On the admissible control-loop delay for the inverted pendulum subject to detuned PDA feedback

• Main Authors: Balogh, T. (Author), Insperger, T. (Author), Varszegi, B. (Author)
• Format: Article
• Language: English
• Published: Academic Press 2022
• Subjects: Acceleration feedback; Admissible control; Control loop; Critical delay; Critical delays; Detuned; Differential equations; Feedback; Inverted pendulum; Multiple time delays; Multiple time-delays; Neutral delay differential equations; Pendulums; Proportional-Derivative; Stabilizability; Time delay
• Online Access: View Fulltext in Publisher
• ISBN: 0022460X (ISSN)
• DOI: 10.1016/j.jsv.2022.116898

In this paper, we consider the stabilization of φ̈(t)−a0φ(t)=−kpφ(t−τ−δp)−kdφ̇(t−τ−δd)−kaφ̈(t−τ−δa),which describes the control of an inverted pendulum by detuned proportional–derivative–acceleration (PDA) feedback. We show that the system can be stabilized using an appropriate choice of the control parameters kp, kd, ka and δp, δd, δa≥0 if τ is smaller than the critical delay τcrit=6/a0. This value is larger by a factor of 3≈1.73 than the critical delay of the proportional–derivative (PD) feedback with a single delay. © 2022 The Authors