Delta Wing Flutter Control Using Spatially Optimized Transducers

This work focuses on the development of a design methodology for optimized flutter control of an aeroelastic delta wing. The approach rests on two main premises. The first is that the application of linear modeling and control design techniques can be used to control the predominantly nonlinear phenomenon of flutter by preventing its onset. This phenomenon is characterized by limit cycle oscillations (LCOs) of very high magnitude. These high magnitude deflections, along with the distinct harmonics commonly seen in fluttering plates, typically require cumbersome nonlinear modeling schemes for analysis. The second lies in the spatial optimization of actuator and sensor parameters to facilitate control of targeted modes while providing roll-off of higher order modes without the need for phase-inducing filters. In order to facilitate these optimizations, a versatile and computationally efficient technique for the modeling of piezo structures into analytical systems is developed. The method uses one a priori calculation of the coupling characteristics of gridded piezoelectric elements, contiguously covering the entire structure. This allows for the rapid calculation of the coupling characteristics of any patch configuration by summing the effects of the elements contained within the patch boundaries. Some additional advantages of this approach include the lack of error checking necessary with respect to trial patches being located within structural boundaries. Also, patch shape restrictions are not tied to difficulties associated with complicated integration limits, and reversed phasing of patch segments is a trivial matter. Another technique used estimates the effects of patch mass and stiffness contributions on the system. This method is entirely parameter-based and does not require explicit system modeling. It is illustrated how these techniques can dramatically expand the range, versatility, and efficiency of transducer optimization routines. Implementation examples as applied to a delta wing are shown. The experiments employing these optimized transducers show substantially increased flutter control authority over nonoptimized systems, and point to the importance of this spatial coupling as well as the transducer mass and stiffness effects.