Iterative piezo response function-based optimization for static shape control of cantilever beam using nonlinear piezoactuators

Abstract

Shape control of complex structures by optimizing the electrode potential is not achievable directly by analytical solutions and piezo response function base-optimization techniques due to the nonlinear response of piezoactuators. In the present work, a metaheuristic iterative piezo response function (iPRF)-based optimization technique is developed to achieve the arbitrary shape of piezoelectric unimorph using nonlinear piezoactuators. In this regard, a piezoelectric unimorph (PU) is fabricated using APC 850 piezoactuator to verify the nonlinear response in bending mode and nonlinear analytical model of PU. After verification, length of the inactive layer and number of piezoactuators in PU are modified to study the shape control. iPRF-based technique is used for the optimization of electric potential to achieve the target shape of modified piezoelectric unimorph (MPU) with varying piezoactuators. The results of iPRF-based technique are compared with the results of simulated annealing-based direct optimization technique. Unlike simulated annealing-based direct optimization technique, prior knowledge of nonlinear coefficients of piezoactuator is not required in iPRF-based technique. Optimum values obtained from both the direct nonlinear solution- and iPRF-based optimization methods are same for all MPUs. Furthermore, the number of iterations of iPRF-based optimization approach is not affected by the number of piezoactuators used to achieve the desired shape.

Measurements for static shape control optimization of silicon mirror using nonlinear piezoceramic actuators

“…The superiority of SA over the other contemporary non-traditional nature inspired optimizations for the analysis of shape control problems can be found in our previous work [35]. Furthermore, the details of iPRF-based optimization can be found in our recent work [52]. This technique is useful for both the generation and control of any arbitrary shape.…”

“…The shape control using nonlinear piezoactuator is a challenging task as both direct nonlinear solution and PRF-based optimization cannot be used to calculate the electric field of piezoelectric actuators to achieve the target profile. An iterative piezo response function (iPRF)-based optimization technique was recently proposed to overcome the issues associated with the nonlinearity of piezoactuators in shape control [52]. The theoretical results demonstrate that iPRF-based metaheuristic approach can optimize the electric field without knowing of nonlinear coefficients of piezoactuators.…”