• Title/Summary/Keyword: State space equation

Search Result 303, Processing Time 0.027 seconds

Numerical Simulation of Gas Flow within a Radial Fracture Created by Single-Hole Blasting (단일공 발파에서 생성된 균열망에 작용하는 가스압의 수치해석적 산정)

  • Jeng, Yong-Hun;Lee, Chung-In
    • Tunnel and Underground Space
    • /
    • v.16 no.5 s.64
    • /
    • pp.413-421
    • /
    • 2006
  • In order to explain entirely dynamic fracture process induced by blasting in rock mass, it needs to consider detonation pressure and gas pressure acting on blasthole wall simultaneously. In this study, prior to simulating the coupling between gas flow and rock mass, we analyzed effects of gas pressure-time history, length of cracks and equation of state adopted to calculate the gas pressure on the gas flow within a radial fracture created by single-hole blasting. The effects were investigated on two assumptions: (a) the radial fracture was composed of 5 cracks which were 0.01 m in length and 0.001 m in asperity each and (b) the PETN explosive which diameter was 36 mm was charged in a blasthole of 45 mm diameter. It was concluded that the maximum gas pressure and its travel time were dependent on characteristics of charged explosives and geometrical properties of radial fracture.

Study on the Time Dependent Stress-Strain Behavior of Clay (점성토의 시간의존적 응력 - 변형 특성에 관한 연구)

  • 지인택;강우묵
    • Magazine of the Korean Society of Agricultural Engineers
    • /
    • v.30 no.4
    • /
    • pp.134-153
    • /
    • 1988
  • This paper was carried out to investigate the existence of a unique stress- strain behavior by obtaining some factors influencing the time dependent stress- strain behavior of clay. The results obtained from this study were summarized as follows ; 1. The relationship between stress ratro and strain in normally consolidated clay was in- dependent on pre-shear consolidation pressure. Therefore, shear strain could be expressed as a function with stress ratio. 2. The constitutive equation of shear strain on Modified Carn Clay Model coincided better with the observed value than Cam Clay Model. 3. The relationships between deviator stress and shear strain, between pore water pressure and shear strain were unified by the mean equivalent pressure. 4. The shear strain contour in norrnally consolidated clay was increased linearly through origin, but that in overconsolidated clay was not in accordance with the result of the former. 5. Because the effective stress path of normally consolidated clay was unified by the mean equivalent pressure, state boundary surface in (e,p,q) space was transformed into two dimensional surface. But it was considered to be suitable that the unified stress- strain in overconsolidated clay be expressed by a function with overconsolidation ratio. 6. The deviator for constant strain was increased linearly with increment of strain rate ($\varepsilon$) on semi-log scale, but pore water pressure was decreased. 7. The behavior of stress relaxation was transformed from linear to curvilinear with inc - rement of strain rate before stress relaxation test, and pore water pressure was increased in total range. 8. The strain of creep was increased linearly with increment of time on semi-log scale. The greater the strain rate before creep test became, the greater the increment of strain of creep became. And the pore water pressure during creep test was increased generally with increment of time on semi-log scale.

  • PDF

Performance Comparison of Various Extended Kalman Filter and Cost-Reference Particle Filter for Target Tracking with Unknown Noise (노이즈 불확실성하에서의 확장칼만필터의 변종들과 코스트 레퍼런스 파티클필터를 이용한 표적추적 성능비교)

  • Shin, Myoungin;Hong, Wooyoung
    • Journal of the Korea Society for Simulation
    • /
    • v.27 no.3
    • /
    • pp.99-107
    • /
    • 2018
  • In this paper, we study target tracking in two dimensional space using a Extended Kalman filter(EKF), various Extended Kalman Filter and Cost-Reference Particle Filter(CRPF), which can effectively estimate the state values of nonlinear measurement equation. We introduce various Extended Kalman Filter which the Unscented Kalman Filter(UKF), the Central Difference Kalman Filter(CDKF), the Square Root Unscented Kalman Filter(SR-UKF), and the Central Difference Kalman Filter(SR-CDKF). In this study, we calculate Mean Square Error(MSE) of each filters using Monte-Carlo simulation with unknown noise statistics. Simulation results show that among the various of Extended Kalman filter, Square Root Central Difference Kalman Filter has the best results in terms of speed and performance. And, the Cost-Reference Particle Filter has an advantageous feature that it does not need to know the noise distribution differently from Extended Kalman Filter, and the simulation result shows that the excellent in term of processing speed and accuracy.

