Earticle

이동로봇팔의 역학 제어기와 신경회로망 보상기가 결합된 제어구조를 제안한다. 신경망 보상이 적응적이 고 추적오차와 파라미터 추정치가 유계가 되는 파라미터 동조 알고리듬과 안정도 증명을 제시한다. 신경망 비선형 보상기를 이동로봇팔에 시뮬레이션 함으로서 비선형성의 해로운 영향을 줄이는 효과를 보여준다.

A control structure that makes possible the integration of a kinematic controller and a neural network(NN) compensator for mobile manipulators is presented. The stability of the closed loop system and the boundness of tracking errors are proved using Lyapunov theory. The NN compensation scheme proposed in this work can deal with unmodeled bounded disturbances and/or unstructured unmodeled dynamic in the mobile manipulator. On-line NN parameter tuning algorithms do no require off-line learning yet guarantee small tracking errors and bounded control signals are utilized.

김규동 초기시 여섯 편을 대상으로 복잡계 이론을 적용하여 시적 구조와 감각의 비선형성을 분석하고, 난해성 파편성 감정의 불연속성이 형성되는 원리를 해명하고자 하였다. 비선형성, 자기조직화, 창발성 개념을 문학 분석 틀로 확장하여 전쟁, 기계, 도시를 중심으로 이미지 구성과 시간 감각, 주체 형상의 상호작용을 해석하였다. 분석 결과 그의 시 언어는 감각, 언어, 정서가 상호작용하는 동역학적 체계로 작동하며, 전쟁 경험은 감정의 비선형적 진동으로, 기계와 도시는 인간-기계 하이브리드 주체의 자기조직적 구조로 재구성된다. 이러한 시적 구조는 혼돈과 질서의 경계에서 의미를 창발하며, 파편성과 불연속성은 해체가 아니라, 새로운 감정 질서를 형성하는 생성 원리로 기능한다. 또한 독자의 참여를 통해 감응적 의미망이 확장되는 특징을 보인다. 이는 전후 한국문학의 존재적 위기를 창조적 에너지로 전환한 미학적 성취를 밝히며, 복잡계 이론의 문학적 적용 가능성을 제시한다. 향후에는 사회적 역사적 맥락과의 결합 분석을 통해 해석의 층위를 확장하는 연구를 하고자 한다.

This study applies complexity theory to six early poems by Kim, Kyu-dong to analyze the nonlinearity of poetic structure and sensory experience, and to elucidate the principles underlying poetic difficulty, fragmentation, and emotional discontinuity. By extending the concepts of nonlinearity, self-organization, and emergence as a framework for literary analysis, the study interprets the interactions among image construction, temporal perception, and subject formation, with a focus on war, machines, and urban spaces. The analysis shows that his poetic language operates as a dynamic system in which sensation, language, and emotion continuously interact. The experience of war is reconfigured as nonlinear oscillations of emotion, while machines and urban spaces are reconstructed as self-organizing structures of a human–machine hybrid subject. Such poetic structures generate meaning at the boundary between chaos and order, where fragmentation and discontinuity function not as mere disintegration but as generative principles that produce new emotional order. In addition, the poems are characterized by the expansion of an affective network of meaning through the active reader participation. This study thus reveals an aesthetic achievement that transforms the existential crisis of postwar Korean literature into creative energy, while also demonstrating the applicability of complexity theory within literary studies. Future research should further expand the interpretive framework by integrating social and historical contextual analyses.

본 연구는 GDP 증가율의 비선형 변환을 이용한 회귀분석을 1970년부터 2019년까지 116개 국 가의 자료에 적용하여 소비위험을 추정한다. 비선형 변환을 위하여 본 연구는 GDP 증가율에 루트를 취하고 이를 회귀분석의 독립변수로 이용한다. 본 연구의 실증분석 결과에 따르면 전 체 국가 중 30개 선진국의 경우 GDP 증가율의 루트 변환 값이 소비증가율에 유의한 영향을 미치기 때문에 GDP 증가율과 소비증가율 사이에 비선형 관계가 존재한다. 반면 86개 개도국 의 경우 GDP 증가율의 루트 변환 값은 소비증가율에 유의한 영향을 미치지 못하며, 따라서 GDP 증가율과 소비증가율 사이에 비선형 관계가 존재하지 않는다. 이러한 결과에 따르면 개 도국의 경우 기존의 선형 회귀분석에 바탕을 둔 소비위험 추정 방법이 타당하나, 선진국의 경 우 선형 회귀분석을 이용하여 소비위험을 측정하는 것은 타당하지 않다. 선진국의 경우 GDP 증가율과 소비증가율이 비선형 관계를 갖는다는 결과에 따라 소비위험의 크기는 GDP 증가율 의 수준에 따라 변한다. 이러한 비선형 관계에 근거하여 소비증가율을 GDP 증가율의 비선형 함수로 설정 후 그 함수를 GDP 증가율에 대해 편미분함으로써 본 연구는 소비위험의 크기를 도출한다. 이와 같이 도출한 소비위험의 크기는 GDP 증가율이 커질수록 감소하며, 소비위험 의 감소폭 역시 GDP 증가율이 커질수록 작아지는 것으로 나타났다. 이러한 결과는 선진국의 소비위험은 경기 변동에 영향을 받을 가능성을 제시한다. 본 연구의 결과는 선진국과 개도국 의 소비위험 사이의 차이가 선진국과 개도국 사이의 금융시스템의 차이에 기인할 수 있다는 시사점을 제공한다.

