• Title/Summary/Keyword: Linear-quadratic model

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Design of nonlinear optimal regulators using lower dimensional riemannian geometric models

  • Izawa, Yoshiaki;Hakomori, Kyojiro
    • 제어로봇시스템학회:학술대회논문집
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    • 1994.10a
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    • pp.628-633
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    • 1994
  • A new Riemannian geometric model for the controlled plant is proposed by imbedding the control vector space in the state space, so as to reduce the dimension of the model. This geometric model is derived by replacing the orthogonal straight coordinate axes on the state space of a linear system with the curvilinear coordinate axes. Therefore the integral manifold of the geometric model becomes homeomorphic to that of fictitious linear system. For the lower dimensional Riemannian geometric model, a nonlinear optimal regulator with a quadratic form performance index which contains the Riemannian metric tensor is designed. Since the integral manifold of the nonlinear regulator is determined to be homeomorphic to that of the linear regulator, it is expected that the basic properties of the linear regulator such as feedback structure, stability and robustness are to be reflected in those of the nonlinear regulator. To apply the above regulator theory to a real nonlinear plant, it is discussed how to distort the curvilinear coordinate axes on which a nonlinear plant behaves as a linear system. Consequently, a partial differential equation with respect to the homeomorphism is derived. Finally, the computational algorithm for the nonlinear optimal regulator is discussed and a numerical example is shown.

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Constrained multivariable model based predictive control application to nonlinear boiler system (제약조건을 갖는 다변수 모델 예측 제어기의 비선형 보일러 시스템에 대한 적용)

  • 손원기;이명의;권오규
    • 제어로봇시스템학회:학술대회논문집
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    • 1996.10b
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    • pp.160-163
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    • 1996
  • This paper deals with MCMBPC(Multivariable Constrained Model Based Predictive Controller) for nonlinear boiler system with noise and disturbance. MCMBPC is designed by linear state space model obtained from some operating point of nonlinear boiler system and Kalman filter is used to estimate the state with noise and disturbance. The solution of optimization of the cost function constrained on input and/or output variables is achieved using quadratic programming, viz. singular value decomposition (SVD). The controller designed is shown to have excellent tracking performance via simulation applied to nonlinear dynamic drum boiler turbine model for 16OMW unit.

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Autopilot design for BTT flight vehicles (이동중인 비행시스템의 자동조종장치 설계)

  • 백운보;허남수;이만형;황창선
    • 제어로봇시스템학회:학술대회논문집
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    • 1989.10a
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    • pp.87-92
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    • 1989
  • An autopilot for the class of Bank-To-Turn missiles is developed using a multivariable plant model & control design methodology. The roll-pitch-yaw cross coupling is included in the design considerations. Feedback system is designed using the Linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR). Nonlinear simulations are presented to demonstrate the performances of the designed system.

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TAR(Threshold Autoregressive) Model for Short-Term Load Forecasting Using Nonlinearity of Temperature and Load (온도와 부하의 비선형성을 이용한 단기부하예측에서의 TAR(Threshold Autoregressive) 모델)

  • Lee, Gyeong Hun;Lee, Yun Ho;Kim, Jin O
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.50 no.9
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    • pp.399-399
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    • 2001
  • This paper proposes TAR(Threshold Autoregressive) model for short-term load forecasting including temperature variable. In the scatter diagram of daily peak load versus daily high or low temperature, we can find out that the load-temperature relationship has a negative slope in the lower regime and a positive slope in the upper regime due to the heating and cooling load, respectively. TAR model is adequate for analyzing these phenomena since TAR model is a piecewise linear autoregressive model. In this paper, we estimated and forecasted one day-ahead daily peak load by applying TAR model using this load-temperature characteristic in these regimes. The results are compared with those of linear and quadratic regression models.

TAR(Threshold Autoregressive) Model for Short-Term Load Forecasting Using Nonlinearity of Temperature and Load (온도와 부하의 비선형성을 이용한 단기부하예측에서의 TAR(Threshold Autoregressive) 모델)

  • Lee, Gyeong-Hun;Lee, Yun-Ho;Kim, Jin-O
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.50 no.9
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    • pp.309-405
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    • 2001
  • This paper proposes TAR(Threshold Autoregressive) model for short-term load forecasting including temperature variable. In the scatter diagram of daily peak load versus daily high or low temperature, we can find out that the load-temperature relationship has a negative slope in the lower regime and a positive slope in the upper regime due to the heating and cooling load, respectively. TAR model is adequate for analyzing these phenomena since TAR model is a piecewise linear autoregressive model. In this paper, we estimated and forecasted one day-ahead daily peak load by applying TAR model using this load-temperature characteristic in these regimes. The results are compared with those of linear and quadratic regression models.

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A study on change-points in simple linear regression (단순선형회귀에서의 변화점에 대한 연구)

  • 정광모;한미혜
    • The Korean Journal of Applied Statistics
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    • v.5 no.1
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    • pp.29-39
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    • 1992
  • A testing and estimation procedure is considered for changes at unknown time point in simple linear regression model. A test statistic of quadratic form is suggested. We also discuss the asymptotic distribution and its level control. The proposed method is compared with the likelihood ratio test through a example.

