An optimized self-sensing piezoelectric cantilever for micro-robotic applications

Quasi-static piezoelectric actuators are used in micro-robotics due to the small displacements they can achieve, and they have been proven to be suitable for Self-Sensing Actuation (SSA) applications. The morphology and material of an actuator, and therefore its characteristics (i.e. stiffness, capacitance), all have an impact on the performance of the SSA implementation. This article presents a methodology that can be used to optimize the design parameters for a piezoelectric quasi-static bimorph cantilever for micro-robotic applications with sub-mN manipulation forces and sub-mu m positioning resolutions in mind. A model is established for this type of actuator, from which an objective function aiming to maximize beta, the charge accumulation coefficient, is defined. Boundary conditions are set on the optimization study by imposing constraints on the design. An analytical optimization approach is then adopted to study the evolution of the objective function across the design space. The study evidences the existence of a subset of solutions satisfying the constraints and maximizing the objective function, and the partial derivatives of this subset are studied, leading to conclusions for an optimized design strategy. Experimental results show that inaccuracies in the prediction of the beta parameter lie within the self-sensing actuator model due to the omission of the thin electrode layers inserted between each piezoelectric layer. Nonetheless, the presented optimization methodology has proven to be suitable to maximize the potential SSA performance of a design, with the fabricated optimized actuator having a higher beta coefficient than a commercial actuator of similar external dimensions by a factor of approximately 7.