Robust Time-Delay Control

1993 ◽  
Vol 115 (2A) ◽  
pp. 303-306 ◽  
Author(s):  
T. Singh ◽  
S. R. Vadali
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Control Unit ◽  
Multiple Time ◽  
Residual Vibration ◽  
Single Time ◽  
Time Delay Control ◽  
Additional Requirement ◽  
Multiple Time Delays ◽  
Delay Control

A method is presented to minimize residual vibration of structures or lightly damped servomechanisms. The method, referred to as the proportional plus multiple delay (PPMD) control, involves the use of multiple time delays in conjunction with a proportional part to cancel the dynamics of the system in a robust fashion. An interesting characteristic of the controller involves addition of a basic single time-delay control unit in cascade to the existing controller, for every additional requirement of robustness. It is shown that the proposed time-delay controller produces results that are exactly the same as those obtained by the shaped input technique. In addition, it is simpler to arrive at the relative amplitudes of the time-delayed signals for any number of delays even in a multi-input setting.

Conversion of SISO processes with multiple time-delays to single time-delay processes

2018 ◽  
Vol 65 ◽  
pp. 84-90 ◽  
Author(s):  
Xiaoli Luan ◽  
Qiang Chen ◽  
Pedro Albertos ◽  
Fei Liu
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Multiple Time ◽  
Single Time ◽  
Multiple Time Delays

scholarly journals Delayed dynamical systems: networks, chimeras and reservoir computing

2019 ◽  
Vol 377 (2153) ◽  
pp. 20180123 ◽  
Author(s):  
Joseph D. Hart ◽  
Laurent Larger ◽  
Thomas E. Murphy ◽  
Rajarshi Roy
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
System Dynamics ◽  
Coupled Oscillators ◽  
Time Delays ◽  
Delay Systems ◽  
Multiple Time ◽  
Reservoir Computing ◽  
Multiple Time Delays ◽  
Network Topologies

We present a systematic approach to reveal the correspondence between time delay dynamics and networks of coupled oscillators. After early demonstrations of the usefulness of spatio-temporal representations of time-delay system dynamics, extensive research on optoelectronic feedback loops has revealed their immense potential for realizing complex system dynamics such as chimeras in rings of coupled oscillators and applications to reservoir computing. Delayed dynamical systems have been enriched in recent years through the application of digital signal processing techniques. Very recently, we have showed that one can significantly extend the capabilities and implement networks with arbitrary topologies through the use of field programmable gate arrays. This architecture allows the design of appropriate filters and multiple time delays, and greatly extends the possibilities for exploring synchronization patterns in arbitrary network topologies. This has enabled us to explore complex dynamics on networks with nodes that can be perfectly identical, introduce parameter heterogeneities and multiple time delays, as well as change network topologies to control the formation and evolution of patterns of synchrony. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

Multiple Time Delays Induced Dynamics of p53 Gene Regulatory Network

2021 ◽  
Vol 31 (15) ◽  
Author(s):  
Yuanhong Bi ◽  
Yanan Li ◽  
Jianmin Hou ◽  
Quansheng Liu
Keyword(s):  
Time Delay ◽  
Equilibrium Point ◽  
Regulatory Network ◽  
Time Delays ◽  
P53 Gene ◽  
Positive Equilibrium ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
Gene Regulatory ◽  
Positive Equilibrium Point

p53 dynamics plays an important role in determining cell arrest or apoptosis upon DNA damage response. In this paper, based on a p53 gene regulatory network composed of its core regulator ATM, Mdm2 and Wip1, the effect of multiple time delays in transcription and translation of Mdm2 and Wip1 gene expression on p53 dynamics are investigated through theoretical and numerical analyses. The stability of the positive equilibrium point and the existence of Hopf bifurcation are demonstrated through analyzing the associated characteristic equation of the corresponding linearized system in five cases. Detailed numerical simulations and bifurcation analyses are performed to support the theoretical results. The results show that with the increase of a time delay, the positive equilibrium point becomes unstable, and the p53 dynamics presents an oscillating state. These results reveal that time delay has a significant impact on p53 dynamics and may provide a useful insight into developing anti-cancer therapy.

scholarly journals Combination Synchronization of Three Different Fractional-Order Delayed Chaotic Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Bo Li ◽  
Xiaobing Zhou ◽  
Yun Wang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Time Delays ◽  
Chaotic Systems ◽  
Multiple Time ◽  
Engineering Systems ◽  
Fractional Order Systems ◽  
Combination Synchronization ◽  
Multiple Time Delays ◽  
Practical Engineering

Time delay is a frequently encountered phenomenon in some practical engineering systems and introducing time delay into a system can enrich its dynamic characteristics. There has been a plenty of interesting results on fractional-order chaotic systems or integer-order delayed chaotic systems, but the problem of synchronization of fractional-order chaotic systems with time delays is in the primary stage. Combination synchronization of three different fractional-order delayed chaotic systems is investigated in this paper. It is an extension of combination synchronization of delayed chaotic systems or combination synchronization of fractional-order chaotic systems. With the help of stability theory of linear fractional-order systems with multiple time delays, we design controllers to achieve combination synchronization of three different fractional-order delayed chaotic systems. In addition, numerical simulations have been performed to demonstrate and verify the theoretical analysis.

Sign in / Sign up

Export Citation Format

Share Document