investigated. Furthermore, we study the effects of different information flow topologies, namely, the unidirectional and bidirectional data transfer structures. Besides, the impacts of increasing the connectivity among the nodes on the security level of the platoon are presented. Simulation results for h–nearest neighbor platoon formations along with experimental results using the scaled cars governed by robotic operating system (ROS) verify the effectiveness of the method.

Optimal Hardware and Control Co-Design Applied to an Active Car Suspension Setup

For complex systems, it is not easy to obtain optimal designs for the hardware architecture and control configurations. Every design aspect influences the final performance, and often the interactions of the different components cannot be clearly determined in advance. In this work, a novel co-design optimization method was applied that allows the optimal placement and selection of actuators and sensors to be performed simultaneously with the determination of the control architecture and associated controller tuning parameters. This novel co-design method was applied to a state-space model of a downscaled active car suspension laboratory setup. This setup mimics a car driving over a specific road surface while active components in the suspension have to increase the driver’s comfort by counteracting unwanted vibrations. The result of this co-design optimization methodology is a Pareto front that graphically represents the trade-off between the maximum performance and the total implementation cost; the co-design results were validated with measurements of the physical active car suspension setup. The obtained controller tuning parameters are compared herein with existing controller tuning methods to demonstrate that the co-design method is able to determine optimal controller tuning parameters.

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.

Optimal Placement of Multi Actuators in Active Control of Building Frames

The optimal placement of the actuator for obtaining the best possible reduction in responses was a topic of interest for researchers. Many optimization techniques were used for obtaining the optimal reduction in responses. Placement of more than three actuators in building frame in practice is difficult and cumbersome. As a result, number of actuators to be placed in the frame is generally restricted as three. For optimization problem, involving three actuators, many computational problems are involved, namely, numerical stability, convergence of the solution, possibility of dynamic instability and in some cases, amplification of some response quantities. The above problems are generally encountered in many standard optimization techniques which are used for optimization. Further, some constraints may have to be imposed in the algorithm for floors where actuators cannot be placed for practical reasons. Under such circumstances, optimal placement of actuator is best achieved using the trial or iterative method.

Investigation of influence of compact actuators on air cavity in water flow under recessed hull

Air cavity drag reduction is one promising method for reducing power consumption of ships. Its current practical applications are rather limited, owing largely to the fact that air cavity size and shape change drastically in response to variations in ship attitude, motions and speed, as well as sea conditions. This study explores how deployment of moveable hydrodynamic actuators near the air cavity on a small-scale simplified hull form can effectively increase the air cavity size in adverse hull positions. Experimentally investigated actuators included an adjustable plate in the front part of an air cavity, a stern spoiler, and a hydrofoil with regulated attack angle and streamwise position beneath the hull. In the cases of significant hull trims that are challenging for maintenance of long air cavities, optimal actuator placement increased cavity length by nearly 110% from its degraded state at negative trim and by 24% at positive trim. Actuator effects were more pronounced at higher water speeds.

Quantification of the redundancy distribution in truss and beam structures

The degree of statical indeterminacy as a fundamental property in structural mechanics is today mainly known as a property of a complete system without any information about its spatial distribution. The redundancy matrix provides information about the distribution of statical indeterminacy in the system and by this gives an additional valuable insight into the load-bearing behaviour. The derivation and definition of the redundancy matrix are presented based on truss systems and its mathematical properties and their mechanical interpretations are provided. The definition of the redundancy matrix is extended to other discrete systems like beam structures and a definition of the redundancy density is given for the continuous 1D case. Potential applications of the concept include robust design of structures, quantification of imperfection sensitivity as well as assessment of optimal actuator placement in adaptive structures.

