Mathematical models and control system designing for flexible missile

Possible approaches to the mathematical description of different types of flexible vehicles are observed. Mass and aerodynamic characteristics are changing considerably during the flight of aerospace vehicles. From the point of view of control theory such vehicles are the typical non-linear and non-steady plants. The aim of designer is to create the light construction. For these reason such objects are deformed in flight, and their elastic properties appear. Elastic longitudinal and lateral oscillations of the complex form arise, which frequencies are changing during the flight. Elastic oscillations are usually described by differential partial equations or ordinary differential equations of the great dimension. Deformation of a body results in appearance of the local attack angles and slide angles. As a result of it, the local forces and moments of forces arise. These forces and moments are synchronized with the changes of local angles of attack and slide. The local forces and moments are the reasons of amplification or attenuation of elastic oscillations. This phenomena is known as aeroflexibility. At excessive development of elastic oscillations the structural failure may take place. Paying attention to these effects has a great importance at control of space stations and space probes, airplanes and other mobile objects liable to the considerable dynamic loads.