• Title/Summary/Keyword: 2nd-order nonlinear function

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The Analysis and Control of Compressed Gas Discharging System (압축가스 방출 유압시스템 해석 및 제어)

  • 장웅락;김정관;한명철;정찬희;박인기
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2004.10a
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    • pp.458-462
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    • 2004
  • The hydraulic system for discharging compressed gas is composed of compressor tank, proportional flow control servo valve, expulsion spool valve and discharging tube. Purpose of this study is to control of expulsion spool valve. First, we analyzed the hydraulic system. The flow control servo valve is modeled as a 2nd order transfer function and friction force of the expulsion spool valve is modeled as nonlinear model with stribeck effect. However, it is difficult to include the flow reaction force in modeling. So, we exchanged from the simplified flow reaction force of the compressed gas affection into the flow analysis code written in FORTRAN code. Our simulation of the oil pressure system for discharging gas used MATLAB/Simulink. So, we realized 'Level -2 S-Function Fortran' to cooperate for MATLAB/Simulink and FORTRAN code. PD controller is selected to control in this system. Simulation results show that with given conditions the controllers give a good tracking performance.

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A Study on the Adaptive Polynomial Neuro-Fuzzy Networks Architecture (적응 다항식 뉴로-퍼지 네트워크 구조에 관한 연구)

  • Oh, Sung-Kwun;Kim, Dong-Won
    • The Transactions of the Korean Institute of Electrical Engineers D
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    • v.50 no.9
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    • pp.430-438
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    • 2001
  • In this study, we introduce the adaptive Polynomial Neuro-Fuzzy Networks(PNFN) architecture generated from the fusion of fuzzy inference system and PNN algorithm. The PNFN dwells on the ideas of fuzzy rule-based computing and neural networks. Fuzzy inference system is applied in the 1st layer of PNFN and PNN algorithm is employed in the 2nd layer or higher. From these the multilayer structure of the PNFN is constructed. In order words, in the Fuzzy Inference System(FIS) used in the nodes of the 1st layer of PNFN, either the simplified or regression polynomial inference method is utilized. And as the premise part of the rules, both triangular and Gaussian like membership function are studied. In the 2nd layer or higher, PNN based on GMDH and regression polynomial is generated in a dynamic way, unlike in the case of the popular multilayer perceptron structure. That is, the PNN is an analytic technique for identifying nonlinear relationships between system's inputs and outputs and is a flexible network structure constructed through the successive generation of layers from nodes represented in partial descriptions of I/O relatio of data. The experiment part of the study involves representative time series such as Box-Jenkins gas furnace data used across various neurofuzzy systems and a comparative analysis is included as well.

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Pole Placement Method to Move a Equal Poles with Jordan Block to Two Real Poles Using LQ Control and Pole's Moving-Range (LQ 제어와 근의 이동범위를 이용한 조단 블록을 갖는 중근을 두 실근으로 이동시키는 극배치 방법)

  • Park, Minho
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.19 no.2
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    • pp.608-616
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    • 2018
  • If a general nonlinear system is linearized by the successive multiplication of the 1st and 2nd order systems, then there are four types of poles in this linearized system: the pole of the 1st order system and the equal poles, two distinct real poles, and complex conjugate pair of poles of the 2nd order system. Linear Quadratic (LQ) control is a method of designing a control law that minimizes the quadratic performance index. It has the advantage of ensuring the stability of the system and the pole placement of the root of the system by weighted matrix adjustment. LQ control by the weighted matrix can move the position of the pole of the system arbitrarily, but it is difficult to set the weighting matrix by the trial and error method. This problem can be solved using the characteristic equations of the Hamiltonian system, and if the control weighting matrix is a symmetric matrix of constants, it is possible to move several poles of the system to the desired closed loop poles by applying the control law repeatedly. The paper presents a method of calculating the state weighting matrix and the control law for moving the equal poles with Jordan blocks to two real poles using the characteristic equation of the Hamiltonian system. We express this characteristic equation with a state weighting matrix by means of a trigonometric function, and we derive the relation function (${\rho},\;{\theta}$) between the equal poles and the state weighting matrix under the condition that the two real poles are the roots of the characteristic equation. Then, we obtain the moving-range of the two real poles under the condition that the state weighting matrix becomes a positive semi-finite matrix. We calculate the state weighting matrix and the control law by substituting the two real roots selected in the moving-range into the relational function. As an example, we apply the proposed method to a simple example 3rd order system.