Force and Shape Control Strategies for Minimum Energy Adaptive Structures

This work presents force and shape control strategies for adaptive structures subjected to quasi-static loading. The adaptive structures are designed using an integrated structure-control optimization method developed in previous work, which produces minimum ‘whole-life energy’ configurations through element sizing and actuator placement optimization. The whole-life energy consists of an embodied part in the material and an operational part for structural adaptation during service. Depending on the layout, actuators are placed in series with the structural elements (internal) and/or at the supports (external). The effect of actuation is to modify the element forces and node positions through length changes of the internal actuators and/or displacements of the active supports. Through active control, the stress is homogenized and the displacements are kept within required limits so that the design is not governed by peak demands. Actuation has been modelled as a controlled non-elastic strain distribution, here referred to as eigenstrain. Any eigenstrain can be decomposed into two parts: an impotent eigenstrain only causes a change of geometry without altering element forces while a nilpotent eigenstrain modify element forces without causing displacements. Four control strategies are formulated: (C1) force and shape control to obtain prescribed changes of forces and node positions; (C2) shape control through impotent eigenstrain when only displacement compensation is required without affecting the forces; (C3) force control through nilpotent eigenstrain when displacement compensation is not required and (C4) force and shape control through operational energy minimization. Closed-form solutions to decouple force and shape control through nilpotent and impotent eigenstrain are given. Simulations on a slender high-rise structure and an arch bridge are carried out to benchmark accuracy and energy requirements for each control strategy and for different actuator configurations that include active elements, active supports and a combination of both.

Using Influence Matrices as a Design and Analysis Tool for Adaptive Truss and Beam Structures

Due to the already high and still increasing resource consumption of the building industry, the imminent scarcity of certain building materials and the occurring climate change, new resource- and emission-efficient building technologies need to be developed. Especially since these effects are further amplified by the growth of population. One proposed technology is that of adaptive load bearing structures. Integrating sensors, actuators and a control unit into the structure enables the structure to react to external loads, when needed. For example, when high but rare loads occur. The goal of the adaptation could be the reduction of deflections or the homogenization of stresses. This allows for ultra-lightweight structures with reduced material consumption and emissions. The two main questions of adaptive truss and beam structures are, first, the question of optimal actuator placement and second, which type of typology (truss, frame, etc.) is most effective for adaptive load bearing structures. One approach for finding the optimal configuration is that of so called influence matrices. Influence matrices, as introduced in this paper, are a type of sensitivity matrix, which describe how and to which extend various properties of a given load bearing structure can be influenced by different types of actuation principles. The method of influence matrices is exemplified by a series of studies on different configurations of a truss structure.

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%).

Optimal sensor and actuator placement for structural health monitoring via an efficient convex cost-benefit optimization

The number and position of sensors and actuators are key decision variables that dictate the performance of any structural health monitoring system. This paper proposes choosing them optimally by using an objective function that combines a measure of parameter uncertainty, the expected information entropy, along with the cost of both sensors and actuators. The resulting optimization problem over discrete decision variables is computationally challenging, but here it is convexified by relaxing them into continuous variables, thus obtaining a significant reduction of the computational cost. The proposed approach is applied to ultrasonic guided-wave based inspection and is illustrated using two case studies with arbitrary geometries and different materials. The results demonstrate the high efficiency and accuracy of the convex optimization in trading-off uncertainty and cost in order to provide optimal sensor configurations in complex structures. As a key contribution, the proposed methodology allows us to include the actuators with the sensors in the optimization problem while still maintaining the efficiency of the minimization process. In the application to ultrasonic guided-waves, the optimal configurations lead to set-ups where the sensors and actuators are coincident in number and position.

Controllability and actuator placement optimization for active damping of a thin rotating ring with piezo-patch transducers

A study on optimal actuator placement for controlling flexural vibration of a thin rotating ring is reported. Piezoelectric patch actuators and sensors may be applied with feedback control to provide active damping of structural vibration involving circumferential travelling waves. To determine the optimum patch positions, a model-based cost function is defined involving a time-weighted controllability Gramian, with balanced model realization for combined treatment of sensors and actuators in collocated pairs. Analytical and numerical results indicate that, without rotation, at least two actuator/sensor pairs are required to achieve controllability of any given set of natural vibration modes. Also, the optimal angular separation varies with rotational speed due to the combined influence of initial damping and Coriolis forces on the vibratory dynamics. To obtain a practical solution, a finite range of speeds is considered within a mini-max optimization criterion for the placement problem. Experiments have been conducted on a thin steel ring where a synthetic proof-mass-damper control law was used to suppress vibration involving the six lowest frequency vibration modes (with natural frequencies of 161, 442 and 846 Hz without rotation). The results show that, although a single actuator-sensor pair can achieve improved damping at high rotational speeds, the optimized configuration of two pairs provides effective damping over the full range of operating speeds.

