Vibrational control concerns the design of a periodic input to stabilize an open-loop unstable equilibrium point without feedback, and so this method of control may succeed where conventional feedback is infeasible. However, traditional vibrational control has seen little use, in part due to results from averaging theory, in which the frequency of the stabilizing signal is not known in advance, and is required to be “sufficiently large.”
This talk presents an alternative approach to vibrational control. Instead of averaging theory, we use the stability map for second-order linear systems with sinusoidal or bilevel periodic inputs. In a fourth-order example based on electrostatic MEMS comb-drive actuators, the method finds a stabilizing input, whereas the averaging method fails. The success of related techniques in the design of quadrupole mass filters and quadrupole ion traps suggests that this approach deserves attention.
Bio: Jordan M. Berg received the BSE and MSE in Mechanical and Aerospace Engineering from Princeton University in 1981 and 1984. He worked in the commercial space industry before returning to graduate school into 1986. He received the PhD in Mechanical Engineering and Mechanics, and the MS in Mathematics and Computer Science from Drexel University in 1992 followed by postdoctoral appointments at the USAF Wright Laboratory in Dayton, OH, and the Institute for Mathematics and Its Applications in Minneapolis, MN. Since 1996 he has been on the Mechanical Engineering faculty of Texas Tech University. In 2008 he was a Visiting Professor at the University of Ruhuna and the University of Peradeniya in Sri Lanka. His current research interests include nonlinear and geometric control, and the control of nano- and microsystems. In 2014 he joined the Civil, Mechanical, and Manufacturing Innovation (CMMI) Division of the Engineering (ENG) Directorate of the National Science Foundation as an IPA rotator. He is currently serving as co-Director of the Dynamics, Control, and System Diagnostic (DCSD) program, and as a Program Director for the National Robotics Initiative.