• International Journal of Control, Automation, and Systems
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• v.3 no.3
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• pp.387-396
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• 2005

The Rotational/Translational Actuator (RTAC) benchmark problem considers a fourth-order dynamical system involving the nonlinear interaction of a translational oscillator and an eccentric rotational proof mass. This problem has been posed to investigate the utility of a rotational actuator for stabilizing translational motion. In order to experimentally implement any of the model-based controllers proposed in the literature, the values of model parameters are required which are generally difficult to determine rigorously. In this paper, an approach to the least-squares estimation of the parameters of a system is formulated and practically applied to the RTAC system. On the other hand, this paper shows how to model a nonlinear system as a linear uncertain system via nonparametric system identification, in order to provide the information required for linear robust $H_\infty$ control design. This method is also applied to the RTAC system, which demonstrates severe nonlinearities, due to the coupling from the rotational motion to the translational motion. Experimental results confirm that this approach can effectively condense the whole nonlinearities, uncertainties, and disturbances within the system into a favorable perturbation block.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.17 no.1
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• pp.42-47
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• 2018

This paper describes the dynamical behavior of the bicycle and its nonlinear effect when magnetic repulsive forces are applied to the bicycle cushion system. A finite-element method was used to obtain its reliabilities by comparing the experimental and numerical values and select the proper magnet sizes. The Equivalent spring stiffness values were evaluated in terms of both linear and nonlinear approximations, where the nonlinear effect was specifically investigated for the ride comfort. The corresponding equations of linear and nonlinear motion were derived for the numerical model with three degrees of freedom. Dynamic behaviors were observed when the bicycle ran over a curvilinear road in the form of a sinusoidal curve. The analysis in this paper for the observed nonlinearity of magnetic repulsive forces will be a useful guide to more accurately predict the cushion design for any vehicle system.

• International Journal of Contents
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• v.9 no.4
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• pp.1-10
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• 2013

The electroencephalogram (EEG) time series is a measure of electrical activity received from multiple electrodes placed on the scalp of a human brain. It provides a direct measurement for characterizing the dynamic aspects of brain activities. These EEG signals are formed from a series of spatial and temporal data with multiple dimensions. Missing data could occur due to fault electrodes. These missing data can cause distortion, repudiation, and further, reduce the effectiveness of analyzing algorithms. Current methodologies for EEG analysis require a complete set of EEG data matrix as input. Therefore, an accurate and reliable imputation approach for missing values is necessary to avoid incomplete data sets for analyses and further improve the usage of performance techniques. This research proposes a new method to automatically recover random consecutive missing data from real world EEG data based on Linear Dynamical System. The proposed method aims to capture the optimal patterns based on two main characteristics in the coevolving EEG time series: namely, (i) dynamics via discovering temporal evolving behaviors, and (ii) correlations by identifying the relationships between multiple brain signals. From these exploits, the proposed method successfully identifies a few hidden variables and discovers their dynamics to impute missing values. The proposed method offers a robust and scalable approach with linear computation time over the size of sequences. A comparative study has been performed to assess the effectiveness of the proposed method against interpolation and missing values via Singular Value Decomposition (MSVD). The experimental simulations demonstrate that the proposed method provides better reconstruction performance up to 49% and 67% improvements over MSVD and interpolation approaches, respectively.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.3
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• pp.173-182
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• 2014

The mixed convolved action principle provides a new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics in terms of mixed formulation, convolution, and fractional calculus. In this paper, its potential in the development of numerical methods for transient problems in various dynamical systems when adopting temporally second order approximation is investigated. For this, the classical single-degree-of-freedom linear elastic dynamical systems are primarily considered to investigate computational characteristics of the developed algorithms. For the undamped system, all the developed algorithms are symplectic with respect to the time step. For the damped system, they are shown to be accurate with good convergence characteristics.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.125-128
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• 1999

A linear time-invariant model can be described either by a parametric model or by a nonparametric model. Nonparametric models, for which a priori information is not necessary, are basically the response of the dynamic system such as impulse response model and frequency models. Parametric models, such as transfer function models, can be easily described by a small number of parameters. In this paper aiming to take benefit from both types of models, we will use linear-combination of basis fuctions in an impulse response using a few parameters. We will expand and generalize the Kautz functions as basis functions for dynamical system representations and we will consider estimation problem of transfer functions using Kautz function. And so we will present the influences of poles settings of Kautz function on the identification accuracy.

