scholarly journals Delay Differential Equation Models for Real-Time Dynamic Substructuring

2005 ◽  
Author(s):  
Max Wallace ◽  
Jan Sieber ◽  
Simon Neild ◽  
David Wagg ◽  
Bernd Krauskopf
Keyword(s):  
Differential Equation ◽  
Real Time ◽  
Delay Differential Equation ◽  
Software Tool ◽  
Test System ◽  
System Stability ◽  
Delay Compensation ◽  
Time Dynamic ◽  
Dynamic Substructuring ◽  
Delay Differential

Real-time dynamic substructuring is a testing technique that models an entire system through the combination of an experimental test piece, representing part of the system, with a numerical model of the rest of the system. Delays can have a significant effect on the technique, as signals are passed between the two parts of the system in real-time. The focus of this paper is the influence of the delay on the dynamics of the substructured system. This is addressed using a linear example which may be described by a delay differential equation (DDE) model. This type of analysis allows critical delay values for system stability to be computed, which in turn can be used to help design the substructuring test system. Two methods are presented for the example considered. The first makes use of an analytical approach and the second of a numerical software tool, DDE-BIFTOOL. Normally, in substructuring tests, the actuator’s response time exceeds the critical delay time and the substructured system is unstable. It is demonstrated that the system can be stabilized using an adaptive delay compensation technique based on forward polynomial prediction. Finally we outline how these techniques may be applied to an industrial example of modelling a nonlinear spring.

A Comparison of Runge Kutta and Novel L-Stable Methods for Real-Time Integration Methods for Dynamic Substructuring

2006 ◽  
Author(s):  
Alicia Gonzalez-Buelga ◽  
David Wagg ◽  
Simon Neild ◽  
Oreste S. Bursi
Keyword(s):  
Real Time ◽  
Experimental Testing ◽  
Time Integration ◽  
Delay Compensation ◽  
Real Time Control ◽  
Time Dynamic ◽  
Time Control ◽  
Dynamic Substructuring ◽  
Integration Algorithms ◽  
Runge Kutta

In this paper we compare the performance of Runge-Kutta and novel L-stable real-time (LSRT) integration algorithms for real-time dynamic substructuring testing. Substructuring is a hybrid numerical-experimental testing method which can be used to test critical components in a system experimentally while the remainder of the system is numerically modelled. The physical substructure and the numerical model must interact in real time in order to replicate the behavior of the whole (or emulated) system. The systems chosen for our study are mass-spring-dampers, which have well known dynamics and therefore we can benchmark the performance of the hybrid testing techniques and in particular the numerical integration part of the algorithm. The coupling between the numerical part and experimental part is provided by an electrically driven actuator and a load cell. The real-time control algorithm provides bi-directional coupling and delay compensation which couples together the two parts of the overall system. In this paper we consider the behavior of novel L-stable real-time (LSRT) integration algorithms, which are based on Rosenbrock's method. The new algorithms have considerable advantages over 4th order Runge-Kutta in that they are unconditionally stable, real-time compatible and less computationally intensive. They also offer the possibility of damping out unwanted high frequencies and integrating stiff problems. The paper presents comparisons between 4th order Runge-Kutta and the LSRT integration algorithms using three experimental configurations which demonstrate these properties.

Stability Switches in a Neutral Delay Differential Equation with Application to Real-Time Dynamic Substructuring

2006 ◽  
Vol 5-6 ◽  
pp. 79-84 ◽  
Author(s):  
Y.N. Kyrychko ◽  
K.B. Blyuss ◽  
A. Gonzalez-Buelga ◽  
S.J. Hogan ◽  
David J. Wagg
Keyword(s):  
Real Time ◽  
Closed Loop ◽  
Numerical Models ◽  
Closed Loop System ◽  
Neutral Delay ◽  
Time Dynamic ◽  
Dynamic Substructuring ◽  
Delay Differential ◽  
Mass Spring ◽  
Theoretical Results

