Problem Of Actuator Placement Research Articles

Optimal actuator placement for control of vibrations induced by pedestrian-bridge interactions

In this paper, an optimal actuator placement problem, with a linear wave equation as the constraint, is considered. In particular, this work presents the framework for finding the best location of actuators depending upon the given initial conditions, and where the dependence on the initial conditions is averaged out. The problem is motivated by the need to control vibrations induced by pedestrian-bridge interactions. An approach based on the shape optimization techniques is used to solve the problem. Specifically, the shape sensitivities involving a cost functional are determined using the averaged adjoint approach. A numerical algorithm based on these sensitivities is used as a solution strategy. Numerical tests illustrate the theoretical results.

Optimal actuator placement in adaptive optics systems

Adaptive optics systems are powerful tools that are implemented to degrade the effects of wavefront aberrations. In this article, the optimal actuator placement problem is addressed for the improvement of disturbance attenuation capability of adaptive optics systems due to the fact that actuator placement is directly related to the enhancement of system performance. For this purpose, the linear-quadratic cost function is chosen, so that optimized actuator layouts can be specialized according to the type of wavefront aberrations. It is then considered as a convex optimization problem, and the cost function is formulated for the disturbance attenuation case. The success of the presented method is demonstrated by simulation results.

Joint Sensor and Actuator Placement for Infinite-Horizon LQG Control

We consider the problem of sensor and actuator (SaA) placement to minimize an infinite-horizon linear quadratic Gaussian (LQG) cost for a discrete-time Gauss–Markov system. Due to financial, topology, and bandwidth limitations, only a subset of SaAs can be selected for placement. Different from existing literature, which successively iterates partial selection to reach a suboptimal solution, this article focuses on a joint placement and encounters fundamental difficulty in the sense that joint SaA placement introduces a term in the LQG cost that is difficult to be convexified. A branch-and-bound algorithm is introduced to search for solutions to an approximate problem obtained by relaxing the Boolean constraints. By deriving a compact search space where any optimal solution belongs to or resides, we derive lower and upper bounds to the optimal solution in each subregion of the search space, and subsequently refine the search space. A suboptimal solution to the original problem is obtained from integer rounding and the optimality gap is further analyzed. Numerical examples are provided to illustrate the effectiveness of the proposed algorithm. This algorithm has significant reduction of iteration numbers compared with the brute-force enumeration especially when the number of states is not large but the number of placement choices is large. In addition, an improvement of LQG cost is obtained compared with the successively iterating partial selection methods, a canonical algorithm for SaA placement in the literature.

Actuator Placement for Symmetric Structural Controllability With Heterogeneous Costs

In this letter, we consider the problem of optimal actuator placement for networked linear time-invariant systems with underlying undirected topologies. We aim to leverage the undirected topology for the design of an actuator deployment strategy that guarantees symmetric structural controllability , i.e., generic controllability of the system subject to symmetric weights. Naturally, the objective is to make this design as cost effective and computationally efficient as possible. Therefore, we focus on two related (yet different) problems: 1) to determine the subset of state nodes that need to be actuated to ensure symmetric structural controllability at the lowest cost incurred by the actuators and 2) given a symmetrically structurally controllable system (whose input nodes may actuate on more than one state node), to determine a subset of its input nodes that still ensure symmetric structural controllability, at the lowest possible cost. We show that both problems can be solved in polynomial time by implicitly providing an efficient algorithm that determines their solutions. Several numerical experiments are provided to illustrate our main results.

Distributed Actuator Selection: Achieving Optimality via a Primal-Dual Algorithm

This letter addresses the actuator selection problem, i.e., given an interconnection of asymptotically stable linear dynamical systems on a network and m possible actuators choose ν among them to achieve a certain objective. In general, this is a combinatorial optimization problem which is hard to solve; convex relaxations do not usually yield an optimal solution for the original problem. In this letter we focus on a particular instance of the actuator selection problem, namely the formulation with the trace of the controllability Gramian matrix as the optimization metric, and show that such a choice gives rise to an integer linear program (LP). Using properties of integral polyhedra, we show through a sequence of reformulations that the optimal solution of this problem can be determined by means of an LP without introducing any relaxation gap. This allows us to obtain the optimal solution using a primal-dual distributed algorithm, thus providing a scalable approach to the problem of actuator placement which has been up to now performed in a centralized manner enumerating all possible placement alternatives. We illustrate the main features of our approach by means of a case study involving a simplified model of the European power grid.

