Noncolocated Control of a Damped String Using Time Delay

1992 ◽  
Vol 114 (4) ◽  
pp. 736-740 ◽  
Author(s):  
B. Yang
Keyword(s):  
Control System ◽  
Time Delay ◽  
Laplace Transform ◽  
Feedback Loop ◽  
Transform Domain ◽  
Flexible Systems ◽  
Specific Time ◽  
Bode Plot ◽  
Control Gain ◽  
The Laplace Transform

Recent research studies noncolocated control of flexible mechanical systems using time delay. The developments are limited to undamped flexible systems; damped flexible systems have not been considered. This paper investigates noncolocated vibration control of a viscously damped string using time delay. The control system is formulated in the Laplace transform domain. Based on the understanding of the system eigenstructure, a modified Bode plot of the feedback controller is introduced in a design region. The Bode plot designed, along with a specific time delay in the feedback loop, proper sensor and actuator positions, and proper control gain, guarantees stabilization of vibration of the damped string.

Stability and Controllability of Euler-Bernoulli Beams With Intelligent Constrained Layer Treatments

1996 ◽  
Vol 118 (1) ◽  
pp. 70-77 ◽  
Author(s):  
I. Y. Shen
Keyword(s):  
Laplace Transform ◽  
Closed Form ◽  
Characteristic Equation ◽  
Matrix Equation ◽  
Homogeneous Equation ◽  
Transform Domain ◽  
Threshold Control ◽  
Control Gain ◽  
The Laplace Transform ◽  
The Stability

This paper studies the stability and controllability of Euler-Bernoulli beams whose bending vibration is controlled through intelligent constrained layer (ICL) damping treatments proposed by Baz (1993) and Shen (1993, 1994). First of all, the homogeneous equation of motion is transformed into a first order matrix equation in the Laplace transform domain. According to the transfer function approach by Yang and Tan (1992), existence of nontrivial solutions of the matrix equation leads to a closed-form characteristic equation relating the control gain and closed-loop poles of the system. Evaluating the closed-form characteristic equation along the imaginary axis in the Laplace transform domain predicts a threshold control gain above which the system becomes unstable. In addition, the characteristic equation leads to a controllability criterion for ICL beams. Moreover, the mathematical structure of the characteristic equation facilitates a numerical algorithm to determine root loci of the system. Finally, the stability and controllability of Euler-Bernoulli beams with ICL are illustrated on three cantilever beams with displacement or slope feedback at the free end.

On Time Delay in Noncolocated Control of Flexible Mechanical Systems

1992 ◽  
Vol 114 (3) ◽  
pp. 409-415 ◽  
Author(s):  
B. Yang ◽  
C. D. Mote
Keyword(s):  
Control System ◽  
Time Delay ◽  
Mechanical System ◽  
Mechanical Systems ◽  
Vibration Measurement ◽  
System Response ◽  
Specific Time ◽  
Sensors And Actuators ◽  
Stabilizing Controllers ◽  
Flexible Mechanical System

A new method is presented for noncolocated control of flexible mechanical systems. The destabilizing effect of noncolocation of sensors and actuators is eliminated through introduction of specific time delay block(s) in the control system. The time delay constants in those blocks depend on the system eigenstructure. For a given flexible mechanical system, if there exists a time delay relation, the system response at one point can be exactly predicted from the vibration measurement at other point(s) of the system. In this case all stabilizing controllers from colocated control can be directly used. The time delay theory is verified by experiments on noncolocated control of a translating string.

scholarly journals Consensus of Multiagent Systems with Directed Topology and Communication Time Delay Bases on the Laplace Transform

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Bo Liu ◽  
Li Wang ◽  
Dehui Sun ◽  
Xinmao Zhu
Keyword(s):  
Time Delay ◽  
Laplace Transform ◽  
Multiagent Systems ◽  
Consensus Problem ◽  
Directed Topology ◽  
Communication Time ◽  
The Laplace Transform ◽  
Initial States ◽  
Directed Topologies ◽  
Theoretical Results

This paper investigates the consensus problem of multiagent systems with directed topologies. Different from the literatures, a new method, the Laplace transform, to study the consensus of multiagent systems with directed topology and communication time delay is proposed. The accurate state of the consensus center and the upper bound of the communication delay to make the agents reach consensus are given. It is proved that all the agents could aggregate and eventually form a cohesive cluster in finite time under certain conditions, and the consensus center is only determined by the initial states and the communication configuration among the agents. Finally, simulations are given to illustrate the theoretical results.

