Act and wait concept meets oscillating delayed feedback control

VERÓNICA E. PASTOR; GRACIELA A. GONZÁLEZ

Punta del Este

Congreso; Dynamics Days Latin American and the Caribbean 2018; 2018

Universidad de la República

The act-and-wait concept developed by Insperger ([1]) is the periodic switchingin and off control with delay. Its advantage is that if the wait-time is longerthan the feedback delay, the dynamics of the controlled system with delay isdescribed by a discrete time system without delay. Based on this concept, adelayed feedback controller has been designed in [2] for equilibrium point stabilization.This controller depends on four parameters: /tau (control gain), (delay), T (control period) and tw (wait time). It has been implemented for a prototype two dimensional oscillator but its successfulness for any case has not been guaranteed. Namely, it is easy to see that in the scalar case, it does not work for any set of control parameters. This is not a limitation for the oscillating delayed feedback control with two delayed states developed in [3] which depends only on the control gain and the delay. In this work, it is considered the introductionof a control period and a wait time into the oscillating delayed feedback control and it is studied how these parameters influences on the control method achievements and performance.References[1] T. Insperger and G. Stepan On the dimension reduction of systems withfeedback delay by act-and-wait control, IMA Journal of MathematicalControl and Information, 27(4), 457-473 (2010).[2] H. Konishi, K. Kokame and N. Hara, Delayed feedback control based onthe act-and-wait concept, Nonlinear Dynamics, 63 (3), 513-519 (2011).[3] V. E. Pastor and G. A. Gonz´alez, Analysis and comparison of two oscillatoryfeedback control schemes for stabilizing equilibrium points, ProceedingSeries of the Brazilian Society of Computational and Applied Mathematics,4 N 1 , 010016-1 ? 010016-7 (2016).