Optimal sensors and actuators placement for large-scale switched systems

The problem of sensor and actuator placement is computationally expensive in particular in dealing with large-scale systems. This problem is even more computationally intensive in the case of switched systems. In this paper, we propose a new numerical approach for sensor and actuator placement for large-scale switched systems. We first introduce restricted genetic algorithm (RGA). RGA is an evolutionary algorithm which is developed specifically for sensors and actuator placement. We then use RGA to reduce the computational burden of the sensor and actuator placement for switched system. The proposed method uses the generalized gramians for switched systems which are called nice gramians. The nice gramians quantify the level of observability and reachability of switched systems. To the best of our knowledge, this paper presents the first results on sensor and actuator placement of switched systems. We show the effectiveness of the approach with the help of numerical examples.

Minimal Actuator Placement With Bounds on Control Effort

We address the problem of minimal actuator placement in linear systems so that the volume of the set of states reachable with one unit or less of input energy is lower bounded by a desired value. First, following the recent work of Olshevsky, we prove that this is NP-hard. Then, we provide an efficient algorithm which, for a given range of problem parameters, approximates up to a multiplicative factor of O(logn), n being the network size, any optimal actuator set that meets the same energy criteria; this is the best approximation factor one can achieve in polynomial time, in the worst case. Moreover, the algorithm uses a perturbed version of the involved control energy metric, which we prove to be supermodular. Next, we focus on the related problem of cardinality-constrained actuator placement for minimum control effort, where the optimal actuator set is selected to maximize the volume of the set of states reachable with one unit or less of input energy. While this is also an NP-hard problem, we use our proposed algorithm to efficiently approximate its solutions as well.

On Submodularity and Controllability in Complex Dynamical Networks

Controllability and observability have long been recognized as fundamental structural properties of dynamical systems, but have recently seen renewed interest in the context of large, complex networks of dynamical systems. A basic problem is sensor and actuator placement: choose a subset from a finite set of possible placements to optimize some real-valued controllability and observability metrics of the network. Surprisingly little is known about the structure of such combinatorial optimization problems. In this paper, we show that several important classes of metrics based on the controllability and observability Gramians have a strong structural property that allows for either efficient global optimization or an approximation guarantee by using a simple greedy heuristic for their maximization. In particular, the mapping from possible placements to several scalar functions of the associated Gramian is either a modular or submodular set function. The results are illustrated on randomly generated systems and on a problem of power electronic actuator placement in a model of the European power grid.

Optimal arrangement of actuators for square mirrors with free edges

It has been shown that the problem of optimal actuator placement for adaptive square mirrors can be reduced to the analytical solution using elements of the theory of unbiased designs for the natural vibrations of a square plate with free edges. A stochastic model for the wavefront has been developed using regression analysis. Formulas are given for calculating the bias in working-out the desired optical surface geometry of an adaptive mirror.

Actuator placement optimization for adaptive trusses using a two-level multipoint approximation method

Parameters in adaptive trusses considering placements of actuators, control gains as well as structure cross-sectional sizes, have been simultaneously optimized to suppress vibrations and to maintain stringent shape specifications. Since the placements of actuators are treated as (0,1) variables but the control gains and structural member sizes are continuous, the studied problem then becomes mixed (0,1)-continuous optimization, which is difficult to be tackled with conventional optimization methods since they are often encountered with local optimal solutions or numerous computational costs. A two-level multipoint approximation strategy combined with genetic algorithm, which proved to be applicable in truss topology-size optimizations involving discrete-continuous design variables, has been developed to address the current actuator placement problem. To enhance the efficiency of this method, a branched multi-point approximation function was introduced to construct the first-level approximation problem. Besides, a new fitness function as well as adaptive crossover and mutation operators were adopted to prevent the optimization process from too early converging to local optimal solutions. Numerical results were presented to illustrate the efficacy of this strategy in dealing with actuator placement problems.

