• Title/Summary/Keyword: quadratic function equation

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A Tuning Algorithm for LQ-PID Controllers using the Combined Time - and Frequency-Domain Control Method

  • Kim, Chang-Hyun;Lee, Ju;Lee, Hyung-Woo
    • Journal of Electrical Engineering and Technology
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    • v.10 no.3
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    • pp.1244-1254
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    • 2015
  • This paper proposes a new method for tuning a linear quadratic - proportional integral derivative controller for second order systems to simultaneously meet the time and frequency domain design specifications. The suitable loop-shape of the controlled system and the desired step response are considered as specifications in the time and frequency domains, respectively. The weighting factors, Q and R of the LQ controller are determined by the algebraic Riccati equation with respect to the limiting behavior and target function matching. Numerical examples show the effectiveness of the proposed LQ-PID tuning method

Design Optimization of an Impingement Jet on Concave Surface for Enhancement of Heat Transfer Performance (곡면에서의 열전달성능 향상을 위한 충돌제트의 최적설계)

  • Heo, M.W.;Lee, K.D.;Kim, K.Y.
    • 한국전산유체공학회:학술대회논문집
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    • 2011.05a
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    • pp.100-103
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    • 2011
  • In the present work, a numerical study of fluid flow and heat transfer on the concave surface with impinging jet has been performed by solving three-dimensional Reynods-averaged Naver-Stokes(RANS) equations. The constant temperature condition was applied to the concave impingement surface. The inclination angle of jet nozzle and the distance between jet nozzles are chosen as design variables under equivalent mass flow rate of working fluid into cooling channel, and area averaged Nusselt number on concave impingement surface is set as the objective function. Thirteen training points are obtained by Latin Hypercube sampling method, and the PEA model is constructed by using the objective function values at the trainging points. And, the sequential quadratic programming is used to search for the optimal paint from the PBA model. Through the optimization, the optimal shape shows improved heat transfer rate as compared to the reference geometry.

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Neural Network Training Using a GMDH Type Algorithm

  • Pandya, Abhijit S.;Gilbar, Thomas;Kim, Kwang-Baek
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.5 no.1
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    • pp.52-58
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    • 2005
  • We have developed a Group Method of Data Handling (GMDH) type algorithm for designing multi-layered neural networks. The algorithm is general enough that it will accept any number of inputs and any sized training set. Each neuron of the resulting network is a function of two of the inputs to the layer. The equation for each of the neurons is a quadratic polynomial. Several forms of the equation are tested for each neuron to make sure that only the best equation of two inputs is kept. All possible combinations of two inputs to each layer are also tested. By carefully testing each resulting neuron, we have developed an algorithm to keep only the best neurons at each level. The algorithm's goal is to create as accurate a network as possible while minimizing the size of the network. Software was developed to train and simulate networks using our algorithm. Several applications were modeled using our software, and the result was that our algorithm succeeded in developing small, accurate, multi-layer networks.

A Study on the Control of Multi-Input Hydraulic System for Robot Leg using LQR Technique (LQR 기법을 이용한 로봇다리의 다중입력 유압시스템 제어에 관한 연구)

  • Yoo, Sam-Hyeon;Lim, Soo-Chul
    • Journal of the Korea Institute of Military Science and Technology
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    • v.12 no.4
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    • pp.540-547
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    • 2009
  • In the near future, military robots are likely to be substituted for military personnel in the field of battle. The power system of a legged robot is considerably more complex than the one used for a land vehicle because of the coordination and stability issues due to the large number of degree of freedom. In this paper, a servovalve-piston combination system for a straight-line motion of robot leg is modeled as three degree of freedom based on double inputs and single output transfer function. The output is the displacement of piston from neutral. The inputs are valve displacement from neutral and arbitrary load force in this system. LQR(Linear Quadratic Regulator) technique is applied in order to achieve robust stability and fast responses of the system. The Kalman filter loop, rejection of disturbance and noise, riccati equation, filter gain matrix, and frequency domain equality are analyzed and designed.

