The Udwadia–Kalaba Trajectory Control Applied to a Cantilever Beam—Experimental Results

Abstract

The Udwadia–Kalaba methodology is a possible way of explicitly obtaining the equations of motion of constrained systems. From these equations of motion, one can estimate the necessary forces in the constraint to keep the system in a given motion. Hence, the Udwadia–Kalaba methodology can also apply to active tracking control of subsystems or the control of points of a structure. In this work, one investigates experimentally the benefits and drawbacks of such control strategy by applying it to the control of out-of-plane vibrations of a cantilever beam. The beam is excited by a shaker mounted near the clamped end of the beam. A second shaker applies the control forces in the free end of the beam, where an accelerometer is used for feedback. The vibration behavior of the beam under excitation/control is measured by a laser vibrometer. Results show that the methodology changes the dynamic behavior of the structure by changing its boundary conditions at the point of control, thus shifting natural frequencies and mode shapes. Results also show that the successful implementation of the method experimentally is sensitive to the quality of modeling of the structure.