A novel approach toward actuator placement for cylindrical shells undergoing axisymmetric buckling

Buckling control of space structures using piezoelectric actuators is an emerging area of research. In particular, cylindrical shells present several challenges as they exhibit multiple buckling modes. This work focuses on placement of ring actuators on cylindrical shells exhibiting axisymmetric buckling. A new method based on the characteristic wavelength of the cylindrical shell is proposed for actuator placement. It is shown by means of numerical studies that passive control of these shells shows a distinct advantage over the conventional actuator placement. It is possible to obtain a stiffer load– axial shortening response as well as a peak load enhancement of the shell using the present approach. The results obtained give important insights into the actuator placement problem for cylindrical shells undergoing axisymmetric buckling.

Optimum placement of actuators in structural and control design using Stackelberg games

Actuator placement has a significant impact on the dynamic response of actively controlled structures. Misplaced actuators and sensors often lead to controllability and observability problems, and the desired system performance may not be achieved with any choice of control law. This paper addresses the design of actively controlled structures wherein both the actuator placement and controller design aspects are addressed simultaneously. It is assumed that a hierarchical structure exists between the actuator placement and controller design objective functions with the actuator placement problem considered as being more important. The resulting multiobjective design problem is solved as a bi-level Stackelberg game. A computational procedure based on variable updating using response surface methods is developed for exchanging information between the two levels (leader and follower). The optimization problem has mixed discrete-continuous variables with discrete variables corresponding to actuator placement and continuous variables associated with the controller design problem. The solution approach includes a blend of genetic algorithms and sequential quadratic programming techniques and is applied to the design of a flexible truss structure. The proposed approach successfully designed an optimum controller while minimizing the weight of the structure and simultaneously maximizing the energy dissipated by the controller to bring the structure to its equilibrium position when subjected to an external disturbance.

Optimal actuator and sensor placement based on balanced reduced models

In this paper, we have considered the problem of optimal actuator and sensor placement for active large flexible structures and proposed a placement optimization method, which is based on balanced reduced models. It overcomes disadvantages arising from demanding numeric procedures related with high order structural models. Optimization procedure relies on H2 and H∞ norms, as well as on controllability and observability Gramians, which are related to structural eigenmodes of interest. Suggested methods for calculating approximate norms are advantageous due to their feasibility with large structures, where exact calculation of norms would cause numeric problems. A rule for determining optimal actuator/sensor placement in relation with actuation load modeling has been derived and proven by examples. The optimization procedure was documented by several examples showing a good agreement between the results obtained using different placement indices.

Actuator and sensor placement in linear advection PDE with building system application

We study the problem of actuator and sensor placement in a linear advection partial differential equation (PDE). The problem is motivated by its application to actuator and sensor placement in building systems for the control and detection of a scalar quantity such as temperature and contaminants. We propose a gramian based approach to the problem of actuator and sensor placement. The special structure of the advection PDE is exploited to provide an explicit formula for the controllability and observability gramian in the form of a multiplication operator. The explicit formula for the gramian, as a function of actuator and sensor location, is used to provide test criteria for the suitability of a given sensor and actuator location. Furthermore, the solution obtained using gramian based criteria is interpreted in terms of the flow of the advective vector field. In particular, the almost everywhere stability property of the advective vector field is shown to play a crucial role in deciding the location of actuators and sensors. Simulation results are performed to support the main results of this paper.

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.

