Zero locus of a beam with varying sensor and actuator locations

Abstract

The nonrational transfer function of an important component of a flexible structure, the beam, is analyzed. The true pattern of zeros of that transfer function is investigated as a function of sensor and actuator separation. Translational displacement sensors are used for two cases in which a force input and a moment input are separately applied at one end of the beam. Contrary to general opinion, zeros do not simply approach the origin along the real axis of the s plane as the sensor is moved away from the point of force/moment application. When the displacement sensor is located at a certain point, the first pair of zeros on the real axis of the s plane arrive at the origin and cancel the rigid-body mode. The location of the translational displacement sensor on the beam at which the rigid-body mode of the beam is unobservable is analyzed as the center of percussion and is uniquely located for each case. If the sensor is moved beyond such a point, a pair of zeros appear on the imaginary axis and move away from the origin along the imaginary axis of the s plane. Finally, the zero migration associated with an angular displacement sensor is briefly considered and compared with the zero migration associated with the translational displacement sensor.