Active Vibration Suppression With Time Delayed Feedback

2003 ◽  
Vol 125 (3) ◽  
pp. 384-388 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Vibration Suppression ◽  
Linear Time ◽  
Direct Method ◽  
System Stability ◽  
Delayed Systems ◽  
Active Vibration Suppression ◽  
Active Vibration ◽  
The Stability

Various active vibration suppression techniques, which use feedback control, are implemented on the structures. In real application, time delay can not be avoided especially in the feedback line of the actively controlled systems. The effects of the delay have to be thoroughly understood from the perspective of system stability and the performance of the controlled system. Often used control laws are developed without taking the delay into account. They fulfill the design requirements when free of delay. As unavoidable delay appears, however, the performance of the control changes. This work addresses the stability analysis of such dynamics as the control law remains unchanged but carries the effect of feedback time-delay, which can be varied. For this stability analysis along the delay axis, we follow up a recent methodology of the authors, the Direct Method (DM), which offers a unique and unprecedented treatment of a general class of linear time invariant time delayed systems (LTI-TDS). We discuss the underlying features and the highlights of the method briefly. Over an example vibration suppression setting we declare the stability intervals of the dynamics in time delay space using the DM. Having assessed the stability, we then look at the frequency response characteristics of the system as performance indications.

A New Perspective for Time Delayed Control Systems With Application to Vibration Suppression

2002 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Time Delay ◽  
Control Systems ◽  
Vibration Suppression ◽  
Linear Time ◽  
Direct Method ◽  
Interesting Property ◽  
System Stability ◽  
Delayed Systems ◽  
Linear Time Invariant ◽  
The Stability

Most control systems are contaminated with some level of time delay. Whether it appears due to the inherent system dynamics or because of the sensory feedback, the delay has to be resolved regarding the system stability. We explain an unprecedented and fundamental treatment of time delay in a general class of linear time invariant systems (LTI) following a strategy, which we call the ‘Direct Method’. The strengths of the method lie in recognizing two interesting and novel features, which are typical for this class of systems. These features enable a structured strategy to be formed for analyzing the stability of LTI-TDS (Time Delayed Systems). Vibration control settings are not immune from time delay effects. We present a case study on active control of vibration using linear full state feedback. We then apply the Direct Method on this structure to display the stability outlook along the axis of delay. There appears an interesting property, which is related to the determination of the imaginary (i.e. marginally stable) roots of LTI-TDS. We state a general lemma and proof on this point.

Degenerate Cases in Using the Direct Method

2003 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Linear Time ◽  
Direct Method ◽  
Degenerate System ◽  
Delayed Systems ◽  
Linear Time Invariant ◽  
The Stability ◽  
Time Invariant ◽  
Degenerate Cases

A practical stability analysis, the Direct Method, for linear time invariant, time delayed systems (LTI-TDS) is revisited in this work considering the degenerate system dynamics. The principal strengths and enabling novelties of the method are reviewed along with its structured steps involved for assessing the stability. Uncommon in the literature, the Direct Method can handle large dimensional systems (e.g. larger than 2) very comfortably, it returns an explicit formula for the exact stability posture of the system for a given time delay, as such it reveals the possible detached stability pockets throughout the time delay axis. Both retarded and neutral classes of LTI-TDS are considered in this work. The main contribution here is to demonstrate the ability of the Direct Method in tackling degenerate cases. Along with the analytical arguments, example case studies are provided for a group of degeneracies. It is shown that the new method is capable of resolving them without any difficulty.

Degenerate Cases in Using the Direct Method

2003 ◽  
Vol 125 (2) ◽  
pp. 194-201 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Linear Time ◽  
Direct Method ◽  
Degenerate System ◽  
Delayed Systems ◽  
Linear Time Invariant ◽  
The Stability ◽  
Time Invariant ◽  
Degenerate Cases

A recent stability analysis, the Direct Method, for linear time invariant, time delayed systems (LTI-TDS) is revisited in this work considering the degenerate system dynamics. The principal strengths and enabling novelties of the method are reviewed along with its structured steps involved for assessing the stability. Uncommon in the literature, the Direct Method can handle large dimensional systems (e.g., larger than two) very comfortably. It returns an explicit formula for the exact stability posture of the system for a given time delay, as such it reveals the possible detached stability pockets throughout the time delay axis. Both retarded and neutral classes of LTI-TDS are considered in this work. The main contribution here is to demonstrate the ability of the Direct Method in tackling degenerate cases. Along with the analytical arguments, example case studies are provided for a group of degeneracies. It is shown that the new method is capable of resolving them without any difficulty.

Stability Analysis of Multiple Time Delayed Systems Using the Direct Method

2003 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delays ◽  
Linear Time ◽  
Direct Method ◽  
Multiple Time ◽  
Delayed Systems ◽  
Practical Applications ◽  
Linear Time Invariant ◽  
Multiple Time Delays ◽  
The Stability

A novel treatment for the stability of a class of linear time invariant (LTI) systems with rationally independent multiple time delays using the Direct Method (DM) is studied. Since they appear in many practical applications in the systems and control community, this class of dynamics has attracted considerable interest. The stability analysis is very complex because of the infinite dimensional nature (even for single delay) of the dynamics and furthermore the multiplicity of these delays. The stability problem is much more challenging compared to the TDS with commensurate time delays (where time delays have rational relations). It is shown in an earlier publication of the authors that the DM brings a unique, exact and structured methodology for the stability analysis of commensurate time delayed cases. The transition from the commensurate time delays to multiple delay case motivates our study. It is shown that the DM reveals all possible stability regions in the space of multiple time delays. The systems that are considered do not have to possess stable behavior for zero delays. We present a numerical example on a system, which is considered “prohibitively difficult” in the literature, just to exhibit the strengths of the new procedure.