Development and Application of Two-Dimensional Numerical Tank using Desingularized Indirect Boundary Integral Equation Method (비특이화 간접경계적분방정식방법을 이용한 2차원 수치수조 개발 및 적용)

  • Oh, Seunghoon;Cho, Seok-kyu;Jung, Dongho;Sung, Hong Gun
    • Journal of Ocean Engineering and Technology
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    • v.32 no.6
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    • pp.447-457
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    • 2018
  • In this study, a two-dimensional fully nonlinear transient wave numerical tank was developed using a desingularized indirect boundary integral equation method. The desingularized indirect boundary integral equation method is simpler and faster than the conventional boundary element method because special treatment is not required to compute the boundary integral. Numerical simulations were carried out in the time domain using the fourth order Runge-Kutta method. A mixed Eulerian-Lagrangian approach was adapted to reconstruct the free surface at each time step. A numerical damping zone was used to minimize the reflective wave in the downstream region. The interpolating method of a Gaussian radial basis function-type artificial neural network was used to calculate the gradient of the free surface elevation without element connectivity. The desingularized indirect boundary integral equation using an isolated point source and radial basis function has no need for information about the element connectivity and is a meshless method that is numerically more flexible. In order to validate the accuracy of the numerical wave tank based on the desingularized indirect boundary integral equation method and meshless technique, several numerical simulations were carried out. First, a comparison with numerical results according to the type of desingularized source was carried out and confirmed that continuous line sources can be replaced by simply isolated sources. In addition, a propagation simulation of a $2^{nd}$-order Stokes wave was carried out and compared with an analytical solution. Finally, simulations of propagating waves in shallow water and propagating waves over a submerged bar were also carried and compared with published data.

Study on Volterra System for Variation of Metacentric Height in Waves and its Application to Analysis of Parametric Roll (볼테라 시스템을 이용한 파랑 중 파라메트릭 횡동요에 대한 연구)

  • Lee, Jae-Hoon;Kim, Yonghwan
    • Journal of the Society of Naval Architects of Korea
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    • v.54 no.3
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    • pp.227-241
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    • 2017
  • In this study, a Volterra system for the variations of metacentric height (GM) in waves is employed to simulate the parametric roll phenomena of ships in head sea condition. Using the present Volterra system, the transfer function of each harmonic component in the GM variation is computed for different ship models, including mathematical models and a real containership, and the results are validated through the comparison with the values obtained using the direct calculations based on a weakly nonlinear time-domain method. Then, a semi-analytic approach employing a 1-degree of freedom equation for roll motion is developed to simulate the parametric roll motions in irregular waves. In the derived approach, the nonlinear and time-varying restoring forces in the waves are approximated using the Volterra system. Through simulations of the parametric roll for different sea states, the effects of the 1st and 2nd-order harmonic components of the variations in the occurrence and amplitude of the parametric roll motions are investigated. Because of the strong nonlinearities in the phenomena, a stochastic analysis is conducted to examine the statistical properties of the roll motions in consideration of the sensitivities and uncertainties in the computations.

Development Time and Development Model of the Green Peach Aphid, Myzus persicae (복숭아혹진딧물(Myzus persicae)의 발육과 발육모형)

  • Kim Ji-Soo;Kim Tae-Heung
    • Korean journal of applied entomology
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    • v.43 no.4 s.137
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    • pp.305-310
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    • 2004
  • The development of Myzus persicae (Sulzer) was studied at temperatures ranging from 15 to $32.5^{\circ}C$ under $70{\pm}5\%$ RH, and a photoperiod of 16:8 (L:D). Mortality of 1st-2nd nymph was higher than that of 3rd-4th nymph at the most temperature ranges whereas at high temperature of $32.5^{\circ}C$, more 3-4nymph stage individuals died. The total developmental time ranged from 12.4 days at $15^{\circ}C$ to 4.9 days at $27.5^{\circ}C$, suggesting that higher the temperature, faster the development. However, at higher end temperature ranges of 30 and $32.5^{\circ}C$, the development took 5.0 and 6.3 days, respectively. The lower developmental threshold temperature and effective accumulative temperatures for the total immature stage were $4.9^{\circ}C$ and 116.5 day-degrees. The nonlinear shape of temperature related development was well described by the modified Sharpe and DeMichele model. When the normalized cumulative frequency distributions of developmental times for each life stage were fitted to the three-parameter Weibull function, attendance of shortened developmental times was apparent with pre-nymph, post-nymph, and total nymph stages in descending order. The coefficient of determination $r^2$ ranged between 0.87 and 0.94.

