Stabilization of Systems with Feedback Delay by the act-and-wait Control Concept
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Control of systems with delay in the feedback loop is a complex task, since infinitely many poles should be controlled using only finite number of control parameters. The act-and-wait control is a special time-periodic control for systems with feedback delay, where the control gains are periodically switched on and off in time. The governing equation is a delay-differential equation with time-periodic coefficients. The merit of the method is that if the switch-off (waiting) period is longer than the feedback delay, then the system can be transformed to a discrete map of finite dimension presenting a finite spectrum assignment problem.
Several (actually, infinitely many) periodic functions could be chosen for time-periodic control gains. The main idea behind choosing the one that involves waiting intervals just longer than the feedback delay is that this kills the memory effect by waiting for the system's response induced by the previous action. Although it might seem unnatural not to actuate during the wait interval at all, the act-and-wait concept is still a natural control logic for time-delayed systems. This is how, for example, one would adjust the shower temperature considering the delay between the controller (tap) and the sensed output (water temperature at skin).
The presentation will start with a description of the act-and-wait control concept for general systems with feedback delay. Then, case studies will be presented including first-order scalar systems with feedback delay and balancing problems with reflex delay.
Biosketch: Tams Insperger received his MSc degree in mechanical engineering in 1999 and his PhD degree in applied mechanics in 2002 form the Budapest University of Technology and Economics, Hungary where he currently holds an associate professor position. He held visiting positions at Auburn University, AL, 1997, University of Kaiserslautern, Germany, 2000, and Washington University, St. Louis, MO, 2001, and he is currently a visiting professor at Claremont Colleges, CA. His research interests are in the area of time-delay systems and digital control focusing on applications like machine-tool vibrations and robotics. He is the author of approximately 100 publications including the book Semi-discretization for time-selay systems, Springer, 2011.