Optimization of vibrator motion with air flow excitation

In the daily life and techniques people constantly interact with continuous media such like air or water. In this paper motion of a vibrator with constant air or water flow excitation is considered. Firstly, motion of the vibrator with constant air or water flow velocity excitation is investigated. The main idea is to determine optimal control law for variation of additional area of vibrating object within limits. The criterion of optimization is time required to move object from initial position to the final one. The maximum principle is used for solution of the high-speed problem. It is demonstrated that optimal control action is on bounds of area limits. Examples of synthesis of real mechatronic systems are given