Stability and Performance Analysis of Time-Delayed Actuator Control Systems

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Bing Ai ◽  
Luis Sentis ◽  
Nicholas Paine ◽  
Song Han ◽  
Aloysius Mok ◽  
...  
Keyword(s):  
Time Delay ◽  
Time Windows ◽  
System Stability ◽  
Robotic Systems ◽  
Delay Systems ◽  
Physical Constraints ◽  
Characteristic Roots ◽  
And Performance ◽  
The Stability ◽  
Actuator Control

Time delay is a common phenomenon in robotic systems due to computational requirements and communication properties between or within high-level and low-level controllers as well as the physical constraints of the actuator and sensor. It is widely believed that delays are harmful for robotic systems in terms of stability and performance; however, we propose a different view that the time delay of the system may in some cases benefit system stability and performance. Therefore, in this paper, we discuss the influences of the displacement-feedback delay (single delay) and both displacement and velocity feedback delays (double delays) on robotic actuator systems by using the cluster treatment of characteristic roots (CTCR) methodology. Hence, we can ascertain the exact stability interval for single-delay systems and the rigorous stability region for double-delay systems. The influences of controller gains and the filtering frequency on the stability of the system are discussed. Based on the stability information coupled with the dominant root distribution, we propose one nonconventional rule which suggests increasing time delay to certain time windows to obtain the optimal system performance. The computation results are also verified on an actuator testbed.

Stability Switches of a Class of Fractional-Delay Systems With Delay-Dependent Coefficients

2018 ◽  
Vol 13 (11) ◽  
Author(s):  
Xinghu Teng ◽  
Zaihua Wang
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Jacobian Determinant ◽  
Stability Switches ◽  
Characteristic Roots ◽  
Fractional Delay ◽  
Analysis Of Stability ◽  
The Stability ◽  
Key Steps ◽  
Delay Dependent

Stability of a dynamical system may change from stable to unstable or vice versa, with the change of some parameter of the system. This is the phenomenon of stability switches, and it has been investigated intensively in the literature for conventional time-delay systems. This paper studies the stability switches of a class of fractional-delay systems whose coefficients depend on the time delay. Two simple formulas in closed-form have been established for determining the crossing direction of the characteristic roots at a given critical point, which is one of the two key steps in the analysis of stability switches. The formulas are expressed in terms of the Jacobian determinant of two auxiliary real-valued functions that are derived directly from the characteristic function, and thus, can be easily implemented. Two examples are given to illustrate the main results and to show an important difference between the fractional-delay systems with delay-dependent coefficients and the ones with delay-free coefficients from the viewpoint of stability switches.

Survey on Recent Results in the Stability and Control of Time-Delay Systems*

2003 ◽  
Vol 125 (2) ◽  
pp. 158-165 ◽  
Author(s):  
Keqin Gu ◽  
Silviu-Iulian Niculescu
Keyword(s):  
Time Delay ◽  
Performance Analysis ◽  
Recent Progress ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Stability And Control ◽  
And Performance ◽  
The Stability ◽  
And Control ◽  
Broad Overview

This paper gives a broad overview of the stability and control of time-delay systems. Emphasis is on the more recent progress and engineering applications. Examples of practical problems, mathematical descriptions, stability and performance analysis, and feedback control are discussed.

scholarly journals Fast Generation of Stability Charts for Time-Delay Systems Using Continuation of Characteristic Roots

2020 ◽  
Vol 15 (11) ◽  
Author(s):  
Surya Samukham ◽  
Thomas K. Uchida ◽  
C. P. Vyasarayani
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Grid Point ◽  
Galerkin Approximation ◽  
Computational Effort ◽  
Numerical Continuation ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Characteristic Roots ◽  
The Stability

Abstract Many dynamic processes involve time delays, thus their dynamics are governed by delay differential equations (DDEs). Studying the stability of dynamic systems is critical, but analyzing the stability of time-delay systems is challenging because DDEs are infinite-dimensional. We propose a new approach to quickly generate stability charts for DDEs using continuation of characteristic roots (CCR). In our CCR method, the roots of the characteristic equation of a DDE are written as implicit functions of the parameters of interest, and the continuation equations are derived in the form of ordinary differential equations (ODEs). Numerical continuation is then employed to determine the characteristic roots at all points in a parametric space; the stability of the original DDE can then be easily determined. A key advantage of the proposed method is that a system of linearly independent ODEs is solved rather than the typical strategy of solving a large eigenvalue problem at each grid point in the domain. Thus, the CCR method can significantly reduce the computational effort required to determine the stability of DDEs. As we demonstrate with several examples, the CCR method generates highly accurate stability charts, and does so up to 10 times faster than the Galerkin approximation method.

