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In the monitoring of structural systems, the use of multiple high end sensors may prove to be economically prohibitive. The alternative approach would be to use fewer devices that move across the span of the structural system. In the proposed approach, the dynamic of a one-dimensional system is evaluated using a velocity sensor that is able to move across the domain and obtains pointwise velocity measurements at the desired locations. Based on the measured velocities, a state estimator is developed. The gain of the filter depends on the motion of the sensor. The motion of the sensor is defined using Lyapunov redesign methods and depends only on the estimation error at the current sensor position. The guidance policy is performance-based and steers the sensor to spatial regions of the structure with larger estimation errors. The proposed approach is validated with a one dimensional flexible structure, described by an Euler-Bernoulli partial differential equation. The moving sensor is simulated with the use of a laser scanning vibrometer, that provides both the moving measurements and additional measurements against which the proposed approach will be validated. Once a large number of locations is measured, the experimental results are fed to the algorithm that selects the instantaneous sensor location. Experimental results for a linear cantilever are presented that show the benefit of using a state estimator with a moving sensor. Analysis on how the state observer gains are optimally chosen will also be presented. The approach is demonstrated to be feasible and robust.

We consider the problem of monitoring and scheduling a network of intelligent sensors and actuators in large flexible structures. A hybrid controller that activates a subset of the devices in the sensor and actuator network is proposed and whose objective is to effectively address the effects of spatiotemporally varying disturbances. It is assumed that the flexible structure is subjected to disturbances and the intelligent control policy attempts to activate the actuators that, over the duration of a time interval, have spatial authority against the spatiotemporally varying disturbances. The hybrid controller switches the relevant actuators on and deactivates the ones that are not used over a given time interval. The basic idea behind the proposed supervisory scheme is to show that using a switched controller, it is possible to simultaneously improve controller performance and reduce the power consumption in the actuator/sensor network. Both analytical and experimental results on a flexible aluminum plate with eight pairs of collocated actuator/sensor PZT pairs are presented.

In this work, we revisit the problem of actuator placement within the context of spatial robustness. When oneoptimizes location-parameterized H 2 or H closed loop measures, arrives at actuator locations that provideperformance optimality. However, these measures assume an a priori given distribution of disturbances. Whenthe above measures include an additional optimization stage whereby one searches for the worst distribution ofdisturbances, then the resulting actuator location will result in both an improved performance and enhancedspatial robustness. Using an analytical bound approach that provides an explicit expression for an upper boundon the H norm of the system transfer function, the worst distribution of disturbances can be found thatmaximizes the open loop H bound. Subsequently, an optimal actuator location is found that minimizes theH bound of the closed loop transfer function. This method minimizes the optimization complexity and providesgreat computational advantages in large scale ”exible systems where the solution to H optimization problemsusing standard tools becomes computationally prohibitive.Keywords: Actuator placement, ”exible beam, distribution of disturbances, PZT actuators.

This paper presents an explicit expression for an upper bound on H 2 norm for structural systems with collocatedsensors and actuators. Using a linear matrix inequality (LMI)-based representation of the H 2 norm of a collocatedstructural system, we determine an explicit upper bound on H 2 norm of such a system. The present paper alsoaddresses the problem of output H 2 feedback controller design for collocated systems. Employing some simplealgebraic tools, we derive an explicit parametrization of H 2 feedback controller gain which guarantees a prescribedlevel of H 2 performance for the closed-loop system. Numerical examples will be “nally provided to validate theeciency and bene“ts of the proposed method. 1. PLANT FORMULATION Consider a structural system with collocated sensors and actuators and velocity measurement in a vector second-order form represented byM q¨(t)+ D q (t)+ Kq (t)= F (u (t)+ w (t))y (t)= F T q (t) (1)where q(t) R n , u (t) R m , w (t) R m , y (t) R m are the state vector representing displacements, controlinput, external/disturbance signal, and measured output, respectively. The matrices F R

The problem of actuator and sensor placement in a flexible plate is revisited within the context of an intelligent control scheme. Instead of considering individual actuators and sensors, we consider groups of actuators and sensors that have the same capacity to address specific modes. The placement optimization procedure chooses actuators and sensors within a given group so that can collectively address a specific range of modal frequencies. Integrated into the control scheme is the ability to select, over a time interval of fixed length, a given group that can best address spatiotemporally varying disturbances in which the spatial distribution of disturbances changes with time. For the numerical studies on a thin aluminum plate, clamped on all sides and employing piezoceramic patches as collocated actuators/sensors, we consider four groups of PZT actuators/sensors wherein each actuator in each group is designed to have a high level of modal controllability with respect to a given modal shape. Incorporated into the above optimization is the influence of each PZT on the plate's modal shapes. The intelligent control then provides the switching scheme in which, at a given time instance, only one of the four groups is active with the remaining three being kept dormant in order to reduce power consumption.