Propagation of Discontinuities in Coupled Thermoelastic Problems

1968 ◽  
Vol 35 (3) ◽  
pp. 489-494 ◽  
Author(s):  
B. A. Boley ◽  
R. B. Hetnarski
Keyword(s):  
Heat Flux ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Applied Strain ◽  
Transform Domain ◽  
Arbitrary Boundary ◽  
One Dimensional ◽  
The Laplace Transform ◽  
Thermoelastic Problems

The character and magnitude of traveling discontinuities in one-dimensional coupled transient thermoelastic problems are studied. For this purpose, 16 different fundamental problems are considered in detail, by examination of the nature of the solutions in the Laplace-transform domain. These problems correspond to various combinations of applied strain or stress as mechanical variables, and of applied temperature or heat flux as thermal variables. A system of classification of discontinuities is devised, which permits the results of the 16 problems to be extended to some general conclusions as to the character of the discontinuities in cases of arbitrary boundary conditions.

Thermodiffusion with two time delays and Kernel functions

2016 ◽  
Vol 23 (2) ◽  
pp. 195-208 ◽  
Author(s):  
Ahmed S El-Karamany ◽  
Magdy A Ezzat ◽  
Alaa A El-Bary
Keyword(s):  
Laplace Transform ◽  
Kernel Functions ◽  
Transform Domain ◽  
Thermoelastic Diffusion ◽  
One Dimensional ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Isotropic Elastic Medium ◽  
Time Variations ◽  
With Memory

The present work is concerned with the investigation of disturbances in a homogeneous, isotropic elastic medium with memory-dependent derivatives (MDDs). A one-dimensional problem is considered for a half-space whose surface is traction free and subjected to the effects of thermodiffusion. For treatment of time variations, the Laplace-transform technique is utilized. The theories of coupled and of generalized thermoelastic diffusion with one relaxation time follow as limit cases. A direct approach is introduced to obtain the solutions in the Laplace transform domain for different forms of kernel functions and time delay of MDDs, which can be arbitrarily chosen. Numerical inversion is carried out to obtain the distributions of the considered variables in the physical domain and illustrated graphically. Some comparisons are made and shown in figures to estimate the effects of MDD parameters on all studied fields.

scholarly journals Transient Analysis of Dynamic Crack Propagation With Boundary Effect

1995 ◽  
Vol 62 (4) ◽  
pp. 1029-1038 ◽  
Author(s):  
Chien-Ching Ma ◽  
Yi-Shyong Ing
Keyword(s):  
Fundamental Solution ◽  
Crack Propagation ◽  
Laplace Transform ◽  
Fundamental Problem ◽  
Boundary Effect ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Transform Domain ◽  
Propagating Crack ◽  
The Laplace Transform

In this study, a dynamic antiplane crack propagation with constant velocity in a configuration with boundary is investigated in detail. The reflected cylindrical waves which are generated from the free boundary will interact with the propagating crack and make the problem extremely difficult to analyze. A useful fundamental solution is proposed in this study and the solution is determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in the Laplace transform domain) on the propagating crack faces. The Cagniard’s method for Laplace inversion is used to obtain the transient solution in time domain. Numerical results of dynamic stress intensity factors for the propagation crack are evaluated in detail.

scholarly journals Dynamic Crack Propagation in a Layered Medium Under Antiplane Shear

1997 ◽  
Vol 64 (1) ◽  
pp. 66-72 ◽  
Author(s):  
Chien-Ching Ma ◽  
Yi-Shyong Ing
Keyword(s):  
Stress Intensity ◽  
Fundamental Solution ◽  
Laplace Transform ◽  
Dynamic Stress ◽  
Layered Medium ◽  
Transform Domain ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Propagating Crack ◽  
The Laplace Transform

In this study, the transient analysis of dynamic antiplane crack propagation with a constant velocity in a layered medium is investigated. The individual layers are isotropic and homogeneous. Infinite numbers of reflected cylindrical waves, which are generated from the interface of the layered medium, will interact with the propagating crack and make the problem extremely difficult to analyze. A useful fundamental solution is proposed in this study, and the solution can be determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in the Laplace transform domain) on the propagating crack faces. The Cagniard’s method for Laplace inversion is used to obtain the transient solution in time domain. The exact closed-form transient solutions of dynamic stress intensity factors are expressed in compact formulations. These solutions are valid for an infinite length of time and have accounted for contributions from all the incident and reflected waves interaction with the moving crack tip. Numerical results of dynamic stress intensity factors for the propagation crack in layered medium are evaluated and discussed in detail.

scholarly journals Synchronization of Different Fractional Order Time-Delay Chaotic Systems Using Active Control

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Jianeng Tang
Keyword(s):  
Time Delay ◽  
Laplace Transform ◽  
Numerical Simulations ◽  
Active Control ◽  
Fractional Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Technique ◽  
The Laplace Transform

Chaos synchronization of different fractional order time-delay chaotic systems is considered. Based on the Laplace transform theory, the conditions for achieving synchronization of different fractional order time-delay chaotic systems are analyzed by use of active control technique. Then numerical simulations are provided to verify the effectiveness and feasibility of the developed method. At last, effects of the fraction order and the time delay on synchronization are further researched.

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