A Maximum Likelihood Estimator Based Tracking Algorithm for GNSS Signals

  • Won, Jong-Hoon;Pany, Thomas;Eissfeller, Bernd
    • Proceedings of the Korean Institute of Navigation and Port Research Conference
    • /
    • v.2
    • /
    • pp.15-22
    • /
    • 2006
  • This paper presents a novel signal tracking algorithm for GNSS receivers using a MLE technique. In order to perform a robust signal tracking in severe signal environments, e.g., high dynamics for navigation vehicles or weak signals for indoor positioning, the MLE based signal tracking approach is adopted in the paper. With assuming white Gaussian additive noise, the cost function of MLE is expanded to the cost function of NLSE. Efficient and practical approach for Doppler frequency tracking by the MLE is derived based on the assumption of code-free signals, i.e., the cost function of the MLE for carrier Doppler tracking is used to derive a discriminator function to create error signals from incoming and reference signals. The use of the MLE method for carrier tracking makes it possible to generalize the MLE equation for arbitrary codes and modulation schemes. This is ideally suited for various GNSS signals with same structure of tracking module. This paper proposes two different types of MLE based tracking method, i.e., an iterative batch processing method and a non-iterative feed-forward processing method. The first method is derived without any limitation on time consumption, while the second method is proposed for a time limited case by using a 1st derivative of cost function, which is proportional to error signal from discriminators of conventional tracking methods. The second method can be implemented by a block diagram approach for tracking carrier phase, Doppler frequency and code phase with assuming no correlation of signal parameters. Finally, a state space form of FLL/PLL/DLL is adopted to the designed MLE based tracking algorithm for reducing noise on the estimated signal parameters.

  • PDF

Sampled-Data Modeling and Dynamic Behavior Analysis of Peak Current-Mode Controlled Flyback Converter with Ramp Compensation

  • Zhou, Shuhan;Zhou, Guohua;Zeng, Shaohuan;Xu, Shungang;Cao, Taiqiang
    • Journal of Power Electronics
    • /
    • v.19 no.1
    • /
    • pp.190-200
    • /
    • 2019
  • The flyback converter, which can be regarded as a nonlinear time-varying system, has complex dynamics and nonlinear behaviors. These phenomena can affect the stability of the converter. To simplify the modeling process and retain the information of the output capacitor branch, a special sampled-data model of a peak current-mode (PCM) controlled flyback converter is established in this paper. Based on this, its dynamic behaviors are analyzed, which provides guidance for designing the circuit parameters of the converter. With the critical stability boundary equation derived by a Jacobian matrix, the stable operation range with a varied output capacitor, proportional coefficient of error the amplifier, input voltage, reference voltage and slope of the compensation ramp of a PCM controlled flyback converter are investigated in detail. Research results show that the duty ratio should be less than 0.5 for a PCM controlled flyback converter without ramp compensation to operate in a stable state. The stability regions in the parameter space between the output capacitor and the proportional coefficient of the error amplifier are enlarged by increasing the input voltage or by decreasing the reference voltage. Furthermore, the ramp compensation also can extend to the stable region. Finally, time-domain simulations and experimental results are presented to verify the theoretical analysis results.

Performance enhancement of base-isolated structures on soft foundation based on smart material-inerter synergism