Analysis of Steady and Unsteady Flow Around a Ship Using a Higher-Order Boundary Element Method (고차경계요소법에 의한 선체주위 유동해석)

  • Sa-Y. Hong;Hang-S. Choi
    • Journal of the Society of Naval Architects of Korea
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    • v.32 no.1
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    • pp.42-57
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    • 1995
  • An efficient and accurate scheme has been constructed by taking advantages of the hi-quadratic spline scheme and the higher-order boundary element method selectively depending on computation domains. Boundary surfaces are represented by 8-node boundary elements to describe curved surfaces of a ship and its neighboring free surface more accurately. The variation of the velocity potential complies with the characteristics of the 8-node element on the body surface. But on the free surface, it is assumed to follow that of the hi-quadratic spline scheme. By which, the free surface solution is free from numerical damping and has better numerical dispersion property. As numerical examples, steady and unsteady Neumann-Kelvin problems are considered. Numerical results for a submerged spheroid, Series 60($C_B=0.6$) and a modified support the proposed method. Finally, a new upstream radiation condition is derived using a wave equation operator in order to deal with problems for subcritical reduced frequency. The relevance of this operator has been confirmed in the case of unsteady Kelvin source potential.

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Structure-Control Combined Design with Structure Intensity

  • PARK JUNG-HYEN;KIM SOON HO
    • Journal of Ocean Engineering and Technology
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    • v.17 no.5 s.54
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    • pp.57-65
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    • 2003
  • This paper proposes an optimum design method of structural and control systems, using a 2-D truss structure as an example. The structure is subjected to initial static loads and disturbances. For the structure, a FEM model is formed. Using modal transformation, the equation of motion is transformed into modal coordinates, in order to decrease D.O.F. of the FEM model. To suppress the effect of the disturbances, the structure is controlled by an output feedback $H_{\infty}$ controller. The design variables of the combined optimal design of the control-structure systems are the cross sectional areas of truss members. The structural objective function is the structural weight. The control objective function is the $H_{\infty}$ norm, the performance index of control. The second structural objective function is the energy of the response related to the initial state, which is derived from the time integration of the quadratic form of the state in the closed-loop system. In a numerical example, simulations have been perform. Through the consideration of structural weight and $H_{\infty}$ norm, an advantage of the combined optimum design of structural and control systems is shown. Moreover, since the performance index of control is almost nearly optimiz, we can acquire better design of structural strength.

Structure-Control Combined Design with Structure Intensity

  • Park, Jung-Hyen;Kim, Soon-Ho
    • International Journal of Ocean Engineering and Technology Speciallssue:Selected Papers
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    • v.6 no.1
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    • pp.60-68
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    • 2003
  • This paper proposes an optimum design method of structural and control systems, using a 2-D truss structure as an example. The structure is subjected to initial static loads and disturbances. For the structure, a FEM model is formed. Using modal transformation, the equation of motion is transformed into modal coordinates, in order to decrease D.O.F. of the FEM model. To suppress the effect of the disturbances, the structure is controlled by an output feedback $H_{\infty}$ controller. The design variables of the combined optimal design of the control-structure systems are the cross sectional areas of truss members. The structural objective function is the structural weight. The control objective function is the $H_{\infty}$ norm, the performance index of control. The second structural objective function is the energy of the response related to the initial state, which is derived from the time integration of the quadratic form of the state in the closed-loop system. In a numerical example, simulations have been perform. Through the consideration of structural weight and $H_{\infty}$ norm, an advantage of the combined optimum design of structural and control systems is shown. Moreover, since the performance index of control is almost nearly optimiz, we can acquire better design of structural strength.

