• Title/Summary/Keyword: Pseudo-inverse Matrix

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Estimation of Vibration Level Inside an Engine Based on Rigid Body Theory and Measurement Technology (강체 운동 해석 및 실험을 통한 엔진 내부 진동 예측에 관한 연구)

  • Kim, Byung-Hyun;Park, Jong-Ho;Kim, Eui-Yeol;Lee, Sang-Kwon;Kim, Tae-Jeong;Heo, Jeong-Ki
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.21 no.11
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    • pp.1043-1050
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    • 2011
  • This paper presents practical results for the estimation of vibration level inside a powertrain based on the rigid body theory and measurement. The vibration level of inside powertrain has been used for the calculation of excitation force of an engine indirectly. However it was difficult to estimate or measure the vibration level inside of a powertrain when a powertrain works on the driving condition of a vehicle. To do this work, the rigid body theory is employed. At the first, the vibration on the surface of a powertrain is measured and its results are secondly used for the estimation the vibration level inside of powertrain together with rigid body theory. Also did research on how to decrease the error rate when the rigid body theory is applied. This method is successfully applied to the estimation of the vibration level on arbitrary point of powertrain on the driving condition at the road.

A Dexterous Motion Control Method of Redundant Robot Manipulators based on Neural Optimization Networks (신경망 최적화 회로를 이용한 여유자유도 로봇의 유연 가조작 모션 제어 방법)

  • Hyun, Woong-Keun;Jung, Young-Kee
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.5 no.4
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    • pp.756-765
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    • 2001
  • An effective dexterous motion control method of redundant robot manipulators based on neural optimization network is proposed to satisfy multi-criteria such as singularity avoidance, minimizing energy consumption, and avoiding physical limits of actuator, while performing a given task. The method employs a neural optimization network with parallel processing capability, where only a simple geometric analysis for resolved motion of each joint is required instead of computing of the Jacobian and its pseudo inverse matrix. For dexterous motion, a joint geometric manipulability measure(JGMM) is proposed. JGMM evaluates a contribution of each joint differential motion in enlarging the length of the shortest axis among principal axes of the manipulability ellipsoid volume approximately obtained by a geometric analysis. Redundant robot manipulators is then controlled by neural optimization networks in such a way that 1) linear combination of the resolved motion by each joint differential motion should be equal to the desired velocity, 2) physical limits of joints are not violated, and 3) weighted sum of the square of each differential joint motion is minimized where weightings are adjusted by JGMM. To show the validity of the proposed method, several numerical examples are illustrated.

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Image Reconstruction of Eigenvalue of Diffusion Principal Axis Using Diffusion Tensor Imaging (확산텐서영상을 이용한 확산 주축의 고유치 영상 재구성)

  • Kim, In-Seong;Kim, Joo-Hyun;Yeon, Gun;Suh, Kyung-Jin;Yoo, Don-Sik;Kang, Duk-Sik;Bae, Sung-Jin;Chang, Yong-Min
    • Investigative Magnetic Resonance Imaging
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    • v.11 no.2
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    • pp.110-118
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    • 2007
  • Purpose: The objective of this work to construct eigenvalue maps that have information of magnitude of three primary diffusion directions using diffusion tensor images. Materials and Methods: To construct eigenvalue maps, we used a 3.0T MRI scanner. We also compared the Moore-Penrose pseudo-inverse matrix method and the SVD (single value decomposition) method to calculate magnitude of three primary diffusion directions. Eigenvalue maps were constructed by calculating of magnitude of three primary diffusion directions. We did investigate the relationship between eigenvalue maps and fractional anisotropy map. Results: Using Diffusion Tensor Images by diffusion tensor imaging sequence, we did construct eigenvalue maps of three primary diffusion directions. Comparison between eigenvalue maps and Fractional Anisotropy map shows what is difference of Fractional Anisotropy value in brain anatomy. Furthermore, through the simulation of variable eigenvalues, we confirmed changes of Fractional Anisotropy values by variable eigenvalues. And Fractional anisotropy was not determined by magnitude of each primary diffusion direction, but it was determined by combination of each primary diffusion direction. Conclusion: By construction of eigenvalue maps, we can confirm what is the reason of fractional anisotropy variation by measurement the magnitude of three primary diffusion directions on lesion of brain white matter, using eigenvalue maps and fractional anisotropy map.

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Investigation of Leksell GammaPlan's ability for target localizations in Gamma Knife Subthalamotomy (감마나이프 시상하핵파괴술에서 목표물 위치측정을 위한 렉셀 감마플랜 능력의 조사)

  • Hur, Beong Ik
    • Journal of the Korean Society of Radiology
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    • v.13 no.7
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    • pp.901-907
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    • 2019
  • The aim of this study is to evaluate the ability of target localizations of Leksell GammaPlan(LGP) in Gamma Knife Subthalamotomy(or Pallidotomy, Thalamotomy) of functional diseases. To evaluate the accuracy of LGP's location settings, the difference Δr of the target coordinates calculated by LGP (or LSP) and author's algorithm was reviewed for 10 patients who underwent Deep Brain Stimulation(DBS) surgery. Δr ranged from 0.0244663 mm to 0.107961 mm. The average of Δr was 0.054398 mm. Transformation matrix between stereotactic space and brain atlas space was calculated using PseudoInverse or Singular Value Decomposition of Mathematica to determine the positional relationship between two coordinate systems. Despite the precise frame positioning, the misalignment of yaw from -3.44739 degree to 1.82243 degree, pitch from -4.57212 degree to 0.692063 degree, and rolls from -6.38239 degree to 7.21426 degree appeared. In conclusion, a simple in-house algorithm was used to test the accuracy for location settings of LGP(or LSP) in Gamma Knife platform and the possibility for Gamma Knife Subthalamotomy. The functional diseases can be treated with Gamma Knife Radiosurgery with safety and efficacy. In the future, the proposed algorithm for target localizations' QA will be a great contributor to movement disorders' treatment of several Gamma Knife Centers.