A Study of the Nonlinear Characteristics Improvement for a Electronic Scale using Multiple Regression Analysis (다항식 회귀분석을 이용한 전자저울의 비선형 특성 개선 연구)

  • Chae, Gyoo-Soo
    • Journal of Convergence for Information Technology
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    • v.9 no.6
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    • pp.1-6
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    • 2019
  • In this study, the development of a weight estimation model of electronic scale with nonlinear characteristics is presented using polynomial regression analysis. The output voltage of the load cell was measured directly using the reference mass. And a polynomial regression model was obtained using the matrix and curve fitting function of MS Office Excel. The weight was measured in 100g units using a load cell electronic scale measuring up to 5kg and the polynomial regression model was obtained. The error was calculated for simple($1^{st}$), $2^{nd}$ and $3^{rd}$ order polynomial regression. To analyze the suitability of the regression function for each model, the coefficient of determination was presented to indicate the correlation between the estimated mass and the measured data. Using the third order polynomial model proposed here, a very accurate model was obtained with a standard deviation of 10g and the determinant coefficient of 1.0. Based on the theory of multi regression model presented here, it can be used in various statistical researches such as weather forecast, new drug development and economic indicators analysis using logistic regression analysis, which has been widely used in artificial intelligence fields.

Analysis of Dynamic Stability of Limit-cycle Navigation Method (Limit-cycle 항법의 동역학적 안정성 분석)

  • Kim, Dong-Han;Kang, Soo-Hyeok;Lee, Eun-Jin;Ko, Kuk-Won;Nam, Sang-Yep
    • 전자공학회논문지 IE
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    • v.46 no.3
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    • pp.33-41
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    • 2009
  • Because the stability of obstacle avoidance ability is important for the safe operation of mobile robots, this paper deals with the analysis of dynamic stability of Limit-cycle navigation method that was proposed by authors. Limit-cycle navigation method is fast and easy to implement for fast moving mobile robots using limit-cycle characteristics of the 2nd-order nonlinear function. It can be applied to robots in dynamically changing environment such as the robot soccer. By adjusting the radius of the motion circle and the direction of the obstacle avoidance, the mobile robot can avoid the collision with obstacles and move to the destination point. The stability of Limit-cycle navigation method is analyzed with a linear model. To demonstrate the effectiveness and applicability, it is applied to the robot soccer Simulations and real experiments ascertain the merits of the proposed method.

Pole Placement Method of a Double Poles Using LQ Control and Pole's Moving-Range (LQ 제어와 근의 이동범위를 이용한 중근의 극배치 방법)

  • Park, Minho
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.21 no.1
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    • pp.20-27
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    • 2020
  • In general, a nonlinear system is linearized in the form of a multiplication of the 1st and 2nd order system. This paper reports a design method of a weighting matrix and control law of LQ control to move the double poles that have a Jordan block to a pair of complex conjugate poles. This method has the advantages of pole placement and the guarantee of stability, but this method cannot position the poles correctly, and the matrix is chosen using a trial and error method. Therefore, a relation function (𝜌, 𝜃) between the poles and the matrix was derived under the condition that the poles are the roots of the characteristic equation of the Hamiltonian system. In addition, the Pole's Moving-range was obtained under the condition that the state weighting matrix becomes a positive semi-definite matrix. This paper presents examples of how the matrix and control law is calculated.

Development Model of the Foxglove Aphid, Aulacorthum solani (Kaltenbach) on Lettuce (상추에서의 싸리수염진딧물(Aulacorthum solani)의 발육과 발육모형)

  • Lee, Sang-Guei;Kim, Hyeong-Hwan;Kim, Tae-Heung;Park, Gil-Jun;Kim, Kwang-Ho;Kim, Ji-Soo
    • Korean journal of applied entomology
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    • v.47 no.4
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    • pp.359-364
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    • 2008
  • The development of Aulacorthum solani (Kaltenbach) was studied at temperatures ranging from 12.5 to $27.5^{\circ}C$ under $65{\pm}5%$ RH, and a photoperiod of 16:8 (L:D). Mortality of $1st{\sim}2nd$ nymph was higher than that of $3rd{\sim}4th$ nymph at the most temperature ranges whereas at high temperature of $27.5^{\circ}C$, more $3{\sim}4th$ nymph stage individuals died. The total developmental time ranged from 16.9 days at $12.5^{\circ}C$ to 6.6days at $22.5^{\circ}C$, suggesting that higher the temperature, faster the development. However, at higher temperature of $25^{\circ}C$ the development took 7.4 days. The lower developmental threshold temperature and effective accumulative temperatures for the total immature stage were $0.08^{\circ}C$ and 162.8 day-degreeslated development. The nonlinear shape of temperature rewas well described by the modified Sharpe and DeMichele model. When the normalized cumulative frequency distributions of developmental times for each life stage were fitted to the three-parameter Weibull function, attendance of shortened developmental times was apparent with in $1{\sim}2nd$ nymph, $3{\sim}4th$ nymph, and total nymph stages in descending order. The coefficient of determination $r^2$ ranged between 0.86 and 0.91.