In this paper, we consider a linear piezoelectric structure which employs a fast-switched, capacitively shunted subsystem
to yield a tunable vibration absorber or energy harvester. The dynamics of the system is modeled as a hybrid system,
where the switching law is considered as a control input and the ambient vibration is regarded as an external disturbance.
It is shown that under mild assumptions of existence and uniqueness of the solution of this hybrid system, averaging
theory can be applied, provided that the original system dynamics is periodic. The resulting averaged system is
controlled by the duty cycle of a driven pulse-width modulated signal. The response of the averaged system
approximates the performance of the original fast-switched linear piezoelectric system. It is analytically shown that the
averaging approximation can be used to predict the electromechanically coupled system modal response as a function of
the duty cycle of the input switching signal. This prediction is experimentally validated for the system consisting of a
piezoelectric bimorph connected to an electromagnetic exciter. Experimental results show that the analytical predictions
are observed in practice over a fixed "effective range" of switching frequencies. The same experiments show that the
response of the switched system is insensitive to an increase in switching frequency above the effective frequency range.
A switching sliding mode controller for the static shape control of a membrane strip is considered. The membrane
strip is augmented with two macro fiber composite (MFC) bimorphs. MFC patches are modeled as monolithic
piezoceramics. The combined structure is modeled as an
Euler-Bernoulli beam under tensile load. The two
bimorphs are actuated independently. One bimorph operates in bending, whereas the other bimorph operates
in tension. The presence of the later causes the system to be nonlinear, hence the use of the sliding mode
technique, and gives rise to a structural singularity. To evade this problem, a switching command is introduced.
Hence, the closed loop system utilizes a hybrid control law, which can cause stability problems. Fortunately, the
same Lyapunov function can be used to analyze the stability of both subsystems. Consequently, the switching
is safe, and asymptotic stability is guaranteed. Simulation results are presented to demonstrate the efficacy of
the switching slide mode controller.
Remote acoustic or seismic forms of excitation for laser Doppler vibration landmine detection are low false alarm rate
detection strategies. A more recent approach now under investigation includes a direct mechanical excitation through a
prodder or probe. In this research, we report on simple laboratory measurements of the VS-1.6 landmine undergoing
direct mechanical excitation from a modified prodder while measuring the landmine's pressure plate vibrational
response with a scanning laser Doppler vibrometer. The direct mechanical excitation mechanism, located near the
prodding end of a rod, consists of a miniature piezoelectric stack actuator. We additionally compare direct excitation to
both acoustic and seismic methods in a large sandbox filled with dry sand. We show that for the landmine buried almost
flush, direct contact mechanical excitation compares favorably to both seismic and acoustic excitation responses for the
(0,1) mode of the pressure plate. We also observe additional features not previously seen in either seismic or acoustic
Conventional control surfaces have been used in most carbon fiber composite, membrane-wing autonomous
micro air vehicles (MAV). In some cases, vehicle morphing is achieved using servo actuators to articulate vehicle
kinematic joints, or to deform crucial wing / tail surfaces. However, articulated lifting surfaces and articulated
wing sections are difficult to instrument and fabricate in a repeatable fashion. Assembly is complex and time
consuming. The goal of this paper is to establish the feasibility of morphing wings on autonomous MAVs that
are actuated via active materials. Active actuation is achieved via a type of piezoceramic composite called Macro
Fiber Composite (MFC). This paper investigates the structural dynamics of morphing wings on MAVs that are
actuated via active composites. This paper continues the work presented in1 by considering structural dynamic
characteristics of the morphing vehicle determined through Scanning Laser Doppler Vibrometry (SLDV).
This paper develops an averaging analysis for qualitative and quantitative study of switched piezostructural systems. The study of piezostructural systems including passive and active shunt circuits has been carried out for some time. Far less is known regarding analytical methods for the study of switched piezostructural systems. The technique developed in this paper is motivated by the success of averaging methods for the analysis of switched power supplies. In this paper it is shown that averaging analysis provides a means of determining time domain as well as frequency domain response characteristics of switched piezostructural systems that include switched capacitive shunt circuits. The time domain and frequency domain performance of a tunable piezoceramic vibration absorber is derived via averaging in this paper. The proposed switching architecture provides an essentially continuous range of tunable notch frequencies, in contrast to a finite and fixed collection of discrete notch frequencies available in some implementations of capacitively shunted piezostructures. The technique for analysis appears promising for the study of vibration damping and energy harvesting piezostructures whose underlying operating principle is similar.
A large-scale survey (~700 m2) of frescos and wall paintings was undertaken in the U.S. Capitol Building in Washington, D.C. to identify regions that may need structural repair due to detachment, delamination, or other defects. The survey encompassed eight pre-selected spaces including: Brumidi's first work at the Capitol building in the House Appropriations Committee room; the Parliamentarian's office; the House Speaker's office; the Senate Reception room; the President's Room; and three areas of the Brumidi Corridors. Roughly 60% of the area surveyed was domed or vaulted ceilings, the rest being walls. Approximately 250 scans were done ranging in size from 1 to 4 m2. The typical mesh density was 400 scan points per square meter. A common approach for post-processing time series called Proper Orthogonal Decomposition, or POD, was adapted to frequency-domain data in order to extract the essential features of the structure. We present a POD analysis for one of these panels, pinpointing regions that have experienced severe substructural degradation.
