Performance and optimal placement of piezoceramic actuators for shape control of a cantilever beam
Treanor, Kirk E.
Agrawal, Brij N.
Meyer, John L.
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Shape control of spaceborne antennas can provide the ability to correct for effects such as thermal distortion and manufacturing errors as well as control the shape of an antenna's radiated beam. This thesis examines the performance of piezoceramic actuators in producing static deformation of a cantilever beam and analyzes the optimal placement of actuators to best approximate a desired deformation profile. Predictions of actuator effectiveness at producing curvature are developed using an Euler-Bernoulli model. An algorithm to determine the optimal locations and input voltages for a fixed set of actuators to achieve a desired deformation profile of a cantilever beam using embedded Nelder and Mead simplex search routines is presented and evaluated for two shape functions and various combinations of actuators. Experimental measurements show that the Euler-Bernoulli model provides a reasonable prediction of actuator performance at low input voltage but does not account for nonlinear behavior of the piezoceramic and the effects of hysteresis and transverse stresses. Further experiments demonstrate the ability of four piezoceramic actuators to produce an approximation of a parabolic deformation profile of a cantilever beam and illustrate the importance of considering these effects in determining the required actuator input voltages
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