Electrical Engineering and Systems Science > Systems and Control
[Submitted on 13 Feb 2023]
Title:Numerical analysis of a multistable capsule system under the delayed feedback control with a constant delay
View PDFAbstract:The vibro-impact capsule system is a self-propelled mechanism that has abundant coexisting attractors and moves rectilinearly under periodic excitation when overcoming environmental resistance. In this paper, we study the control of coexisting attractors in this system by using a delayed feedback controller (DFC) with a constant delay. The aim of our control is to steer this complex system toward an attractor with preferable performance characteristics among multiple coexisting attractors, e.g., a periodically fast forward progression. For this purpose, we give an example of a feedback-controlled transition from a period-3 motion with low progression speed to a period-1 motion with high progression speed at the system parameters where both responses coexist. The effectiveness of this controller is investigated numerically by considering its convergence time and the required control energy input to achieve transition. We combine pseudo-spectral approximation of the delay, event detection for the discontinuities and path-following (continuation) techniques for non-smooth delay dynamical systems to carry out bifurcation analysis. We systematically study the dynamical performance of the controlled system when varying its control gain and delay time. Our numerical simulations show the effectiveness of DFC under a wide range of system parameters. We find that the desired period-1 motion is achievable in a range of control delays between a period-doubling and a grazing bifurcation. Therefore, two-parameter continuation of these two bifurcations with respect to the control delay and control gain is conducted to identify the delay-gain parameter region where the period-1 motion is stable. The findings of this work can be used for tuning control parameters in experiments, and similar analysis can be carried out for other non-smooth dynamical systems with a constant delay term.
Current browse context:
eess.SY
References & Citations
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.