Observability-Based Sensor Selection for a Planar Bending Beam Attached to a Rotating Body

Observability of a cantilever beam attached to a rigid body rotating and translating in the plane is considered first using a differential-geometric approach and then using the empirical Gramian. Based on a modal approximation of the beam, the rank condition of the observability codistribution indicates that the body rotation rate and rigid body motion parallel to the length of the beam can be observed with strain sensors and accelerometers located on the flexible beam through the passive motion coupling so long as the body rotation rate is nonzero, however the rigid body motion lateral to the beam cannot. The empirical observability Gramian, generated through MATLAB and finite element analysis simulations, is used to provide further understanding of the observability characteristics and serves as a basis for the sensor selection problem for the cantilevered beam. Multiple objective functions are considered and a comparison of the sensor selection results is performed; differences in performance are demonstrated through the error estimates of an unscented Kalman filter run with simulated measurement data.