Purpose : This study purposes to evaluate consumption risk by applying regression analysis with nonlinearly transformed GDP growth rates. Research design, data, methodology : This paper considers data for 116 countries from 1970 to 2019 and includes square root of GDP growth rates as a regressor for the regression analysis. The estimate for the square root of GDP growth rate is to be used for evaluating the partial derivative of per capita consumption growth rate with respect to per capita GDP growth rate. In this study, those calculated derivatives are used as a measure of consumption risk. Results : The results show that the square root of GDP growth rate has significant effects on the consumption growth rate for 30 advanced countries while it has no significant impacts for 87 developing countries. For those advanced economies, this study calculates the partial derivatives using the estimates for the square root of GDP growth rates. According to the results for the partial derivative, consumption risk for advanced countries decrease with their GDP growth rates and, in addition, decrease at slower speed for the larger GDP growth rates. In contrast, consumption risk is found to be independent of GDP growth rates for the developing countries. Conclusions : The results suggest that business cycles affect consumption risk for the advanced countries while they have no relationship with consumption risk for the developing countries. A possible implication for such difference is that different county-level of financial system can lead to contrast in consumption risk between advanced and developing countries.

본 연구는 2011년 1월부터 2018년 12월까지 연구기간 동안 환태평양 지역의 7개 주요 국가(i.e., 호주, 중국, 홍콩, 일본, 한국, 뉴질 랜드)의 주식과 국채 시장 간 시간가변적인 동조화와 이것의 주요 결정변수를 실증분석 한다. 본 실증분석을 효과적으로 수행하기 위 하여, 우리는 실현상관관계 추정법과 조건부분위회귀분석기법을 사용한다. 본 연구는 금융시장의 불확실성이 높을수록 환태평양 지역 주요 국가에서의 주식시장과 국채 시장 간 동조화는 낮아짐을 확인하였다. 이것은 시장의 불확실성과 두 자산시장 간의 낮은 동조화를 설명하는 ‘안전자산선호’ 가설을 지지한다. 또한, 본 연구는 이 지역에서 두 자산시장 간 동조화는 각국의 미래 경제적 상황에 대한 시 장참여자의 기대가 낙관적일수록 시장동조화가 더 높아진다는 실증적 결과를 제시한다. 이러한 결과는 미래경제상황에 대한 투자자의 낙관적인 기대는 보다 위험이 높은 주식자산에 대한 투자를 더 선호함을 설명하는 ‘부의 효과’가설을 효과적으로 지지한다. 흥미롭게 도, 본 연구는 이 지역 주요 국가의 주식과 국채시장 간 동조화를 설명하는 각 변수의 설명력은 두 자산시장동조화의 수준(종속변수)의 차이에 따라 상이하게 나타나는 비선형성 효과를 실증적으로 규명한다.

Using the nonlinear quantile regression and realized moments techniques, this study finds evidence that financial uncertainty is negatively associated with a sustainable interdependence (i.e., comovement) of stock and government bond markets in the Pacific basin region. Besides, investors’ affirmative expectation for the future economic state is positively associated with comovement of the asset markets in this region. The former supports the validity of the flight-to-quality for the asset market comovement and the latter validates the wealth effectin this region. Our findings imply that interdependence of stock and bond markets is crucial for investors’ efficient diversification and sustainable economic growth via effective securities financing of companies in the country.