  • Feng Wang;Liyuan Cao;Chunxiang Li
    • Earthquakes and Structures
    • /
    • v.27 no.1
    • /
    • pp.1-15
    • /
    • 2024
  • In order to enhance the seismic performance of base-isolated structures on soft foundations, the hybrid system of base-isolated system (BIS) and shape memory alloy inerter (SMAI), referred to as BIS+SMAI, is for the first time here proposed. Considering the nonlinear hysteretic relationships of both the isolation layer and SMA, and soil-structure interaction (SSI), the equivalent linearized state space equation is established of the structure-BIS+SMAI system. The displacement variance based on the H2 norm is then formulated for the structure with BIS+SMAI. Employing the particle swarm optimization, the optimization design methodology of BIS+SMAI is presented in the frequency domain. The evolvement rules of BIS+SMAI in the effectiveness, robustness, SMA driving force, inertia force, stroke, and damping enhancement effect are revealed in the frequency domain through changing the inerter-mass ratio, structural height, aspect ratio, and relative stiffness ratio between the soil and structure. Meanwhile, the validation of BIS+SMAI is conducted using real earthquake records. Results demonstrate that BIS+SMAI can effectively reduce the isolation layer displacement. The inerter can significantly increase the hysteretic displacement of SMA and thus enhance its energy dissipation capacity, implying that BIS+SMAI has better effectiveness than BIS+SMA. Although BIS+SMAI and BIS+ tuned inerter damper (TID) have practically the same effectiveness, BIS+SMAI has the lower optimum damping, significantly smaller inertia force, and higher robustness to perturbations of the optimum parameters. Therefore, BIS+SMAI can be used as a more engineering realizable hybrid system for enhancing the performance of base-isolated structures in soft soil areas.

Dynamic Control Allocation for Shaping Spacecraft Attitude Control Command

  • Choi, Yoon-Hyuk;Bang, Hyo-Choong
    • International Journal of Aeronautical and Space Sciences
    • /
    • v.8 no.1
    • /
    • pp.10-20
    • /
    • 2007
  • For spacecraft attitude control, reaction wheel (RW) steering laws with more than three wheels for three-axis attitude control can be derived by using a control allocation (CA) approach.1-2 The CA technique deals with a problem of distributing a given control demand to available sets of actuators.3-4 There are many references for CA with applications to aerospace systems. For spacecraft, the control torque command for three body-fixed reference frames can be constructed by a combination of multiple wheels, usually four-wheel pyramid sets. Multi-wheel configurations can be exploited to satisfy a body-axis control torque requirement while satisfying objectives such as minimum control energy.1-2 In general, the reaction wheel steering laws determine required torque command for each wheel in the form of matrix pseudo-inverse. In general, the attitude control command is generated in the form of a feedback control. The spacecraft body angular rate measured by gyros is used to estimate angular displacement also.⁵ Combination of the body angular rate and attitude parameters such as quaternion and MRPs(Modified Rodrigues Parameters) is typically used in synthesizing the control command which should be produced by RWs.¹ The attitude sensor signals are usually corrupted by noise; gyros tend to contain errors such as drift and random noise. The attitude determination system can estimate such errors, and provide best true signals for feedback control.⁶ Even if the attitude determination system, for instance, sophisticated algorithm such as the EKF(Extended Kalman Filter) algorithm⁶, can eliminate the errors efficiently, it is quite probable that the control command still contains noise sources. The noise and/or other high frequency components in the control command would cause the wheel speed to change in an undesirable manner. The closed-loop system, governed by the feedback control law, is also directly affected by the noise due to imperfect sensor characteristics. The noise components in the sensor signal should be mitigated so that the control command is isolated from the noise effect. This can be done by adding a filter to the sensor output or preventing rapid change in the control command. Dynamic control allocation(DCA), recently studied by Härkegård, is to distribute the control command in the sense of dynamics⁴: the allocation is made over a certain time interval, not a fixed time instant. The dynamic behavior of the control command is taken into account in the course of distributing the control command. Not only the control command requirement, but also variation of the control command over a sampling interval is included in the performance criterion to be optimized. The result is a control command in the form of a finite difference equation over the given time interval.⁴ It results in a filter dynamics by taking the previous control command into account for the synthesis of current control command. Stability of the proposed dynamic control allocation (CA) approach was proved to ensure the control command is bounded at the steady-state. In this study, we extended the results presented in Ref. 4 by adding a two-step dynamic CA term in deriving the control allocation law. Also, the strict equality constraint, between the virtual and actual control inputs, is relaxed in order to construct control command with a smooth profile. The proposed DCA technique is applied to a spacecraft attitude control problem. The sensor noise and/or irregular signals, which are existent in most of spacecraft attitude sensors, can be handled effectively by the proposed approach.