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A Linear Sliding Surface Design Method for a Class of Uncertain Systems with Mismatched Uncertainties (불확실성이 매칭조건을 만족시키지 않는 선형 시스템을 위한 슬라이딩 평면 설계 방법)

  • 최한호
    • Journal of Institute of Control, Robotics and Systems
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    • v.9 no.11
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    • pp.861-867
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    • 2003
  • We propose a sliding surface design method for linear systems with mismatched uncertainties in the state space model. In terms of LMIs, we derive a necessary and sufficient condition for the existence of a linear sliding surface such that the reduced-order equivalent sliding mode dynamics restricted to the linear sliding surface is not only stable but completely invariant to mismatched uncertainties. We give an explicit formula of all such linear switching surfaces in terms of solution matrices to the LMI existence condition. We also give a switching feedback control law, together with a design algorithm. Additionally, we give some hints for designing linear switching surfaces guaranteeing pole clustering constraints or linear quadratic performance bound constraints. Finally, we give a design example in order to show the effectiveness of the proposed methodology.

Evaluation of the heat island in transition zone of three cities in Kyungpook, Korea (추이대(推移帶)를 중심으로 한 경상북도 3개 도시의 열섬 평가)

  • Park, In Hwan;Jang, Gab Sue;Kim, Jong Yong
    • Journal of Environmental Impact Assessment
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    • v.8 no.2
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    • pp.73-82
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    • 1999
  • This study analyzed the relationship between NDVI(Normalized Difference Vegetation Index) and urban heat island in three cities: Daegu, Kyungju, and Pohang for understanding the degree of nature conservation concentrating in the transition zone of them. Daegu city is the third city in Korea which has a dense population. Kyungju is a traditional city which has good nature. Pohang is an industrial city which has those of characters of Daegu and Kyungju. Landsat 1M data in May 17, 1997 were used for the analysis of heat island. There were about four theoretical models to estimate the surface temperature from TM data: Two-point linear model, Linear regression model, Quadratic regression model, and Cubic regression model. In this study, Linear regression model had been utilized to analyze the urban heat island. On the resultant images, the transition zone of Daegu was urbanized more extremely than those of other two cities. It is thought that the analysis of relationship between NDVI and surface temperature, used in this study, is regarded as one of effective methodologies for urban-environmental detection from satellite imageries.

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Study on Optimal Damping Model of Very Large Offshore Semi-submersible Structure (초대형 반잠수식 해양 구조물의 최적 감쇠 모델에 대한 고찰)

  • Lee, Hyebin;Bae, Yoon Hyeok;Kim, Dongeun;Park, Sewan;Kim, Kyong-Hwan;Hong, Keyyong
    • Journal of Ocean Engineering and Technology
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    • v.32 no.1
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    • pp.1-8
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    • 2018
  • In order to analyze the response of the offshore structure numerically, the linear potential theory is generally applied for simplicity, and only the radiation damping is considered among various damping forces. Therefore, the results of a numerical simulation can be different from the motion of the structure in a real environment. To reduce the differences between the simulation results and experimental results, the viscous damping, which affects the motion of the structure, is also taken into account. The appropriate damping model is essential for the numerical simulation in order to obtain precise responses of the offshore structure. In this study, various damping models such as linear or quadratic damping and the nonlinear drag force from numerous slender bodies were used to simulate the free decay motion of the platform, and its characteristics were confirmed. The optimized damping model was found by comparing the simulation results to the experimental results. The hydrodynamic forces and wave exciting forces of the structure were obtained using WAMIT, and the free decay test was simulated using OrcaFlex. A free decay test of the scale model was performed by KRISO.

LQG/LTR-PID based Controller Design of UAV Slung-Load Transportation System (LQG/LTR과 PID 기반의 무인항공기 슬렁-로드 수송 시스템의 제어기 설계)

  • Lee, Hae-In;Yoo, Dong-Wan;Lee, Byung-Yoon;Moon, Gun-Hee;Lee, Dong-Yeon;Tahk, Min-Jea
    • Journal of Institute of Control, Robotics and Systems
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    • v.20 no.12
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    • pp.1209-1216
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    • 2014
  • This paper copes with control design for unmanned aerial vehicle transportation system. Moving pendulum dynamics of slung-load system is derived using two methods: Udwadia-Kalaba equation and Newtonian approach. PID controller is applied to Udwadia-Kalaba equation model for structural consistency and linear quadratic Gaussian / Loop Transfer Recovery (LQG/LTR) technique is employed for Newtonian model with minimal state-space realization. Characteristics of PID and LQG/LTR controller are compared, and two controllers are combined to compensate the drawbacks of each other. Numerical simulation is set for two cases and conducted to evaluate performance of designed controllers. The result proves that combination of LQG/LTR and PID control performs stable and robust.