• Bulletin of the Korean Chemical Society
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• v.24 no.8
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• pp.1107-1110
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• 2003

Valuable insight into the nonlinear dynamics of a system can be gleaned from its response to a single intense short pulse. We derive expressions for the corresponding nonlinear response functions and show that the fluctuation-dissipation theorem may be extended beyond the linear response limit to an arbitrary pulse intensity. As an illustrative example, we calculate response functions up to 11th order for the regular Lorentz gas in two dimensions.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.7
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• pp.483-490
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• 2004

The descriptor system model has a high ability in representing dynamical systems. It can preserve physical parameters in the coefficient matrices, and describe the dynamic part, static part, and even the improper part of the system in the same form. The design of mixed $H_{2}/H_{\infty}$ controllers for linear time-invariant descriptor systems is considered in this paper. Firstly, an $H_2$ and $H_{\infty}$ synthesis problems fur a descriptor system are presented separately in terms of linear matrix inequalities (LMIs) based on the bounded real lemma. Then, we show that the existence of a mixed $H_2/H_{\infty}$ controller by which the $H_2$ norm of the second channel is minimized while keeping the $H_2$ norm bound of the first channel less than ${\gamma}$, is reduced to the linear objective minimization problem. The class of desired controllers that are assumed to have the same structure as the plant is parameterized by using the linearizing change of variables.

• Structural Engineering and Mechanics
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• v.32 no.1
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• pp.179-191
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• 2009

A stochastic response spectrum method is proposed for simple evaluation of the structural response of an actively controlled aseismic structure. The response spectrum is constructed assuming a linear structure with an active mass damper (AMD) system, and an earthquake wave model given by the product of a non-stationary envelope function and a stationary Gaussian random process with Kanai-Tajimi power spectral density. The control design is executed using a linear quadratic Gaussian control strategy for an enlarged state space system, and the response amplification factor is given by the combination of the obtained statistical response values and extreme value theory. The response spectrum thus produced can be used for simple dynamical analyses. The response factors obtained by this method for a multi-degree-of-freedom structure are shown to be comparable with those determined by numerical simulations, demonstrating the validity and utility of the proposed technique as a simple design tool. This method is expected to be useful for engineers in the initial design stage for structures with active aseismic control.

• Journal of Mechanical Science and Technology
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• v.19 no.spc1
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• pp.227-236
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• 2005

Multibody system dynamics is based on classical mechanics and its engineering applications originating from mechanisms, gyroscopes, satellites and robots to biomechanics. Multibody system dynamics is characterized by algorithms or formalisms, respectively, ready for computer implementation. As a result simulation and animation are most convenient. Recent developments in multibody dynamics are identified as elastic or flexible systems, respectively, contact and impact problems, and actively controlled systems. Based on the history and recent activities in multibody dynamics, recursive algorithms are introduced and methods for dynamical analysis are presented. Linear and nonlinear engineering systems are analyzed by matrix methods, nonlinear dynamics approaches and simulation techniques. Applications are shown from low frequency vehicles dynamics including comfort and safety requirements to high frequency structural vibrations generating noise and sound, and from controlled limit cycles of mechanisms to periodic nonlinear oscillations of biped walkers. The fields of application are steadily increasing, in particular as multibody dynamics is considered as the basis of mechatronics.

• Journal of Wetlands Research
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• v.21 no.3
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• pp.236-243
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• 2019

Hydrologic time series has been analyzed and forecasted by using classical linear models. However, there is growing evidence of nonlinear structure in natural phenomena and hydrologic time series associated with their patterns and fluctuations. Therefore, the classical linear techniques for time series analysis and forecasting may not be appropriate for nonlinear processes. Daily streamflow series at St. Johns river near Cocoa, Florida, USA showed an interesting result of a low dimensional, nonlinear dynamical system but daily inflow at Soyang reservoir, South Korea showed stochastic property. Based on the chaotic dynamical characteristic, DVS (deterministic versus stochastic) algorithm is used for short-term forecasting, as well as for exploring the properties of the system. In addition to the use of DVS algorithm, a neural network scheme for the forecasting of the daily streamflow series can be used and the two techniques are compared in this study. As a result, the daily streamflow which has chaotic property showed much more accurate result in short term forecasting than stochastic data.