In recent years piezoelectric materials have been increasingly adopted in industrial applications. The growing market presence is reflected in the field of application. There are utilizations as sensors and as actuators in the ultrasonic range, in motors and vibrating conveyors, as acceleration sensors and drives for micropositioning. The focus is increasingly placed on complete solutions of piezoelectric actuators or sensors and their electronic control. However, such system solutions are very complex and require an overall view of the problem. For this reason the emphasis in this work is placed on the joint consideration of a piezoelectric bending actuator and its control electronics. The challenge of this holistic approach is the interpretation of both systems. In order to keep the costs and development times for prototypes of a system solution low, the entire system of actuator and electronic is optimized. The optimization is done by the software package SyMSpace, developed by Linz Center of Mechatronics GmbH (LCM), which enables automated simulations, optimizations and validations. The cornerstone of this work is a linear, analytical model of a piezoelectric bending transducer, which is used for excitation of mechanical vibrations. The model is based on the Euler-Bernoulli beam theory. In addition to the analytical model, finite element models in ANSYS and NGSolve are established. Based on measurements, the created models are verified and adjusted if necessary. The control electronic units of the actuator consists of a voltage source, which must be adapted to the properties of the piezoelectric actuator with a transformer and a subsequent demodulator. The advantage of the transformer is the simple implementation, electrical isolation of the two electrical circuits and contactless power transmission (similar to inductive charging). Both subsystems actuator and control electronics are coupled together in the free network simulation program LTSpice and then optimized with the optimization tool SyMSpace using several optimization loops. Finally, an optimal configuration of the entire system can be selected from a variety of possible solutions.