Optimal control of infinite-order smart composite structural systems using distributed sensors

In recent years there has been considerable interest in the design of spatially shaped distributed sensors for the control of infinite-order structural systems. The smart materials polyvinylidene fluoride (PVDF) and shape-memory alloys can be utilized in the development of customized distributed sensors. Sensor shape-optimization techniques are needed for the implementation of optimal control strategies. In this paper, a method for generating the shapes of distributed sensors using finite-dimensional approximations to desired curvature and curvature rate kernels is examined. The output of these spatially distributed sensors is utilized directly as the control signal for suppressing vibrations in infinite-order structural systems. This paper shows that the desired kernels can be generated directly from finite element models of distributed structures without generating displacement and displacement-rate kernels. The curvature and curvature-rate kernels are the desired kernels in the development of shape functions for PVDF sensors for the implementation of controllers. This procedure requires covering the entire structure with a customized sensor for each kernel. To alleviate this problem, a sensor is proposed which covers a portion of the structure with spatially distributed material and uses an observer for the estimation of the states. The original control algorithm is implemented by using the proposed sensor and observer. The usefulness of a single, relatively small customized PVDF film sensor along with an observer to provide full state-feedback information for the entire structure is examined. The complexity and performance of the proposed control scheme are compared with the original distributed sensor implementation.