Design of 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 proved suitable for Self-Sensing Actuation (SSA) applications. The fabrication parameters of an actuator (i.e. morphology, stiffness, capacitance) will have an impact on the performance of the SSA implementation, and this study intends to examine how to optimize those parameters for a piezoelectric cantilever. A model is established for this type of actuator, from which an objective function 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 constraint and maximizing the objective function, and the monotonicity of this subset is demonstrated. It is concluded that to obtain an optimal solution, one must maximize the length, minimize the number of layers and their thickness, and derive the appropriate width from these parameters applied to the constraint imposed on the objective function.