A Study on the Relation between Towing Force of Tow Vessel and Towing Point and Behavior of Towed Ship (예인력과 피예인선의 예인 지점과 거동에 관한 연구)

  • Nam, Taek-Kun
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.19 no.6
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    • pp.637-642
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    • 2013
  • In this paper, an analysis results of towing force and towing points which are dominating factors to determine the behavior of towed ship are introduced. The towing force and towing points to achive the desired posture and its position of the towed vessel are derived based on simplified dynamics and linearization method. LQR algorithm for posture control is applied to linearized system and numerical simulation is also executed. Force based on COG(cneter of gravity) and gain of controller to achieve desired posture for target vessel are obtained by using Riccati matrix equation and pseudo inverse matrix is applied to analyze the relation between the derived force and its towing point. Based on this analysis method, towing force need to move the towed vessel from its initial position to target position can be calculated. The towing method including towing point and direction is also considered on this method. Finally, the relation between towing force and towing point is confirmed from the analysis and the results can be applied to arrangement of tug boats during salvage works.

Strategy of Multistage Gamma Knife Radiosurgery for Large Lesions (큰 병변에 대한 다단계 감마나이프 방사선수술의 전략)

  • Hur, Beong Ik
    • Journal of the Korean Society of Radiology
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    • v.13 no.5
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    • pp.801-809
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    • 2019
  • Existing Gamma Knife Radiosurgery(GKRS) for large lesions is often conducted in stages with volume or dose partitions. Often in case of volume division the target used to be divided into sub-volumes which are irradiated under the determined prescription dose in multi-sessions separated by a day or two, 3~6 months. For the entire course of treatment, treatment informations of the previous stages needs to be reflected to subsequent sessions on the newly mounted stereotactic frame through coordinate transformation between sessions. However, it is practically difficult to implement the previous dose distributions with existing Gamma Knife system except in the same stereotactic space. The treatment area is expanding because it is possible to perform the multistage treatment using the latest Gamma Knife Platform(GKP). The purpose of this study is to introduce the image-coregistration based on the stereotactic spaces and the strategy of multistage GKRS such as the determination of prescription dose at each stage using new GKP. Usually in image-coregistration either surgically-embedded fiducials or internal anatomical landmarks are used to determine the transformation relationship. Author compared the accuracy of coordinate transformation between multi-sessions using four or six anatomical landmarks as an example using internal anatomical landmarks. Transformation matrix between two stereotactic spaces was determined using PseudoInverse or Singular Value Decomposition to minimize the discrepancy between measured and calculated coordinates. To evaluate the transformation accuracy, the difference between measured and transformed coordinates, i.e., ${\Delta}r$, was calculated using 10 landmarks. Four or six points among 10 landmarks were used to determine the coordinate transformation, and the rest were used to evaluate the approaching method. Each of the values of ${\Delta}r$ in two approaching methods ranged from 0.6 mm to 2.4 mm, from 0.17 mm to 0.57 mm. In addition, a method of determining the prescription dose to give the same effect as the treatment of the total lesion once in case of lesion splitting was suggested. The strategy of multistage treatment in the same stereotactic space is to design the treatment for the whole lesion first, and the whole treatment design shots are divided into shots of each stage treatment to construct shots of each stage and determine the appropriate prescription dose at each stage. In conclusion, author confirmed the accuracy of prescribing dose determination as a multistage treatment strategy and found that using as many internal landmarks as possible than using small landmarks to determine coordinate transformation between multi-sessions yielded better results. In the future, the proposed multistage treatment strategy will be a great contributor to the frameless fractionated treatment of several Gamma Knife Centers.

Displacement Control Technique of Pre-stressable Cable Structures by Force Method (하중법을 이용한 케이블 구조물의 변위제어기법에 관한 연구)

  • Shon, Su-Deok;Kwan, Alan S.K.;Lee, Seung-Jae
    • Journal of Korean Association for Spatial Structures
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    • v.11 no.2
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    • pp.139-149
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    • 2011
  • A cable structures have the advantage that cover a large space without column but it is very sensitive to deal with shape control because of its flexibility. Especially, location of control member and needed elongation of member are important things. Therefore, the purpose of this paper is studied on displacement control technique for pre-stressed cable structures by force method considering order of control. The layout of this paper is as follows. Firstly, in section 2, the control technique by force method for cable structures is given. Secondly, section 3 briefly introduces simple cable net in order to apply control technique considering ordering of actuator. Finally, more complex example for effective member and the conclusion are in section 4 and 5, respectively.

Dynamic Control Allocation for Shaping Spacecraft Attitude Control Command

  • Choi, Yoon-Hyuk;Bang, Hyo-Choong
    • International Journal of Aeronautical and Space Sciences
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    • v.8 no.1
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    • pp.10-20
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    • 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.