Optimal position of piezoelectric actuators for active vibration reduction of beams

Abstract This paper investigates the optimal placement of piezoelectric actuators for the active vibration attenuation of beams. The governing equation of the beam is achieved by coupled first order shear deformation theory with two node element. The velocity feedback controller is designed and used to calculate the feedback gain and then apply to the beam. In order to search for the optimal placement of the piezoelectric actuators, a new optimization criterion is considered based on the use of genetic algorithm to reduce the displacement output of the beam. The proposed optimization technique has been tested for two boundary conditions configurations; clamped -free and clamped-clamped beam. Numerical examples have been provided to analyze the effectiveness of the proposed technic.

Robust controllability assessment and optimal actuator placement in dynamic networks

This paper presents a new framework for the optimal placement of actuators in uncertain dynamic networks. The objective is to select a subset of nodes from a set of potential actuator placements, such that the controllability of the network with norm-bounded perturbation is preserved over the entire uncertain region. Evaluation of robust controllability is known to be computationally intractable. The recent results of Babazadeh and Nobakhti (2016) are utilized to establish equivalent conditions for robust controllability of uncertain networks. It is shown that for a large class of dynamic systems, including undirected networks, the exact distance to uncontrollability is evaluated by solving a convex program. Properties of positive-definite polynomial matrices and duality theory facilitate formation of a non-convex optimization problem with linear matrix inequalities whose solution is the exact distance to uncontrollability for a general uncertain network. The underlying optimization averts the difficulty of gridding over the complex plane. A customized optimization algorithm is outlined to solve the equivalent non-convex problem whose solution is ensured to be a stationary point of the original problem. The method is further utilized to address the optimal placement of actuators by maximizing the network robust controllability index and simultaneously regularizing the number of actuators in the network graph. The proposed framework is implemented efficiently using convex optimization solvers and offers a fast and reliable tool for the assessment of robust controllability and optimal selection of control nodes. Analogous results can be established for robust observability and optimal sensor placement.

Probabilistic State Transfer, Estimation and Measures for Optimal Actuator/Sensor Placement for Linear Systems With Packet Dropouts

We consider linear systems subject to packet dropouts and obtain necessary and sufficient conditions for an arbitrary state transfer and state estimation over a finite time instance $T$. The data loss signal is modeled using the Bernoulli random variable. We leverage properties of the Hadamard product in our approach and use the derived necessary and sufficient conditions to compute the probability that an arbitrary state transfer is possible at a specified time instant. Similarly, the probability of finding an exact state estimate is found using the observability counterparts of the results. Using the necessary and sufficient conditions obtained for the invertibility of the Gramian, we give new probabilistic measures for optimal actuator and sensor placement problems and obtain optimal/sub-optimal solutions. We demonstrate by an example how the probabilities of packet dropouts influence the choice of an optimal actuator. We also discuss how to implement feedback laws and the LQR problem for these models involving packet dropouts.

Optimal Placement of Actuators Via Sparse Learning for Composite Fuselage Shape Control

Shape control is a critical task in the composite fuselage assembly process due to the dimensional variabilities of incoming fuselages. To realize fuselage shape adjustment, actuators are used to pull or push several points on a fuselage. Given a fixed number of actuators, the locations of actuators on a fuselage will impact on the effectiveness of shape control. Thus, it is important to determine the optimal placement of actuators in the fuselage shape control problem. In current practice, the actuators are placed with equal distance along the edge of a fuselage without considering its incoming dimensional shape. Such practice has two limitations: (1) it is non-optimal and (2) larger actuator forces may be applied for some locations than needed. This paper proposes an optimal actuator placement methodology for efficient composite fuselage shape control by developing a sparse learning model and corresponding parameter estimation algorithm. The case study shows that our proposed method achieves the optimal actuator placement for shape adjustments of the composite fuselage.