Using the novel methods of the conditional nonlinear quantile regression and pairwise realised moments, we aim to shed lights on its economic drivers on dynamic integration of stock markets in the Pacific basin for the full sample periods 1990-2012. We find empirical evidence that the recent integration of stock markets in the Pacific basin region have been significantly driven by the lower differences (i.e., higher similarities) of a variety of the economic performances between sample countries over the recent decades. In particular, this study suggests an interesting existence of nonlinearities for the effects of the economic drivers on the integration of stock markets in this region.

본 논문은 KOSPI와 KOSDAQ 양 주식시장에 상장된 제조업 기업의 가치에 대한 외국인지분율의 영향을 실증분석 하였다. 이를 위해 본 연구는 전통적 선형 OLS회귀분석과 비선형 조건부분위회귀분석 기법을 사용하였다. 전체 표본기업에 대하여 OLS회귀분석 결과, 외국인지분율의 증가는 선진 경영기법과 기술의 전수 및 경영자 사적이익추구를 위한 경영의사결정을 효과적으로 감시, 통제하는 역할을 통해 기업의 가치를 제고시키는 것으로 나타났다. 비선형 조건부분위회귀분석은 기업가치가 높은 집단일수록 외국인지분율의 효과는 더 커지는 비선형성의 존재를 규명하였다. 다양한 하위표본에 대한 분석결과, 외국인지분율이 높은 기업, 대기업, 및 KOSPI 기업의 가치는 외국인 지분율과 유의한 정(+)의 관계를 보인 반면, 외국인지분율이 낮은 기업과 중소기업의 가치는 유의한 관련성을 보여주지 못하였다. 전자의 기업들에 대한 외국인투자는 해당기업에게 선진경영기법과 기술의 전수 및 경영자의 사적이익추구에 대한 통제와 감시를 통해 기업성과에 기여하는 반면 후자의 기업들에 대한 그들의 투자는 적극적인 경영참가를 통한 기업가치의 제고보다는 단순히 시세차익을 통한 부의 증진에 더 큰 관심을 반영하는 결과로 해석된다. 하위표본에 대한 비선형 조건부분위회귀분석도 선형 OLS회귀분석결과들을 지지하였으며, 변수 간 비선형효과도 제시하였다. 기업가치에 대한 외국인지분투자 효과는 기업의 가치가 높은 집단에서 더 크게 나타나는 비선형성을 처음으로 확인한 본 논문은 기업가치의 극대화를 추구하는 재무관리자에게 외국인투자자의 영향에 관한 보다 정교하고 엄격한 분석을 위해 의미있는 시사점을 제공한다.

This paper empirically investigates impacts of foreigner ownership on Korean manufacturing firms listed on Korean stock markets. The linear OLS regressions indicate that an increase on foreigner ownership are significantly associated with enhancement on value of their firm via a transfer of an advanced managerial technique and technology and an effective monitoring and control for managers' decision for their private interest. Supporting the results obtained from the linear OLS regressions, nonlinear conditional quantile regressions present an existence of nonlinearity that as firm value goes up, the effect of foreigner ownership on it become greater. Our study, whereby firstly reports the nonlinearity across firm value and foreigner ownership based on the degree of firm value, provides financial managers who seek for a maximisation of firm value with a meaningful implication for a more delicate and accurate examination on impacts of foreigner ownership on it.

We analyzed long-run adjustment process to equilibrium and short-run dynamics with WTI spot and futures prices using bivariate 3-regime TVECM. After dividing the entire sample period into 5 sub-samples, we applied this model to each sub-sample. This allows us to figure out the differentiable effects of market conditions which can vary by sub-samples and regimes, on investors' behaviors. The estimation results showed quite interesting points. First, the middle regimes of all 5 sub-samples were not targeted by investors, so we could find their activities only in lower and/or upper regimes. Second, we can make 3 different groups with 5 sub-samples. Period 1 showed brisk movements in futures markets under the price information leadership of spot markets and relatively longer adjustment time compared to the other 4 periods. Period 2, 3, and 4 showed the opposite phenomena to period 1 probably caused by sporadic big shocks on world economy. Period 5 showed mixed results in lower and upper regimes. We could analyze quite differentiable and opposite adjustments according to regimes in this period even under the dominated contango condition, which could be regarded as the precious harvest of employing a bivariate 3-regime TVECM in this paper.

