Adaptive modification of the delayed feedback control algorithm with a continuously varying time delay

2011 ◽  
Vol 375 (44) ◽  
pp. 3866-3871 ◽  
Author(s):  
V. Pyragas ◽  
K. Pyragas
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Control Algorithm ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Adaptive Modification ◽  
Varying Time Delay

An Efficient Approach for Stability Analysis and Parameter Tuning in Delayed Feedback Control of a Flying Robot Carrying a Suspended Load

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Wei Dong ◽  
Ye Ding ◽  
Luo Yang ◽  
Xinjun Sheng ◽  
Xiangyang Zhu
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Spectral Radius ◽  
Stability Region ◽  
Parameter Tuning ◽  
Suspended Load ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
The Stability ◽  
Flying Robot

This paper presents an accurate and computationally efficient time-domain design method for the stability region determination and optimal parameter tuning of delayed feedback control of a flying robot carrying a suspended load. This work first utilizes a first-order time-delay (FOTD) equation to describe the performance of the flying robot, and the suspended load is treated as a flying pendulum. Thereafter, a typical delayed feedback controller is implemented, and the state-space equation of the whole system is derived and described as a periodic time-delay system. On this basis, the differential quadrature method is adopted to estimate the time-derivative of the state vector at concerned sampling grid point. In such a case, the transition matrix between adjacent time-delay duration can be obtained explicitly. The stability region of the feedback system is thereby within the unit circle of spectral radius of this transition matrix, and the minimum spectral radius within the unit circle guarantees fast tracking error decay. The proposed approach is also further illustrated to be able to be applied to some more sophisticated delayed feedback system, such as the input shaping with feedback control. To enhance the efficiency and robustness of parameter optimization, the derivatives of the spectral radius regarding the parameters are also presented explicitly. Finally, extensive numeric simulations and experiments are conducted to verify the effectiveness of the proposed method, and the results show that the proposed strategy efficiently estimates the optimal control parameters as well as the stability region. On this basis, the suspended load can effectively track the pre-assigned trajectory without large oscillations.

BIFURCATION, CHAOS AND THEIR CONTROL IN A TIME-DELAY DIGITAL TANLOCK LOOP

2013 ◽  
Vol 23 (08) ◽  
pp. 1330029 ◽  
Author(s):  
TANMOY BANERJEE ◽  
BISHWAJIT PAUL ◽  
B. C. SARKAR
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Parameter Space ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Convergence Time ◽  
Stable Phase ◽  
Bifurcation And Chaos ◽  
Global Parameter ◽  
Time Delayed Feedback

This paper reports the detailed parameter space study of the nonlinear dynamical behaviors and their control in a time-delay digital tanlock loop (TDTL). At first, we explore the nonlinear dynamics of the TDTL in parameter space and show that beyond a certain value of loop gain parameter the system manifests bifurcation and chaos. Next, we consider two variants of the delayed feedback control (DFC) technique, namely, the time-delayed feedback control (TDFC) technique, and its modified version, the extended time-delayed feedback control (ETDFC) technique. Stability analyses are carried out to find out the stable phase-locked zone of the system for both the controlled cases. We employ two-parameter bifurcation diagrams and the Lyapunov exponent spectrum to explore the dynamics of the system in the global parameter space. We establish that the control techniques can extend the stable phase-locked region of operation by controlling the occurrence of bifurcation and chaos. We also derive an estimate of the optimum parameter values for which the controlled system has the fastest convergence time even for a larger acquisition range. The present study provides a necessary detailed parameter space study that will enable one to design an improved TDTL system.

DELAYED FEEDBACK CONTROL OF A PACED EXCITABLE OSCILLATOR

2000 ◽  
Vol 10 (03) ◽  
pp. 603-609 ◽  
Author(s):  
MICHAEL E. BLEICH ◽  
JOSHUA E. S. SOCOLAR
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Numerical Experiment ◽  
Delayed Feedback ◽  
Feedback Stabilization ◽  
Delayed Feedback Control ◽  
Regular Behavior ◽  
Nagumo Equations ◽  
Rapid Pacing

A simple numerical experiment on Fitzhugh–Nagumo equations demonstrates that time-delay feedback methods can stabilize regular behavior in a paced, excitable oscillator without using large applied pulses. The method is robust against slow variations in the pacing rate and can be used to track an orbit into a parameter regime where it is unstable. Moreover, the method requires no information about the desired orbit other than period, which is determined directly by the observation of the pacing signal. Results are presented for feedback stabilization of a nonspiking orbit in the rapid pacing regime.

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