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

Kyrychko, Yuliya N.; Blyuss, Konstantin B.; Gonzalez-Buelga, Alicia; Hogan, S. J.; Wagg, DJ

doi:10.1098/rspa.2005.1624

Cited by 94 publications

(120 citation statements)

References 20 publications

(38 reference statements)

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“…For example, some numerical results on state-dependent DDEs are ahead of the theory and suggest that certain conditions imposed in the theory are rather technical and not fundamental. One of the areas for future work for both theory and numerical methods is that of piecewisesmooth delayed systems, which have important applications, for example, in control theory [4,68], hybrid testing [51,69] and machining [22, ? ].…”

Section: Discussionmentioning

confidence: 99%

Continuation and Bifurcation Analysis of Delay Differential Equations

Roose

Szalai

2007

Understanding Complex Systems

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Mathematical modeling with delay differential equations (DDEs) is widely used in various application areas of science and engineering (e.g., in semiconductor lasers with delayed feedback, high-speed machining, communication networks, and control systems) and in the life sciences (e.g., in population dynamics, epidemiology, immunology, and physiology). Delay equations have an infinite-dimensional state space because their solution is unique only when an initial function is specified on a time interval of length equal to the largest delay. Consequently, analytical calculations are more difficult than for ordinary differential equations andnumerical methods are generally the only way to achieve a complete analysis, prediction and control of systems with time delays.Delay differential equations are a special type of functional differential equation (FDE). In FDEs the time evolution of the state variable can depend on the past in an arbitrary way as long as the dependence is a bounded function of the past. However, DDEs impose a constraint on this dependence, namely that the evolution depends only on certain past values of the state at discrete times. (We do not consider here the case of distributed delay.) The delays can be constant or state dependent. The equations can also involve delayed values of the derivative of the state, which leads to equations of neutral type.In this chapter we mainly discuss the simplest case, namely a finite number of constant delays. Specifically, we consider a nonlinear system of DDEs with constant delays τ j 0, j = 1, . . . , m, of the formwhere x(t) ∈ R n , and f : R (m+1)n+p → R n is a nonlinear smooth function depending on a number of (time-independent) parameters η ∈ R p . We assume that the delays are in increasing order and denote the maximal delay by

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Section: Discussionmentioning

confidence: 99%

Continuation and Bifurcation Analysis of Delay Differential Equations

Roose

Szalai

2007

Understanding Complex Systems

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“…In figure 1b, the pendulum oscillation angle is denoted as θ; non-zero θ(t) indicates that the excitation energy of m 1 + m 2 is transferred to drive the pendulum oscillation, such that the z N /z P vibration is reduced. Figure 6b shows the MSDP Σ P2 test rig, and an introduction to MSDP dynamics is referred to in [8,9,25]. This section will focus on presenting the experimental setting and results.…”

Section: (C) Implementation Studiesmentioning

confidence: 99%

“…In order to verify and generalize the proposed AFP improvement methods, mass-springdamper (MSD) [7] and MSD-pendulum (MSDP) [8,25] DSSs are presented in this section for implementation studies. cell is attached to the actuator in order to measure and give feedback on the force constraint signal y i .…”

Section: (C) Implementation Studiesmentioning

confidence: 99%

Modelling and control issues of dynamically substructured systems: adaptive forward prediction taken as an example

Hsiao

Chen

2014

Proc. R. Soc. A.

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Testing techniques of dynamically substructured systems dissects an entire engineering system into parts. Components can be tested via numerical simulation or physical experiments and run synchronously. Additional actuator systems, which interface numerical and physical parts, are required within the physical substructure. A high-quality controller, which is designed to cancel unwanted dynamics introduced by the actuators, is important in order to synchronize the numerical and physical outputs and ensure successful tests. An adaptive forward prediction (AFP) algorithm based on delay compensation concepts has been proposed to deal with substructuring control issues. Although the settling performance and numerical conditions of the AFP controller are improved using new directcompensation and singular value decomposition methods, the experimental results show that a linear dynamics-based controller still outperforms the AFP controller. Based on experimental observations, the least-squares fitting technique, effectiveness of the AFP compensation and differences between delay and ordinary differential equations are discussed herein, in order to reflect the fundamental issues of actuator modelling in relevant literature and, more specifically, to show that the actuator and numerical substructure are heterogeneous dynamic components and should not be collectively modelled as a homogeneous delay differential equation.

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“…They are applicable to situations in which the test structure can be divided into parts: one for which the structural behaviour is well understood and, therefore, is amenable to reliable numerical modelling, and, another that displays complicated structural behaviour and thus requires to be tested experimentally. Here the numerical and experimental models are coupled: the solution of the numerical model and the testing of the experimental model take place in real time [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. This strategy enables testing of structures with modest testing facilities.…”

Section: Introductionmentioning

confidence: 99%

Numerical aspects of a real‐time sub‐structuring technique in structural dynamics

Sajeeb¹,

Roy²,

Manohar³

2007

Numerical Meth Engineering

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SUMMARYA time domain coupling technique, involving combined computational and experimental modelling, for vibration analysis of structures built-up of linear/non-linear substructures is developed. The study permits, in principle, one or more of the substructures to be modelled experimentally with measurements being made only on the interfacial degrees of freedom. The numerical and experimental substructures are allowed to communicate in real time within the present framework. The proposed strategy involves a two-stage scheme: the first is iterative in nature and is implemented at the initial stages of the solution in a non-real-time format; the second is non-iterative, employs an extrapolation scheme and proceeds in real time. Issues on time delays during communications between different substructures are discussed. An explicit integration procedure is shown to lead to solutions with high accuracy while retaining path sensitivity to initial conditions. The stability of the integration scheme is also discussed and a method for numerically dissipating the temporal growth of high-frequency errors is presented. For systems with nonlinear substructures, the integration procedure is based on a multi-step transversal linearization method; and, to account for time delays, we employ a multi-step extrapolation scheme based on the reproducing kernel particle method. Numerical illustrations on a few low-dimensional vibrating structures are presented and these examples are fashioned after problems of seismic qualification testing of engineering structures using real-time substructure testing techniques.

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

Cited by 94 publications

References 20 publications

Continuation and Bifurcation Analysis of Delay Differential Equations

Continuation and Bifurcation Analysis of Delay Differential Equations

Modelling and control issues of dynamically substructured systems: adaptive forward prediction taken as an example

Numerical aspects of a real‐time sub‐structuring technique in structural dynamics

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