A radio over fiber (RoF) system is a kind of analog optical transmission system and considered as a strong candidate for the next-generation fronthaul link in the future mobile network. In RoF systems, nonlinearity compensation is essential to increase the link capacity. In this paper, we propose a nonlinearity detection and compensation scheme using a monitoring channel in RoF systems. A monitoring channel is added at the transmitter site and used for transmitting a reference signal in an RoF transmission. The nonlinearity in the RoF transmission is detected by comparing the received monitoring signal and the original reference signal at the receiver site. Finally, the nonlinearity is compensated at the receiver by giving the reverse function of the detected nonlinearity. Our results show that the proposed scheme can almost remove the error vector magnitude degradation induced by the nonlinearity in the RoF system.

Scads of earthquake-resistant systems are being invented around the globe to ensure structural resistance against the lateral forces induced by earthquake loadings considering structural safety, efficiency, and economic aspects. Shear wall and Bracing systems are proved to be two of the most viable solutions for seismic strengthening of structures. In the present study, three numerical models of a G+10 storied building are developed in commercial building analysis software considering shear wall and bracing systems for earthquake resistance. Material nonlinearity is introduced by using plastic hinges. Analyses are performed utilizing two dynamic methods: Response Spectrum analysis and nonlinear Time-history analysis using Kobe and Loma Prieta earthquake data and results are compared to observe the nonlinear behavior of structures. The outcomes exposed that a significant increase in the seismic responses occurs due to the nonlinearity in the building systems. It was also found that building with shear wall exhibits maximum resistance and minimum nonlinearity when subjected to dynamic loadings.

In radio-over-fiber (RoF) systems, nonlinear compensation is essential to improve performance. Among the several existing nonlinear compensation techniques, we investigate a predistortion technique for a directly modulated laser in an RoF system. First, we obtain the input-to-output response of a directly modulated laser at 160, 820, and 1,540 MHz. The results show that the laser response is dependent on the frequency band. Second, we design an optimal predistortion circuit to compensate for the nonlinear responses of three frequency bands. We design the predistortion circuit with two options: each predistortion circuit for each frequency band and one single predistortion circuit for all the three frequency bands. Finally, we present the simulation results of the predistortion system obtained using a commercial simulator. These results show that the third intermodulation distortion (IMD3) is improved by 0.6-9 dB for the three frequency bands with only a single predistortion circuit.

There are increasing needs to inspect micro-pattern of flat panel display (FPD) device such as PDP and LCD. The inspection system should be able to measure over large size mother glass with high productivity and accuracy. Stylus profilers are adopted as an inspection system. To scan over large and heavy FPD device specimen, a "tip-scanning" head for stylus profiler is required. A simple method to realize a tip-scanning system is to miniaturize the whole scanning unit. In this study, a novel stylus profiler is proposed as a tip-scanning stylus profiler. The novel stylus profiler has leaf spring instead of conventional lever and pivot. To measure position of stylus an optical senor is used. Linear variable differential transformer is applied to feed-back scanning stage displacement. The stage is actuated by a voice coil motor (VCM). Target performances of the stylus profiler head are in the stroke over $20\;{\mu}m$ with high accuracy. Specifications of xy-scanning stage are over $250\;{\mu}m{\times}250\;{\mu}m$ and high bandwidth over 20 Hz. The magnetic and elastic characteristics of the mechanism are designed based on finite element (FE) analysis. After fabrication of the head and stage, they are integrated. Current amplifier and feedback controller are also developed. The performance of the stylus profiler is also validated by inspecting standard sample.

The development of the high-efficiency machine-tools equipment and new cutting tool materials with high hardness, heat- and wear-resistance has opened the way to application of high-speed cutting process. The basic argument of using of high-speed cutting processes is the reduction of time and the respective increase of machining productivity. In this sense, the spindle units may be regarded as one of the most important units, directly affecting many parameters of high-speed machining efficiency. One of the possible types of spindle units for high-speed cutting is the air-bearing type. In this paper, we propose the mathematical model of the dynamic behavior of the air-bearing spindle. To provide the high-level of speed capacity and spindle rotation accuracy we need the adequate model of "spindle-bearings" system. This model should consider characteristics of the interactions between system components and environment. To find the working characteristics of spindle unit we should derive the equations of spindle axis movement under the affecting factors, and solve these equations together with equations which describe the behavior of lubricant layer in bearing (bearing stiffness equations). In this paper, the three influence coefficients are introduced, which describe the center of spindle mass displacement, angle of shaft rotation around the axes under the unit force application and that under the unit torque application. These coefficients are operated in the system of differential equations, which describes the spindle axis spatial movement. This system is solved by Runge-Kutta method. Obtained trajectories and amplitude-frequency characteristics were then compared to experimental ones. The analysis shows good agreement between theoretical and experimental results, which confirms that the proposed model of air-bearing spindle is correctis correct