On the stability of a class of nonlinear time delay systems

1999 ◽  
Author(s):  
Dan Ivancscu ◽  
Silviu-Iulian Niculcscu ◽  
Jcan-Michcl Dion ◽  
Luc Dugard
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Time Delay Systems ◽  
The Stability

scholarly journals Dynamics of a Duopoly Game with Two Different Delay Structures

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Shumin Jiang ◽  
Fei Xu ◽  
Zhanwen Ding ◽  
Chen Yang ◽  
Huanhuan Liu
Keyword(s):  
Time Delay ◽  
Market Price ◽  
Period Doubling ◽  
System Stability ◽  
Delayed Feedback Control ◽  
System Control ◽  
Heterogeneous Players ◽  
Cournot Game ◽  
The Stability ◽  
Time Delayed Feedback

Two different time delay structures for the dynamical Cournot game with two heterogeneous players are considered in this paper, in which a player is assumed to make decision via his marginal profit with time delay and another is assumed to adjust strategy according to the delayed price. The dynamics of both players output adjustments are analyzed and simulated. The time delay for the marginal profit has more influence on the dynamical behaviors of the system while the market price delay has less effect, and an intermediate level of the delay weight for the marginal profit can expand the stability region and thus promote the system stability. It is also shown that the system may lose stability due to either a period-doubling bifurcation or a Neimark-Sacker bifurcation. Numerical simulations show that the chaotic behaviors can be stabilized by the time-delayed feedback control, and the two different delays play different roles on the system controllability: the delay of the marginal profit has more influence on the system control than the delay of the market price.

Stability and Control of Tooling System for High-Speed Machining

2014 ◽  
Vol 684 ◽  
pp. 375-380
Author(s):  
Deng Sheng Zheng ◽  
Jian Chen ◽  
D.F. Tao ◽  
L. Lv ◽  
Gui Cheng Wang
Keyword(s):  
Natural Frequency ◽  
High Speed ◽  
System Stability ◽  
Finite Model ◽  
High Speed Machining ◽  
Cnc Machine ◽  
And Performance ◽  
The Stability ◽  
Tooling System ◽  
And Control

Tooling system for high-speed machining is one of the key components of high-end CNC machine , its stability and reliability directly affects the quality and performance of the machine. Based on the finite element method, developing a 3D finite model of high-speed machining tool system, studying on the stability of the high Speed machining tool from the natural frequency by the method of modal analysis. Analysis the amount of the overhang and clamping of the tooling , different shank taper interference fit and under different speed conditions, which affects the natural frequency of high-speed machining tool system. Proposed to the approach of improving system stability, which also provides a theoretical basis for the development of new high-speed machining tool system.

scholarly journals New model transformations for the stability analysis of time-delay systems

2018 ◽  
Vol 51 (14) ◽  
pp. 124-129
Author(s):  
Mohammed Safi ◽  
Lucie Baudouin ◽  
Alexandre Seuret
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Delay Systems ◽  
Model Transformations ◽  
Time Delay Systems ◽  
New Model ◽  
The Stability

scholarly journals A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-26
Author(s):  
Baltazar Aguirre-Hernández ◽  
Raúl Villafuerte-Segura ◽  
Alberto Luviano-Juárez ◽  
Carlos Arturo Loredo-Villalobos ◽  
Edgar Cristian Díaz-González
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Complex Dynamical Systems ◽  
The Stability ◽  
Numerical Approaches

This paper presents a brief review on the current applications and perspectives on the stability of complex dynamical systems, with an emphasis on three main classes of systems such as delay-free systems, time-delay systems, and systems with uncertainties in its parameters, which lead to some criteria with necessary and/or sufficient conditions to determine stability and/or stabilization in the domains of frequency and time. Besides, criteria on robust stability and stability of nonlinear time-delay systems are presented, including some numerical approaches.

Sign in / Sign up

Export Citation Format

Share Document