Multiplicity-induced optimal gains of an inverted pendulum system under a delayed proportional-derivative-acceleration feedback

Abstract This paper studies the stabilization to an inverted pendulum under a delayed proportional-derivative-acceleration (PDA) feedback, which can be used understand human balance in quiet standing. The closed-loop system is described by neutral delay differential equation (NDDE). optimal feedback gains (OFGs) that make exponential decaying rate maximized are determined when characteristic of has repeated real root with multiplicity 4. Such property called multiplicity-induced dominancy time-delay systems, and been discussed intensively many authors for retarded equations (RDDEs). shows achieved NDDEs. In addition, OFGs delay-dependent, decrease sharply small numbers correspondingly as increases from zero varies slowly respect moderate delays. Thus, well-stabilized delays relatively gains. result might understandable elderly obvious response PDA controller.