In this paper delay differential equations approach is used to model a real-time dynamic substructuring experiment. Real-time dynamic substructuring involves dividing the structure under testing into two or more parts. One part is physically constructed in the lab- oratory and the remaining parts are being replaced by their numerical models. The numerical and physical parts are connected via an actuator. One of the main difficulties of this testing technique is the presence of delay in a closed loop system. We apply real-time dynamic sub- structuring to a nonlinear system consisting of a pendulum attached to a mass-spring-damper. We will show how a delay can have (de)stabilising effect on the behaviour of the whole system. Theoretical results agree very well with experimental data.

scholarly journals The performance of delay compensation in real-time dynamic substructuring

2017 ◽  
pp. 107754631774048 ◽  
Author(s):  
Zhenyun Tang ◽  
Matt Dietz ◽  
Zhenbao Li ◽  
Colin Taylor
Keyword(s):  
Real Time ◽  
Delay Compensation ◽  
Time Dynamic ◽  
Dynamic Substructuring

A NOTE ON THE QUANTUM OF TIME

2008 ◽  
Vol 23 (16) ◽  
pp. 1161-1165 ◽  
Author(s):  
JOSÉ M. ISIDRO ◽  
J. L. GONZÁLEZ-SANTANDER ◽  
P. FERNÁNDEZ DE CÓRDOBA
Keyword(s):  
Differential Equation ◽  
Quantum Mechanics ◽  
Evolution Equation ◽  
Real Time ◽  
Delay Differential Equation ◽  
Quantum Fluctuations ◽  
Time Variable ◽  
Delay Differential

Quantum mechanics rests on the assumption that time is a classical variable. As such, classical time is assumed to be measurable with infinite accuracy. However, all real clocks are subject to quantum fluctuations, which leads to the existence of a nonzero uncertainty in the time variable. The existence of a quantum of time modifies the Heisenberg evolution equation for observables. Here we propose and analyse a generalisation of Heisenberg's equation for observables evolving in real time (the time variable measured by real clocks), that takes the existence of a quantum of time into account. This generalisation of Heisenberg's equation turns out to be a delay-differential equation.

scholarly journals Prediction of Transient Stability Using Wide Area Measurements Based on ANN

2021 ◽  
Vol 9 (11) ◽  
pp. 1373-1378
Keyword(s):  
Power System ◽  
Real Time ◽  
Transient Stability ◽  
Early Time ◽  
Test System ◽  
System Stability ◽  
Area Measurement ◽  
Wide Area ◽  
Unstable State ◽  
Time Dynamic

The concept of wide-area control and protection as an application on real-time wide-area measurement systems makes the transient stability prediction more accurate in early time after fault occurrences. The transient prediction is the first step in the dynamic control system to avoid any unwanted emergency or non-stable power system state. In this paper, an early predictionof the power system stability once the fault cleaning using real-time dynamic data collected by WAMS is proposed based on an artificial neural network (ANN). The dataset collected by the different contingency analyses on the IEEE 39 bus test system is used to train a multilayer perceptron network. Pre-fault, during- fault, and post-fault generators' speeds are fed to ANN as inputs, and the status of the overall system, either stable or not, is the output of ANN. The proposed model can predict an unstable state within 100 ms after the fault. NEPLAN simulator is used to simulate the dynamic analysis ofthe IEEE 39-Bus test system, and MATLAB 2019a is used to design the ANN.

scholarly journals Real-time dynamic substructuring in a coupled oscillator–pendulum system

2006 ◽  
Vol 462 (2068) ◽  
pp. 1271-1294 ◽  
Author(s):  
Y.N Kyrychko ◽  
K.B Blyuss ◽  
A Gonzalez-Buelga ◽  
S.J Hogan ◽  
D.J Wagg
Keyword(s):  
Real Time ◽  
Experimental Tests ◽  
Quantitative Agreement ◽  
Physical Structure ◽  
Transfer System ◽  
Neutral Delay ◽  
Pendulum System ◽  
Time Dynamic ◽  
Dynamic Substructuring ◽  
Delay Differential