Optimal actuator placement for controlling concentration profiles via process tomography

In this article, the optimal control of a chemical plant driven by an inverse problem is considered. More specifically, the problem of optimal actuator placement when controlling the concentration of a target substance in rapidly moving fluid is investigated. In this example, the actuators are injectors through which strong concentrate is injected into the fluid in order to obtain a desired concentration profile. The target substance is assumed to obey the stochastic convection-diffusion model and the process is monitored with electrical impedance tomography, the inverse problem of which is notoriously ill-posed even under stationary conditions. The associated reconstruction problem is formulated as a state estimation problem and is intertwined with the determination of the optimal time-varying controls. The model-based linear quadratic Gaussian control strategy is used in the determination of the control inputs. The controller settings affect both the overall controller capabilities per se and the performance of the controller via the embedded state estimation procedure. Although it is obvious that proper actuator setting can have a major impact on the control performance of the system, the optimisation has seldom been carried out over the entire controller chain which includes also the state estimation procedure. When the observation modality exhibits ill-posed characteristics, the state estimates may be rendered useless and the controls far from optimal. The studied case shows that the actuator setting affects the state estimation accuracy and the controller quality significantly.

A bell-curve based algorithm for mixed continuous and discrete structural optimization

An evolutionary based strategy utilizing two normal distributions to generate children is developed to solve mixed integer nonlinear programming problems. This Bell-Curve Based (BCB) evolutionary algorithm is similar in spirit to (μ+μ) evolutionary strategies and evolutionary programs but with fewer parameters to adjust and no mechanism for self adaptation. First, a new version of BCB to solve purely discrete optimization problems is described and its performance tested against a tabu search code for an actuator placement problem. Next, the performance of a combined version of discrete and continuous BCB is tested on two-dimensional shape problems and on a minimum weight hub design problem. In the latter case the discrete portion is the choice of the underlying beam shape (I, triangular, circular, rectangular, or U).

Optimal actuator placement for large scale systems: A reduced-order modelling approach

A recently developed, extended balanced realization, reduced order modelling technique for large-scale distributed systems is applied to the problem of optimal actuator placement for hyperthermia treatments. Extended balanced realization develops low-order models whose state reconstructions are robust to actuator and sensor placement changes, and hence can be effectively used to find optimal placements in a computationally efficient manner. This optimization approach has been tested on simulations of a scanned focused, ultrasound hyperthermia system and found to be robust and accurate over a wide range of models, and the savings in computational costs were found to be significant.

Combining genetic and deterministic algorithms for locating actuators on space structures

Genetic algorithms are a powerful tool for the solution of combinatorial problems such as the actuator placement problem. However, these algorithms require a large number of analyses with the attendant high computational costs. Therefore, it is useful to tune the operators and parameters of the algorithm on problems with inexpensive analyses that are similar to computationally more expensive problems. An easy-to-calculate measure of actuator effectiveness is employed to evaluate several genetic algorithms for a problem of placing actuators at 8 of 1507 possible locations. Even with the best of the algorithms and with optimum mutation rates, tens of thousands of analyses are required for obtaining near-optimum locations. A hybrid procedure is proposed that first estimates near-optimum locations with a deterministic algorithm and then seeds these locations in the initial population of a genetic algorithm. A simulated annealing technique is also applied as a mutation operator for the genetic algorithm. The hybrid procedure reduces the cost of the genetic optimization by an order of magnitude.

Placing actuators on space structures by genetic algorithms and effectiveness indices

Genetic algorithms are a powerful tool for the solution of combinatorial problems such as the actuator placement problem. However, they require a large number of analyses with correspondingly high computational costs. Therefore, it is useful to tune the operators and parameters of the algorithm on simple problems that are similar to more complex and computationally expensive problems. The present paper employs an easy-tocalculate measure of actuator effectiveness to evaluate several genetic algorithms. Additionally, the effects of population size and mutation rates are also investigated for a problem of placing actuators at 8 of 1507 possible locations. We find that even with the best of the algorithms and with optimum mutation rates, tens of thousands of analyses are required for obtaining near optimum locations. We propose a procedure that estimates the effectiveness of the various locations and discards ineffective ones, and find it helpful for reducing the cost of the genetic optimization.