Optimum actuator placement for damping of vibrations using the Prestress-Accumulation Release control approach

This paper proposes a quantitative criterion for optimization of actuator placement for the Prestress–Accumulation Release (PAR) strategy of mitigation of vibrations. The PAR strategy is a recently developed semi-active control approach that relies on controlled redistribution of vibration energy into high-order modes, which are high-frequency and thus effectively dissipated by means of the natural mechanisms of material damping. The energy transfer is achieved by a controlled temporary removal of selected structural constraints. This paper considers a short-time decoupling of rotational degrees of freedom in a frame node so that the bending moments temporarily cease to be transferred between the involved beams. We propose and test a quantitative criterion for placement of such actuators. The criterion is based on local modal strain energy that can be released into high-order modes. The numerical time complexity is linear with respect to the number of actuators and potential placements, which facilitates quick analysis in case of large structures.

Neural Network-Based Adaptive Sliding Mode Control for Gyroelastic Body

Gyroelastic body refers to a flexible structure with a cluster of angular momentum devices. The torques exerted by the angular momentum devices can be used for active vibration suppression. This paper addresses the vibration suppression of gyroelastic body in the presence of uncertainties and external disturbances. Considering that the modal variables of the gyroelastic body cannot be measured directly. Therefore, a neural network (NN) based adaptive modal observer is designed to estimate the modal information of the gyroelastic body. Based on the modal observer, a NN-based adaptive sliding mode output feedback controller (NNASMOFC) is designed. The stabilities of the NN-based modal observer and the NNASMOFC are proved using Lyapunov theory. The possible spillover problem is considered by optimal actuator placement. Simulation results demonstrate the effectiveness of the proposed controller and observer.

Static Shape Adjustment and Actuator Layered Optimization for Planar Phased Array Satellite Antenna

Shape accuracy is of great importance in space antennas, especially in large-scale planar phased array antenna. To maintain the performance of the planar phased array antenna, shape accuracy must be strictly controlled. This paper proposes an optimization method using diagonal cables as actuators to achieve the shape adjustment. As for shape control, actuator placement has a significant impact on the controlled shape accuracy. Misplaced actuators always lead to control problems, and the desired performance may not be achieved with any choice of control forces, so the actuator placement optimization is needed. The optimization problem is challenging because of the mixed discrete–continuous nature of design variables: the actuator placement corresponds to discrete variables and the control forces are continuous variables. A layered optimization method is proposed in this paper to solve the optimal actuator placement and the corresponding control forces. A genetic algorithm is applied in the outside layer to achieve the optimization of the actuator placement, and the quadratic programming method is used in the inside layer to get the corresponding optimal control forces. The proposed layered optimization method is successfully applied to the large-scale planar phased array antenna. Using this method, the influence of the number of actuators on the controlled shape accuracy is also studied.

Optimal Actuator Placement and Static Load Compensation for Euler-Bernoulli Beams with Spatially Distributed Inputs

Adaptive structures in civil engineering are based on active structural elements. In this paper, an active beam element is considered with potentially multiple fluidic inputs spatially distributed over the beam’s length. It is modeled by a one-dimensional beam equation. The inputs are realized as torque inputs, where the torque is proportional to the pressure of the fluid. A method to calculate the optimal input values analytically depending on a given static load case is presented in the first part of the paper. In the second part, by generalizing the static load using a sufficient number of discrete loads evenly distributed along the beam, optimal actuator positions can be calculated for a given number of actuators. The cost function is based on extending the idea of the Gramian compensability matrix to systems governed by spatially distributed ordinary differential equations. Since the number of actuators can be a design variable, this yields a Pareto front supporting the user in selecting an appropriate number. A fluidic actuator serves as example to illustrate the potential of the proposed placement algorithm.

An optimality criteria-based method for the simultaneous optimization of the structural design and placement of piezoelectric actuators

This work provides an optimality criteria-based method for the simultaneous optimization of the structural design and optimal placement of piezoelectric actuators for statically loaded structures. The goal of the topology optimization is to find the optimal distribution of the structural and piezoelectric materials in the compliance minimization context with a volume constraint for each material. All expressions used in the implementation of the resulting algorithm are developed in detail. Some numerical complications inherent to the type of problem we are dealing with are discussed and a numerical procedure is proposed for each one. Results are shown for two-dimensional beams through four numerical examples.