Calculation of Failure Load of V-shaped Rock Notch Using Slip-line Method (Slip-line법을 이용한 V형 암석 노치의 파괴하중 계산)

  • Lee, Youn-Kyou
    • Tunnel and Underground Space
    • /
    • v.30 no.4
    • /
    • pp.404-416
    • /
    • 2020
  • An analytical procedure for calculating the failure load of a V-shaped rock notch under two-dimensional stress conditions was developed based on the slip-line plastic analysis method. The key idea utilized in the development is the fact that the α-line, one of the slip-lines, extends from the rock notch surface to the horizontal surface outside the notch when the rock around the notch is in the plastic state, and that there exists an invariant which is constant along the α-line. Since the stress boundary condition of the horizontal surface outside the rock notch is known, it is possible to calculate the normal and shear stresses acting on the rock notch surface by solving the invariant equation. The notch failure load exerted by the wedge was calculated using the calculated stress components for the notch surface. Rock notch failure analysis was performed by applying the developed analytical procedure. The analysis results show that the failure load of the rock notch increases with exponential nonlinearity as the angle of the notch and the friction of the notch surface increase. The analytical procedure developed in this study is expected to have applications to the study of fracture initiation in rocks through wedge-shaped notch formation, calculation of bearing capacity of the rock foundation, and stability analysis of rock slopes and circular tunnels.

Identification of Nonstationary Time Varying EMG Signal in the DCT Domain and a Real Time Implementation Using Parallel Processing Computer (DCT 평면에서의 비정상 시변 근전도 신호의 인식과 병렬처리컴퓨터를 이용한 실시간 구현)

  • Lee, Young-Seock;Lee, Jin;Kim, Sung-Hwan
    • Journal of Biomedical Engineering Research
    • /
    • v.16 no.4
    • /
    • pp.507-516
    • /
    • 1995
  • The nonstationary identifier in the DCT domain is suggested in this study for the identification of AR parameters of above-lesion upper-trunk electromyographic (EMG) signals as a means of developing a reliable real time signal to control functional electrical stimulation (FES) in paraplegics to enable primitive walking. As paraplegic shifts his posture from one attitude to another, there is transition period where the signal is clearly nonstationary. Also as muscle fatigues, nonstationarities become more prevalent even during stable postures. So, it requires a develpment of time varying nonstationary EMG signal identifier. In this paper, time varying nonstationary EMG signals are transformed into DCT domain and the transformed EMG signals are modeled and analyzed in the transform domain. In the DCT domain, we verified reduction of condition number and increment of the smallest eigenvalue of input correlation matrix that influences numerical properties and mean square error were compared with SLS algorithm, and the proposed algorithm is implemented using IMS T-805 parallel processing computer for real time application.

  • PDF

Comparison with SAR Patterns of Biological Objects Contacted with Coaxial Waveguide Antenna Using MUR and GPML ABCs in the FDTD Method (유한차분법에서 MUR과 GPML 흡수경계조건을 이용한 동축 도파관 안테나에 접촉된 생체의 SAR 패턴 비교)

  • 구성모;권광희;이창원;원철호;조진호
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
    • /
    • v.9 no.2
    • /
    • pp.149-158
    • /
    • 1998
  • The SAR patterns of biological objects contacted with coaxial waveguide antennal has been investigated, in which the biological object was modeled by a homogeneous and four-layered lossy human body. We derived the finite-difference time-domain(FDTD) algorithm and equation of MUR and generalized perfectly matched layer(GPML) ABCs in cylindrical coordination. The coupling between coaxial waveguide antenna and a biological object was analyzed by use of MUR and GPML ABCs in the FDTD method to obtain the absorbed power patterns in the media. The specific absorption rates (SAR) distribution which was corresponding to the temperature distribution was calculated in each region by use of the steady-state response in the FDTD method. The SAR patterns of the FDTD method using MUR absorbing boundary conditions(ABCs) was compared with those of the FDTD method using GPML ABCs. The comparison exhibits that the penetration depth of the SAR patterns using MUR ABCs is deeper than that of the SAR patterns using GPML ABCs because of loss in free space. However, the spread in the lateral directions of the SAR patterns using GPML ABCs is smaller than of the SAR patterns using MUR ABCs.

  • PDF