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Non linear analysis of a functionally graded square plate with two smart layers as sensor and actuator under normal pressure

  • Arefi, M.;Rahimi, G.H.
    • Smart Structures and Systems
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    • v.8 no.5
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    • pp.433-447
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    • 2011
  • The present paper addresses the nonlinear response of a FG square plate with two smart layers as a sensor and actuator under pressure. Geometric nonlinearity was considered in the strain-displacement relation based on the Von-Karman assumption. All the mechanical and electrical properties except Poisson's ratio can vary continuously along the thickness of the plate based on a power function. Electric potential was assumed as a quadratic function along the thickness direction and trigonometric function along the planar coordinate. By evaluating the mechanical and electrical energy, the total energy equation can be minimized with respect to amplitude of displacements and electrical potential. The effect of non homogenous index was investigated on the responses of the system. Obtained results indicate that with increasing the non homogenous index, the displacements and electric potential tend to an asymptotic value. Displacements and electric potential can be presented in terms of planar coordinate system. A linear analysis was employed and then the achieved results are compared with those results that are obtained using the nonlinear analysis. The effect of the geometric nonlinearity is investigated by using the comparison between the linear and nonlinear results. Displacement-load and potential-load curves verified the necessity of a nonlinear analysis rather than a linear analysis. Improvement of the previous results (by the linear analysis) through employing a nonlinear analysis can be presented as novelty of this study.

Optimization of Plasma Process to Improve Plasma Gas Dissolution Rate using Three-neck Nozzle (3구 노즐을 이용한 플라즈마 가스 용존율 향상을 위한 플라즈마 공정의 최적화)

  • Kim, Dong-Seog;Park, Young-Seek
    • Journal of Environmental Science International
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    • v.30 no.5
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    • pp.399-406
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    • 2021
  • The dissolution of ionized gas in dielectric barrier plasma, similar to the principle of ozone generation, is a major performance-affecting factor. In this study, the plasma gas dissolving performance of a gas mixing-circulation plasma process was evaluated using an experimental design methodology. The plasma reaction is a function of four parameters [electric current (X1), gas flow rate (X2), liquid flow rate (X3) and reaction time (X4)] modeled by the Box-Behnken design. RNO (N, N-Dimethyl-4-nitrosoaniline), an indictor of OH radical formation, was evaluated using a quadratic response surface model. The model prediction equation derived for RNO degradation was shown as a second-order polynomial. By pooling the terms with poor explanatory power as error terms and performing ANOVA, results showed high significance, with an adjusted R2 value of 0.9386; this indicate that the model adequately satisfies the polynomial fit. For the RNO degradation, the measured value and the predicted values by the model equation agreed relatively well. The optimum current, gas flow rate, liquid flow rate and reaction time were obtained for the highest desirability for RNO degradation at 0.21 A, 2.65 L/min, 0.75 L/min and 6.5 min, respectively.

Stability and nonlinear vibration of a fuel rod in axial flow with geometric nonlinearity and thermal expansion

  • Yu Zhang;Pengzhou Li;Hongwei Qiao
    • Nuclear Engineering and Technology
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    • v.55 no.11
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    • pp.4295-4306
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    • 2023
  • The vibration of fuel rods in axial flow is a universally recognized issue within both engineering and academic communities due to its significant importance in ensuring structural safety. This paper aims to thoroughly investigate the stability and nonlinear vibration of a fuel rod subjected to axial flow in a newly designed high temperature gas cooled reactor. Considering the possible presence of thermal expansion and large deformation in practical scenarios, the thermal effect and geometric nonlinearity are modeled using the von Karman equation. By applying Hamilton's principle, we derive the comprehensive governing equation for this fluid-structure interaction system, which incorporates the quadratic nonlinear stiffness. To establish a connection between the fluid and structure aspects, we utilize the Galerkin method to solve the perturbation potential function, while employing mode expansion techniques associated with the structural analysis. Following convergence and validation analyses, we examine the stability of the structure under various conditions in detail, and also investigate the bifurcation behavior concerning the buckling amplitude and flow velocity. The findings from this research enhance the understanding of the underlying physics governing fuel rod behavior in axial flow under severe yet practical conditions, while providing valuable guidance for reactor design.