In this note, we revisit the problem of actuator/sensor placement in large civil infrastructures and flexible space structures within the context of spatial robustness. The positioning of these devices becomes more important in systems employing wireless sensor and actuator networks (WSAN) for improved control performance and for rapid failure detection. The ability of the sensing and actuating devices to possess the property of spatial robustness results in reduced control energy and therefore the spatial distribution of disturbances is integrated into the location optimization measures. In our studies, the structure under consideration is a flexible plate clamped at all sides. First, we consider the case of sensor placement and the optimization scheme attempts to produce those locations that minimize the effects of the spatial distribution of disturbances on the state estimation error; thus the sensor locations produce state estimators with minimized disturbance-to-error transfer function norms. A two-stage optimization procedure is employed whereby one first considers the open loop system and the spatial distribution of disturbances is found that produces the maximal effects on the entire open loop state. Once this "worst" spatial distribution of disturbances is found, the optimization scheme subsequently finds the locations that produce state estimators with minimum transfer function norms. In the second part, we consider the collocated actuator/sensor pairs and the optimization scheme produces those locations that result in compensators with the smallest norms of the disturbance-to-state transfer functions. Going a step further, an intelligent control scheme is presented which, at each time interval, activates a subset of the actuator/sensor pairs in order provide robustness against spatiotemporally moving disturbances and minimize power consumption by keeping some sensor/actuators in sleep mode.

The objective of this investigation is to present a computational scheme for the optimal placement of actuating devices in flexible plates that utilize piezoceramic patches as actuators. In addition to controllability criteria, the candidate locations are required to also exhibit robustness with respect to the spatial distribution of disturbances. These PZT actuators are bonded at optimal locations that are determined by statically minimizing the optimal value of a disturbance-to-output transfer function with respect to the worst distribution of disturbances. Once the optimal actuator locations are determined, that in addition to performance specifications also satisfy a spatial robustness criterion, a suitable LQR-based controller is designed. At a given interval of time, only one PZT is activated and the remaining ones are kept dormant. The rationale of actuator/controller switching is to demonstrate the better vibration alleviation characteristics of switching between actuators over the use of a single actuator that is always in continuous use. The optimality of switching is made with respect to a cost-to-go performance index that corresponds to each actuating device. Extensive computer simulations with repeatable spatiotemporally varying disturbance profiles, reveal that this algorithm offers better performance over the non-switched case.© (2005) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The objective of this paper is to provide an experimental verification of a new H-infinity control scheme on a flexible beam which uses a collocated PZT actuator/sensor pair. We use an analytical bound approach that provides an explicit expression of an upper bound on the H-infinity norm of the closed-loop system and an explicit parametrization of the corresponding output feedback control gains. The method has great computational advantages for large scale structural systems where the solution of H-infinity optimization problems using standard tools could be computationally prohibitive. Both experimental and numerical results are presented that provide a comparison of the performance and the computational requirements on the controller design using the standard H-infinity formulation and the proposed analytical bound approach.

An experimental implementation of an actuator switching scheme in a flexible structure that employs multiple piezoceramic actuators is reported in this manuscript and whose results support theoretical predictions and agree with numerical findings. The proposed supervisory control scheme attempts to improve controller performance of a system subject to spatiotemporally varying disturbances. The intelligent controller achieves its tasks by switching to different actuating devices at different time intervals. Specifically, the flexible structure under study is assumed to have multiple piezoceramic actuators available with only one being active over a time interval of fixed length while the remaining ones are kept dormant. By monitoring the state of the system, the supervisory controller engages the actuator that lies "spatially" closer to the region (epicenter) of a spatially varying disturbances within the spatial domain. This actuator switching scheme mimics the case of a moving actuator capable of residing in predetermined positions within the spatial domain of the flexible structure. Numerical studies for a flexible beam are presented in conjunction to the experimental ones to support the analytical findings of this work.

The dynamics of intelligent actuators utilized in vibration control of flexible structures may exhibit nonlinear behavior under extreme environments and/or prolonged/repeated usage. When transitions to nonlinearities are not accounted for in the controller design, they might compromise controller performance and even destabilize the very system they are designed to control. A novel approach that addresses the issue of actuator nonlinearities is presented here. Specifically, the actuators considered are those that at some initial period exhibit linear behavior and enter a nonlinear regime thereafter. The method studied here only utilizes these actuators while on their linear behavior by proposing an optimal activation sequence of these actuators. At a given time interval of fixed length, only a single actuator is activated while the remaining ones are kept dormant. The reason is to ensure that at each time instance, a single actuator with linear dynamics is active. When the active actuator is about to become nonlinear, then the algorithm switches to and activates the next available actuator in an optimal fashion. The optimality of switching is with respect to the minimal cost of an associated LQR performance index that corresponds to each actuator. In the proposed algorithm, a control logic is incorporated that only selects the next actuator to be activated from the set of the remaining actuators that are considered healthy(linear); an example of this would be SMA actuators that had enough time to cool down and thus when activated again can exhibit linear dynamics.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.