Iterative subcarrier regularization (ISR) has been recently proposed to mitigate the nonlinear noise caused by the saturation of power amplifiers in orthogonal frequency-division multiplexing systems. The generalized Papoulis?Gerchberg algorithm (GPGA) used in ISR exploits the frequency-domain prior knowledge specified by standards and time-domain prior knowledge reserved by low nonlinearity amplitudes. It is a reconstruction-based method that may cause bit error rate (BER) degradation when coding techniques are applied. In this work, a dual-loop structure of the GPGA is presented to integrate the cancellation-based methods for maintaining the coding gain. By using a well-known cancellation-based method, iterative clipping noise cancellation (ICNC), as an example, simulations based on the IEEE 802.11ah verified that the proposed scheme effectively maintains the contribution of both the reconstruction-based and cancellation-based methods, thus significantly outperforming the ISR or ICNC in terms of coded BER.

In this note, we are concerned with a class of semi-linear elliptic pdes with exponential nonlinearity in a bounded domain. Here, the nonlinearity is more or less growing exponentially with power p. We consider the problem under two types of Dirichlet boundary condition. We give existence and non-existence of solutions for those problems and some asymptotics.

수문시계열 분석과 예측을 위하여 통상적으로 기존의 선형적인 모형들을 이용하여 왔다. 그러나 최근 자연현상이나 수문시계열의 패턴 그리고 변동성에 비선형구조가 존재하고 있다는 것이 입증되고 있다. 따라서 기존의 선형적인 방법들에 의한 시계열분석이나 예측은 비선형 시스템에 대해서 적절하지 않을 것이다. 최근, 시계열의 비선형성 구조를 판단하기 위해 카오스 이론을 토대로 한 상관적분으로부터 BDS(Brock-Dechert-Scheinkman) 통계 기법이 유도되었다. BDS 통계는 시스템의 비선형구조와 무작위성 구조를 구별하는데 매우 효과적으로 이용되어 오고 있다. 또한 DVS(Deterministic Versus Stochastic) 알고리즘은 카오스와 추계학적 시스템을 구별하고 예측하는데 주로 이용되어 왔다. 그러나 본 연구에서는 DVS 알고리즘에 의해 시계열의 비선형성을 판별할 수 있음을 보이고자 한다. 따라서 본 연구에서는 추계학적 시계열과 수문학적 시계열들의 비선형성을 검사하고자 한다. ARMA 모형과 TAR(Threshold autoregressive) 모형으로부터로 발생시킨 추계학적 시계열, 미국 유타주 GSL 체적자료, 미국 플로리다 주 St. Johns 강 Cocoa 지점의 유출량 자료, 소양강 댐 일 유입량 자료 등의 수문시계열에 대해 비선형성 분석을 수행하고 그 결과를 비교하였다. 분석결과 BDS 통계가 선형 및 비선형 시계열을 구분하는데 매우 강력한 도구임을 보였고, DVS 알고리즘 또한 시계열의 비선형성을 구별하는데 효과적으로 이용될 수 있음을 보였다.

Classical linear models have been generally used to analyze and forecast hydrologic time series. 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. In recent, the BDS (Brock-Dechert-Scheinkman) statistic instead of conventional techniques has been used for detecting nonlinearity of time series. The BDS statistic was derived from the statistical properties of the correlation integral which is used to analyze chaotic system and has been effectively used for distinguishing nonlinear structure in dynamic system from random structures. DVS (Deterministic Versus Stochastic) algorithm has been used for detecting chaos and stochastic systems and for forecasting of chaotic system. This study showed the DVS algorithm can be also used for detecting nonlinearity of the time series. In this study, the stochastic and hydrologic time series are analyzed to detect their nonlinearity. The linear and nonlinear stochastic time series generated from ARMA and TAR (Threshold Auto Regressive) models, a daily streamflow at St. Johns river near Cocoa, Florida, USA and Great Salt Lake Volume (GSL) data, Utah, USA are analyzed, daily inflow series of Soyang dam and the results are compared. The results showed the BDS statistic is a powerful tool for distinguishing between linearity and nonlinearity of the time series and DVS plot can be also effectively used for distinguishing the nonlinearity of the time series.