The Stability Analysis and Planning for Multivariable Linear Time-Delay Systems and its Application in Supervision Oilfield

2013 ◽  
Vol 709 ◽  
pp. 727-730
Author(s):  
Ren Wang ◽  
Xue Kun Qi ◽  
Long Xing
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Linear Time ◽  
Control Process ◽  
Delay Systems ◽  
Sufficient Condition ◽  
Water Separation ◽  
Delayed Systems ◽  
Delayed System ◽  
The Stability

Based on Lyapunovs theory of stability, analyze on a control process of oil-water separation with time-delay, coupling and uncertainty in the unite station. a equation of sufficient condition for multi-variable Linear Delayed Systems with delayed independent stabilization is derived and another forms are also given. Based on this, several simple criterions for judging independent stabilization from linear delayed system are presented. We also discuss the exponential stability for delayed system and also provide the sufficient condition of exponential stability with any appointed convergent rate and its corresponding deductions. Using these conditions, we can choose a set of suitable parameters to reduce the conservation. By calculating and being compared with methods of the literature, the results show that our methods have less conservation.

Design and Stability Analysis of Delayed Resonator With Acceleration Feedback

2013 ◽  
Author(s):  
Tomáš Vyhlídal ◽  
Nejat Olgac ◽  
Vladimír Kučera
Keyword(s):  
Vibration Suppression ◽  
Dynamics Analysis ◽  
Stability Boundaries ◽  
Single Degree Of Freedom ◽  
Stability Margins ◽  
Single Degree ◽  
Active Vibration Suppression ◽  
Acceleration Feedback ◽  
Active Vibration ◽  
The Stability

This paper deals with the problem of active vibration suppression using the concept of delayed resonator with acceleration feedback. A complete dynamics analysis of the resonator and its coupling with a single degree of freedom mechanical system are performed. It is shown that due to presence of a delay in the derivative feedback, the dynamics of the resonator itself, as well as the dynamics of its coupling with the system are of neutral character. Subsequently, the spectral approach is used to obtain the stability boundaries in the space of the resonator parameters. Both, analytical and numerical methods are employed in the analysis. As the contributions, we display a methodology to determine the resonator parameters in order to guarantee desirable functioning of the resonator and to provide safe stability margins. An example is included to demonstrate these analytical results.

Synthesis and Experimental Validation of a Delayed Reference Controller for Active Vibration Suppression in Mechanical Systems

2004 ◽  
Vol 72 (4) ◽  
pp. 623-627 ◽  
Author(s):  
P. Gallina ◽  
A. Trevisani
Keyword(s):  
Time Delay ◽  
Vibration Control ◽  
Experimental Validation ◽  
Vibration Suppression ◽  
Overhead Cranes ◽  
Simple Pendulum ◽  
Active Vibration Suppression ◽  
Control Scheme ◽  
Active Vibration ◽  
Two Degree Of Freedom

This paper introduces a non-time-based control scheme for active position and vibration control of two-degree-of-freedom systems by applying it to the path-tracking and swing control of a system composed of a trolley and a simple pendulum. The basic idea behind such a scheme is to make the path reference of the trolley a function of the time and of a time delay. This latter, which is affected by the measured oscillation, is calculated on-the-fly in order to reduce the swing phenomenon. The effectiveness of the proposed control scheme, which may have application to the control of overhead cranes, is proved experimentally.

scholarly journals Agile Attitude Maneuvers with Active Vibration-suppression for Flexible-spacecraft

2021 ◽  
Author(s):  
Zhang Jianqiao ◽  
Xianglong Kong ◽  
Chuang Liu ◽  
Qing Deng
Keyword(s):  
Vibration Suppression ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Flexible Spacecraft ◽  
Robust Controller ◽  
Adaptive Sliding Mode Controller ◽  
Control Moment ◽  
Active Vibration Suppression ◽  
Active Vibration ◽  
The Stability

Abstract This paper addresses the agile attitude stabilization maneuver control of flexible-spacecraft using control moment gyros (CMGs) in the absence of modal information. Here, piezoelectric actuators are employed to actively suppress the vibration of flexible appendages. Both the attitude dynamics and the proposed robust controller are globally developed on the Special Orthogonal Group SO(3), avoiding ambiguities and singularities associated with other attitude representations. More specifically, an observer is first designed to estimate the modal information of vibration. A robust control law is developed by synthesizing a proportional derivative (PD) controller, an adaptive sliding mode controller, and an active vibration-suppression controller, which use the information of the estimated structural modes. The stability of the closed-loop system is proved using Lyapunov stability theory. Finally, numerical examples are performed to show the effectiveness of the proposed method.

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