• Journal of Institute of Control, Robotics and Systems
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• v.16 no.4
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• pp.313-318
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• 2010

This paper deals with the relationship between zeros and step response of the second and third order LTI (Linear Time Invariant) SISO (Single-Input and Single-Output) systems with complex poles. Although it has been known that the maximum number of local extrema is less than the number of zeros in the system with only real poles[8], some cases with complex poles are shown in this paper to have many local extrema. This paper proposes monotone nondecreasing conditions and describes the relationship between the transient response and the number of local extrema in step response with each region of zeros.

• Proceedings of the KIEE Conference
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• 1993.07a
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• pp.323-325
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• 1993

In this paper, an output feedback controller is proposed for continuous time-invariant linear systems. The proposed controller, LQ-FIR consists of an LQ control gain and an optimal FIR filter. The LQ-FIR controller is derived, and the stability of the closed loop system is proved. The bounds of parameter variations guaranteeing the closed loop stability are obtained, when the LQ-FIR controller is applied to the system with model uncertainties.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.25 no.6
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• pp.422-432
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• 2013

A System Identification method to develop parametric models linking free surface elevation and wave pressure is presented and two models are built allowing for either wave pressure or free surface elevation simulation. Linear, time invariant model structures with static nonlinearities are assumed and solutions are sought in a form of autoregressive model with extra input (ARX). An arbitrary chosen free-surface elevation and wave pressure dataset is used for estimation of the models, which are subsequently verified against datasets with similar pressure gauge depth but different free-surface elevation spectra due to different meteorological conditions. It is shown that free-surface simulation using System Identification methods can perform better than traditional linear transfer function derived from linear wave theory (LTF), while wave pressure simulation quality using presented methods is generally similar to that obtained with corrected LTF.

• Journal of Advanced Navigation Technology
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• v.19 no.6
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• pp.574-580
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• 2015

The stability condition of linear discrete interval systems with a time-varying delay time is considered. The considered system has interval system matrices for both non-delayed and delayed states with time-varying delay time within given interval values. The proposed condition is derived by using Lyapunov stability theory and expressed by very simple inequality. Compared to previous results, the stability issue on the interval systems is expanded to time-varying delay. Furthermore, the new condition can imply the existing results on the time-invariant case and show the relation between interval time-varying delay time and stability of the system. The proposed condition can be applied to find the stability bound of the discrete interval system. Some numerical examples are given to show the effectiveness of the new condition and comparisons with the previously reported results are also presented.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.4
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• pp.289-294
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• 2011

Digital redesign is yet another efficient tool to convert a pre-designed analog controller into a sampled-data one to maintain the analog closed-loop performance in the sense of state matching. A rising difficulty in developing a digital redesign technique for trackers with time-varying references is the unavailability of a closed-form discrete-time model of a system, even if it is linear time-invariant. A way to resolve this is to approximate the time-varying reference as a piecewise constant one, which deteriorates the state matching performance. Another remedy may be to decrease a sampling period, which however could numerically destabilize the optimization-based digital redesign condition. In this paper, we develop a digital redesign condition for time-varying trackers by approximating the time-varying reference through a triangular hold and by introducing delta-operated discrete-time models. It is shown that the digitally redesigned sampled-data tracker recovers the performance of the pre-designed analog tracker under a fast sampling limit. Simulation results on the formation flying of satellites convincingly show the effectiveness of the development.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.5
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• pp.411-418
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• 2006

There are mainly two types of bang-bang controllers for nominal linear time-invariant (LTI) system. Optimal bang-bang controller is designed based on optimal control theory and suboptimal bang-bang controller is obtained by using Lyapunov stability condition. In this paper, the suboptimal bang-bang control method is extended to LTI system involving both control input saturation and structured real parameter uncertainties by using Lyapunov robust stability condition. Two robust optimal bang-bang controllers are derived by minimizing the time derivative of Lyapunov function subjected to the limit of control input. The one is developed based on the classical quadratic stability(QS), and the other is developed based on the affine quadratic stability(AQS). And characteristics of the two controllers are compared. Especially, bounds of parameter uncertainties which theoretically guarantee robust stability of the two controllers are compared quantitatively for 1DOF vibrating system. Moreover, the validity of robust optimal bang-bang controller based on the AQS is shown through numerical simulations for this system.

