Modeling and analysis of dynamic contact point sensing by a flexible beam

A dynamic active antenna sensor for locating a contact point is considered in this paper. In its simpliest realization the sensor can be implemented in the form of a flexible beam rotating in plane. The main feature of the sensor is the use of the frequency-contact point curve which, for some regions, may be a multi-valued function. One way of 'improving' the curve could be concerned with the non-uniform mass and stiffness distribution of the beam, which would lead to a rather complicated sensor design. Another way to remedy the situation is to change the sensing strategy by adding a proper control action at the joint of the beam. To study the sensor's response to the control, a dynamic model of the beam in contact with the external environment is developed. Analysis of the frequency equation shows how a simple proportional control law changes the sensing curve. It is found that in some limiting, but practically attainable cases the sensing curve becomes a single-valued function. Thus, the solution proposed can significantly simplify the identification procedure.