The microstructural effects on the ultrasonic nonlinearity were investigated in isothermally degraded ferritic 2.25Cr-1Mo steel and low cycle fatigued copper. The variation in ultrasonic nonlinearity (${\beta}/{\beta}_0$) was interpreted as resulting from microstructural changes supported by the electron microscopy and X-ray diffraction, in addition to the mechanical test (Victor's hardness and ductile-brittle transition temperature). The ultrasonic nonlinearity of 2.25Cr-1Mo steel increased abruptly in the initial 1,000 h of degradation, and then changed little due to the coarsening of carbide and precipitation of stable $M_6C$ carbide during isothermal degradation. The ultrasonic nonlinearity of copper increased with the fatigue cycles due to the evolution of dislocation cell substructure.

국내의 경우 도로포장설계시 외국의 설계법을 단순히 도입하여 사용하고 있지만 건설재료, 기후 및 교통조건 등이 외국과 상이하기 때문에 근본적인 제한성이 있다. 특히, 국내 포장구조해석에서 아스팔트층 거동특성만을 중요시하는 해석은 포장구조체가 각 층의 영향을 받는 종합적인 거동특성을 보인다는 포장구조체 시스템적인 특성을 고려한다면 많은 문제점을 내포하고 있다. 따라서, 도로포장 설계시 합리적이고 경제적인 설계를 할 수 있도록 포장구조체의 해석시스템을 구축하여야 한다. 본 연구에서는 포장하부의 다층구조로서의 역학적 거동을 정확히 해석하기 위하여 비파괴 시험장비인 FWD(Falling Weight Deflectometer) 를 이용하여 층 재료 자체의 성질을 대변하는 모델 중 포장하부를 구성하는 재료에 대한 비선형 탄성모델의 적용성을 검토하고, 복잡한 실험을 통해 얻게되는 비선형탄성모델의 구성인자인 재료상수를 FWD 시험자료로부터 직접 추정하는 체계를 제안하였다. 먼저, FWD 시험의 비선형성을 고찰하고, 실내 $M_R$ 시험을 통해 결정되는 재료상수를 현장에서 수집된 FWD 자료로부터 추정하는 체계를 제안하였다. 제안된 체계로부터 추정된 재료상수는 실내시험을 통해 제안된 국내 보조기층의 재료상수 범위 내에 있음을 알 수 있었다. FWD 를 이용한 비선형모델 적용의 신뢰성을 검증하기 위하여 깊이별 처짐 측정장비인 MDD(Multi-Depth Deflectometer) 현장시험자료를 이용하였다. 검증결과, 본 연구에서 제안한 비선형탄성모델을 적용한 방법이 기존의 선형탄성모델보다 실제 MDD 실측값에 더 가까운 결과를 나타냄을 알 수 있었다.

This study examines which models are more suitable for representing mechanical property of unbound materials to analyze behavior of asphalt pavement structure. Results from FWD (Falling Weight Deflectometer) test were used to apply to nonlinear elastic model. The new method which can deduct material constants of nonlinear elastic model is suggested from FWD test data rather than laboratory resilient modulus ($M_R$) test. It is confirmed that the material constants are within the common range in subbase. Test output from FWD and MDD (Multi-Depth Deflectometer) was used to verify reliability of the model. From the results of verification, this study shows that a non-linear elastic model agrees to MDD test data more than a linear elastic model does.

This paper describes lost motion analysis for a novel 6-DOF ultra-precision positioning stage. In the case of flexure hinge based precision positioning stage, lost motion is generated when the displacement of actuator is not delivered completely to the end-effector because of the elasticity of flexure hinge. Consequently, it is need to compute amount of lost motion to compensate the motion or to decide appropriate control method for precision positioning. Lost motion analysis for the vertical actuation unit is presented. The analysis results are presented in two ways: analytic and numerical analyses. It is found that they closely coincide with each other by 1% error. In finite element analysis result, the amount of lost motion is turned out to be about 3%. Although, the amount is not so large, it is necessary procedure to check the lost motion to establish the control method.

The nonlinearity of a laser interferometer usually ranges from sub-nanometer to several manometers. This nonlinearity, which has periodic characteristics, limits the accuracy of the interferometer at the sub-nanometer level. The nonlinearity error of the one-frequency homodyne interferometer with quadrature fringe detection results from a number of factors including polarization mixing by imperfect optical elements, unequal gain of photo detectors, lack of quadrature between two signals and misalignment. In this paper, we described a method for measuring and compensating the nonlinearity of homodyne interferometer using the elliptical fitting technique with least-square method. Experimental results demonstrate that $^\pm$3.5 nm nonlinearity can be reduced to $^\pm$0.2 nm level.