• Structural Engineering and Mechanics
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• v.49 no.4
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• pp.427-448
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• 2014

At present, the time of easy oil and gas is over. Now, the largest part of fossil fuels is concentrated in the deepest levels of tectonic structures and in the sea shelves. One of the most cumbersome operations of their extraction is the bore-hole drilling. In connection with austere tectonic and climate conditions, their drivage every so often is associated with great and diversified technological difficulties causing emergencies on frequent occasions. As a rule, they are linked with drill string accidents. A key role in prediction of these situations should play methods of theoretical modelling. For this reason, there is a growing need for development and implementation of new numerical methods for computer simulation of critical and post-critical behavior of drill strings (DSs). In this paper, the processes of non-linear deforming of a DS in cylindrical cavity of a deep bore-hole are considered. On the basis of the theory of curvilinear flexible rods, non-linear constitutive differential equations are deduced. The effects of the longitudinal non-uniform preloading, action of torque and interaction between the DS and the bore-hole surface are taken into account. Owing to the use of curvilinear coordinates in the constraining cylindrical surface and a specially chosen concomitant reference frame, it became possible to separate the desired variables and to reduce the total order of the equation system. To solve it, the method of continuation the solution by parameter and the transfer matrix technique are applied. As a result of the completed numerical analysis, the critical states of the DS loading in the cylindrical channels of inclined bore-holes are found. It is shown that the modes of the post-critical deforming of the DS are associated with its irregular spiral curving prevailing in the zone of bottom-hole-assembly. The possibility of invariant state generation during post-critical deforming is established, condition of its bifurcation is formulated. It is shown that infinite variety of loads can correspond to one geometrical configuration of the DS. They differ each from other by contact force functions.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.8
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• pp.78-86
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• 2000

This study identified a linear time-invariant mathematical model of each stand of a five-stand tandem cold mill. Two model identification methods are applied to construct a linear model of each stand of the tandem cold mill. For the model identification the input-output data that have interstand interference property in tandem cold rolling are obtained from a nonlinear simulator of the tandem cold mill. And a linear model of each stand is identified with N4SD(numerical algorithms for subspace state space system identification) method based on a state-space model and Least Square algorithm based on a transfer function. Furthermore a modeling error of the tandem cold mill is quantitatively analyzed from a maximum singular value plot of error function between an identified nominal model and uncertain model. In conclusion the comparison of the output signals between the existing Taylor linearized model the identified linear model and the nonlinear model of the tandem cold mill shows the accuracy and the applicability of the proposed identified model.

• Journal of Power Electronics
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• v.8 no.1
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• pp.91-100
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• 2008

The d-q harmonic detecting algorithms are dominant methods to generate current references for active power filters (APF). They are often implemented in the synchronous frame and time domain. This paper researches the frequency characteristics of d-q synchronous transformations, which are closely related to the analysis and design issues of control system. Intuitively, the synchronous transformation is explained with amplitude modulation (AM) in this paper. Then, the synchronous filter is proven to be a time-invariant and linear system, and its transfer function matrix is derived in the stationary frames. These frequency-domain models imply that the synchronous transformation has an equivalent effect of frequency transformation. It is because of this feature, the d-q method achieves band-pass characteristics with the low pass filters in the synchronous frame at run time. To simplify these analytical models, an instantaneous positive-negative sequence frame is proposed as expansion of traditional symmetrical components theory. Furthermore, the synchronous filter is compared with the traditional bind-pass filters based on these frequency-domain analytical models. The d-q harmonic detection methods are also improved to eliminate the inherent coupling effect of synchronous transformation. Typical examples are given to verify previous analysis and comparison. Simulation and experimental results are also provided for verification.

• Structural Engineering and Mechanics
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• v.31 no.2
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• pp.211-223
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• 2009

Transient response analysis can be conducted either in the time domain, or via the frequency domain. Sometimes a frequency domain method (FDM) has advantages over a time domain method. A practical issue in the FDM is to find out an appropriate extended period, which may be affected by several factors, such as the excitation duration, the system damping, the artificial damping, the period of interest, etc. In this report, the extended period of the FDM based on the Duhamel's integral is investigated. This Duhamel's integral based FDM does not involve the unit impulse response function (UIRF) beyond the period of interest. Due to this fact, the ever-lasting UIRF can be simply set as zero beyond the period of interest to shorten the extended period. As a result, the preferred extended period is the summation of the period of interest and the excitation duration. This conclusion is validated by numerical examples. If the extended period is too short, then the front portion of the period of interest is more prone to errors than the rear portion, but the free vibration segment is free of the wraparound error.