Real-time dynamic substructuring is a powerful testing method, which brings together analytical, numerical and experimental tools for the study of complex structures. It consists of replacing one part of the structure with a numerical model, which is connected to the remainder of the physical structure (the substructure) by a transfer system. In order to provide reliable results, this hybrid system must remain stable during the whole test. A primary mechanism for destabilization of these type of systems is the delays which are naturally present in the transfer system. In this paper, we apply the dynamic substructuring technique to a nonlinear system consisting of a pendulum attached to a mechanical oscillator. The oscillator is modelled numerically and the transfer system is an actuator. The system dynamics is governed by two coupled second-order neutral delay differential equations. We carry out local and global stability analyses of the system and identify the delay dependent stability boundaries for this type of system. We then perform a series of hybrid experimental tests for a pendulum–oscillator system. The results give excellent qualitative and quantitative agreement when compared to the analytical stability results.

scholarly journals Modelling real-time dynamic substructuring using partial delay differential equations

2007 ◽  
Vol 463 (2082) ◽  
pp. 1509-1523 ◽  
Author(s):  
Y.N Kyrychko ◽  
S.J Hogan ◽  
A Gonzalez-Buelga ◽  
D.J Wagg
Keyword(s):  
Real Time ◽  
Virtual Environment ◽  
Experimental Tests ◽  
Beam Equation ◽  
Real Time Control ◽  
Oscillator System ◽  
Time Dynamic ◽  
Time Control ◽  
Dynamic Substructuring ◽  
Delay Differential

Real-time dynamic substructuring is a new component testing method for simulating the dynamics of complex engineering systems. The physical component is tested within a computer-generated ‘virtual’ environment using real-time control techniques. Delays in communication which occur between the component and the virtual environment can potentially destabilize the simulation. In this paper, the mechanism for this instability is examined using a beam-oscillator system as a case study. We will show how the stability and the amplitude response of the system change with the time delay. Numerical simulations of the reduced system as well as a full-delayed beam equation are performed. A series of experimental tests is carried out on a beam-oscillator system. Comparison of the theoretical, numerical and experimental results is presented and these agree remarkably well.

scholarly journals An adaptive polynomial based forward prediction algorithm for multi-actuator real-time dynamic substructuring

2005 ◽  
Vol 461 (2064) ◽  
pp. 3807-3826 ◽  
Author(s):  
M.I Wallace ◽  
D.J Wagg ◽  
S.A Neild
Keyword(s):  
Real Time ◽  
Numerical Models ◽  
Single Step ◽  
Prediction Algorithm ◽  
Delay Compensation ◽  
Basic Algorithm ◽  
Time Dynamic ◽  
Dynamic Substructuring ◽  
Forward Prediction ◽  
Mass Spring

Real-time dynamic substructuring is a novel experimental technique used to test the dynamic behaviour of complex structures. The technique involves creating a hybrid model of the entire structure by combining an experimental test piece—the substructure—with a set of numerical models. In this paper we describe a multi-actuator substructured system of a coupled three mass–spring–damper system and use this to demonstrate the nature of delay errors which can first lead to a loss of accuracy and then to instability of the substructuring algorithm. Synchronization theory and delay compensation are used to show how the delay errors, present in the transfer systems, can be minimized by online forward prediction. This new algorithm uses a more generic approach than the single step algorithms applied to substructuring thus far, giving considerable advantages in terms of flexibility and accuracy. The basic algorithm is then extended by closing the control loop resulting in an error driven adaptive feedback controller which can operate with no prior knowledge of the plant dynamics. The adaptive algorithm is then used to perform a real substructuring test using experimentally measured forces to deliver a stable substructuring algorithm.

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