Previous research has demonstrated that rigorous modeling and identification theory can be derived for structural dynamical models that incorporate control influence operators that are static Krasnoselskii-Pokrovskii integral hysteresis operators. Experimental evidence likewise has shown that some dynamic hysteresis models provide more accurate representations of a class of structural systems actuated by some active materials including shape memory alloys and piezoceramics. In this paper, we show that the representation of control influence operators via static hysteresis operators can be interpreted in terms of a homogeneous Young's measure. Within this framework, we subsequently derive dynamic hysteresis operators represented in terms of Young's measures that are parameterized in time. We show that the resulting integrodifferential equations are similar to the class of relaxed controls discussed by Warga10, Gamkrelidze24, and Roubicek25. The formulation presented here differs from that studied in 10, 24 and 25 in that the kernel of the hysteresis operator is a history dependent functional, as opposed to Caratheodory integral satisfying a growth condition. The theory presented provides representations of dynamic hysteresis operators that have provided good agrement with experimental behavior in some active materials. The convergence of finite dimensional approximations of the governing equations is also proven.
An experimental testbed is described that is used to study the feasibility of control of a class of flows that have low Reynolds numbers. The experimental testbed is comprised of a thin airfoil with a backward facing step machined into the upper surface. A thin PZT composite flap is mounted at the edge of the backward facing step to enable modification of the flow. Output measurement sensors consist of MEMs-based shear stress sensors, and conventional pressure taps, located on the surface of the airfoil. This paper derives a control framework for the synthesis of control methodologies for the testbed. A reduced order control model is obtained by employing reduced basis approximations of the two dimensional Navier-Stokes equations. Preliminary open loop experimental results are reported that illustrate the existence of convected large scale structures in the flow.
This paper presents recent analytical and experimental research to modify and control low Reynolds number flows over prototypical airfoils associated with micro-air-vehicles. The simplified experimental test geometry consists of a meso-scale piezoceramic actuated flap that undergoes peak amplitude displacements of 40 microns. The flap actuator array is designed to modify separation and reattachment location on the airfoil. The location of the reattachment on the upper surface of the prototypical airfoil is measured by an array of MEM's shear stress sensors located downstream. The focus of this paper is the discussion of the status and applicability of reduced order modeling techniques for the derivation of active feedback flow control strategies for the prototypical active airfoil. Frequently, reduced order models are derived from a library of component fluid modes which serve as the basis for a low dimensional approximation of the nonlinear Navier Stokes equations. The methodology discussed in this paper differs markedly from these approaches. We derive a technique employing multiresolution and wavelet approximations of nonlinear Volterra series that represent the input-output dynamics of the system. The accuracy of the resultant low- dimensional input-output models is validated on a benchmark nonlinear aeroelastic testbed.
While PZT exhibits only mild nonlinear response at low voltage levels, it is well-known that the response can be profoundly nonlinear at high field strengths. Moreover, the use of mechanical linkages and structural design to amplify the stroke of PZT-based actuation likewise can couple with this material nonlinearity to yield a structural level nonlinearity that is non-negligible. In this paper, we investigate such a nonlinear response in a PZT actuated trailing edge flap attached to a scaled helicopter rotor blade. While the example studied in this paper is quite specific, the methodology derived is generally applicable. We extend the recent results of [18,19] for the derivation of closed loop control for active material actuated devices. In this technique, a compensator derived from an offline identification of a Krasnoselski-Pokrovski hysteresis operator is cascaded with the plant. We show that the methodology is well-posed for the class of problems under consideration; we derive closed loop stability and robustness conditions that can be associated with the prediction error in the identified hysteresis operator. We study the performance of our methodology in numerical examples and discuss relevant experimental results.
This paper presents a framework for the identification of the constitutive law for a class of nonlinear models of shape memory alloys (SMA) embedded elastomeric rods. Specifically, a formulation of the transient response of elastomeric rods with embedded shape memory alloy actuators that incorporate the inherent coupling between the dynamics of deformation at the structural level, the thermal response and the constitutive law describing the shape memory alloy is described. Previous work by the authors has shown that the incorporation of shape memory alloy actuation is distributed parameter systems can induce a large class of nonlinearities including hysteresis effects in the SMA constitutive law, nonlinear kinematics of large deformation, and, in some cases, local plasticity effects. To derive a methodology to control the dynamics for the class of SMA embedded elastomeric rods considered in this paper, it is essential that the system characteristics of the nonlinear distributed parameter system be identified accurately. This paper presents an identification theory applicable to the coupled system of partial differential equations. The results are validated using both numerical simulations and experimental results.
This paper presents a formulation of the transient response of elastomeric rods with embedded shape memory alloy actuators that incorporate the inherent coupling between the dynamics of deformation at the structural level, the thermal response and the constitutive law describing the shape memory alloy. Previous work by the authors has shown that the incorporation of shape memory alloy actuation in distributed parameter systems can induce a large class of nonlinearities including hysteresis effects in the SMA constitutive law, nonlinear kinematics of large deformation, and, in some cases, local plasticity effects. To derive a control methodology for the class of SMA embedded elastomeric rods considered in this paper, it is essential that the system characteristics of the nonlinear distributed parameter system be identified accurately. This paper presents an identification theory applicable to the coupled system of partial differential equations. The results are validated using both numerical simulation and experimental results.
Adaptive control of spacecraft and large structures using Radial Basis Function (RBF) based Artificial Neural Networks (ANN) is investigated. The centers of approximation of the RBFs are allowed to be dynamic in order to provide persistent excitation and a small window of approximation. Both state and time based RBFs are investigated for their ability to identify unmodeled and persistent effects. Integral feedback of the attitude seems necessary, especially when the initial estimates are poor, to eliminate steady state errors for pointing applications. Examples of motion-to-rest as well as tracking maneuvers and vibration suppression are presented.