Arrays of sensors and actuators designed to provide robust broadband feedback control with high performance and limited modeling are the subject of this paper. The reconfigurable array technique proposed here enables the design of reduced- order controllers for complex structures and offers the potential to improve closed-loop robustness and to broaden the region of good performance even as the plant changes. The weighted summation of sensor signals senses the modes that are relevant to performance while rejecting the remaining modes; therefore reducing the required complexity of the controller. These weights are obtained from the minimization of a cost function and under certain assumptions; it can be shown that a single optimum solution exists. The use of reconfigurable arrays is motivated by the need to control the vibration of complex structures. A thirty element collocated actuator and sensor array was bonded to a cylinder section. Array weights were computed and successfully applied to isolate target modes. Different methods of computing the weights are implemented and compared. The deleterious effects of spatial aliasing and the performance as a function of the array size are experimentally explored.
KEYWORDS: Acoustics, Chemical elements, Finite element methods, Skin, Aluminum, Aircraft structures, Systems modeling, Control systems, Spherical lenses, Computer aided design
A cylindrical test-bed has been designed and modeled to aid in the study and control of interior acoustics in aircraft. The test-bed accounts for local as well as global structural- acoustic dynamics encountered in typical aircraft. The design is based on several existing aircraft and models used to study aircraft dynamics. The test-bed incorporates the basic geometry and materials common to a majority of aircraft, including an aluminum skin shrouding a framed structure composed of ribs and stringers. The design is approximately a one-third scale representation with a cylindrical geometry measuring 0.91 m diameter and 1.98 m long. The test-bed has been modeled using finite element method and Rayleigh-Ritz assumed modes analysis. The models were used to refine the design of the test-bed as well as to model the coupled structural-acoustic dynamics. The models predict that the test-bed will have a modal structure commensurate with experimental identifications on existing aircraft.
Electrostrictors are often avoided in structural control applications due to the non-linearity and temperature sensitivity of the electro-mechanical coupling. This paper describes control techniques so that constant performance is obtained from an electrostrictor in a feedback control system at temperatures ranging from 5 degree(s)C to 57 degree(s)C and at field levels ranging from 90 V/mm to 950 V/mm. The control techniques are experimentally implemented on a cantilevered beam with a 0.9 MN - 0.1 PT electrostrictor. With output linearization and temperature-gain scheduling, the electrostrictive system reduces the RMS strain vibration by 61%. An identical system with a G-1195 piezoceramic controller is used for comparison. The piezoceramic system reduced the strain vibrations by 55% which was robust to temperature variation but not robust to variations in the bias field. Extensive unconstrained wafer characterization as a function of temperature is also presented in the context of relevant constitutive equations.
This paper develops a model for the behavior of an electrostrictively coupled electromechanical system. The framework for the derivation of the governing equations is sufficiently general to model the dynamics of any nonlinear electroceramic actuated system which can be described by a set of constitutive relationships. The constitutive relations for electrostrictors are reviewed and are simplified to contain a single quadratic nonlinearity. By introducing the constitutive relations into Hamilton's equation and then assuming mode shapes, the general system equations are derived. Experimental validation of the equations is accomplished with an electrostrictive wafer surface-bonded to a cantilevered beam. The range of validity of the simplified constitutive relationships is also experimentally investigated.
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