Fin type propulsive devices with varying working area of vibrating tail

The object of the study is a fin type propulsive device of robotic fish moving inside water. The aim of the study is to establish optimal control law for variation of additional area of vibrating tail, which ensures maximal positive impulse of motive forces acting on tail. The problem has been solved using the maximum principle of Pontryagin. It is demonstrated that optimal control action corresponds to the case of bound values of area limits. The proposed method makes it possible to increase effective surface area of the fin within motion cycles, when useful tractive force is formed. But within cycles, when fin motion is hindered by water resistance forces, effective surface area is decreased. Thanks to this energy losses are minimized, and operation of fin propulsive device becomes more effective. Examples on synthesis of real mechatronic systems are provided as well