• Journal of Institute of Control, Robotics and Systems
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• v.4 no.2
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• pp.170-177
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• 1998

In this paper, a unified solution of Hankel norm approximation problem is proposed by $\delta$-operator. To derive the main result, all-pass property is derived from the inner and co-inner property in the $\delta$-domain. The solution of all-pass becomes an optimal Hankel norm approximation problem in .delta.-domain through LLFT(Low Linear Fractional Transformation) inserting feedback term $\phi(\gamma)$, which is a free design parameter, to hold the error bound desired against the variance between the original model and the solution of Hankel norm approximation problem. The proposed solution does not only cover continuous and discrete ones depending on sampling interval but also plays a key role in robust control and model reduction problem. The verification of the proposed solution is exemplified via simulation for the zero-order Hankel norm approximation problem and the model reduction problem applied to a 16th order MIMO system.

• International Journal of Ocean System Engineering
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• v.1 no.1
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• pp.28-31
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• 2011

An attempt was made to compute the free surface deformation due to the impact of a water droplet. The Cauchy Poisson, i.e. the initial value problem, was solved with the kinematic and dynamic free surface boundary conditions linearized. The zero order Hankel transformation and Laplace transform were applied to the related equations. The initial condition for the free surface profile was derived from a captured video image. The effect of the surface tension was not significant with the water mass used in this investigation. The computed and observed free surface deformations were compared.

• Structural Engineering and Mechanics
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• v.82 no.2
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• pp.225-232
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• 2022

In this paper, the physical neutral surface concept is applied to study the wave propagation of functionally graded (FG) circular plate, the wave equation is derived by Hamiltonian variational principle and the first-order shear deformation plate model. Then, we convert the equations to dimensionless equations. The exact solution of wave propagation problem is obtained by Laplace integral transformation, the first order Hankel integral transformation and the zero order Hankel integral transformation. The results obtained by the current model are very close to those obtained in the existing literature, which indicates the correctness and reliability of this study. Moreover, the effects of the functionally graded index parameters and pore volume fraction on the wave propagation are also discussed in detail.

• Coupled systems mechanics
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• v.8 no.1
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• pp.55-70
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• 2019

This investigation is focused on the variations in transversely isotropic thick circular plate due to time harmonic thermomechanical sources. The homogeneous thick circular plate in presence and absence of energy dissipation and two temperatures has been considered. Hankel transform is used for solving field equations. The analytical expressions of conductive temperature, displacement components, and stress components are computed in the transformed domain. The effects of frequency at different values are represented graphically. Some specific cases are also figured out from the current research.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.2
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• pp.99-112
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• 2013

This paper presents a subspace system identification for estimating the stiffness matrix and flexural rigidities of a shear building. System matrices are estimated by LQ decomposition and singular value decomposition from an input-output Hankel matrix. The estimated system matrices are converted into a real coordinate through similarity transformation, and the stiffness matrix is estimated from the system matrices. The accuracy and the stability of an estimated stiffness matrix depend on the size of the associated Hankel matrix. The estimation error curve of the stiffness matrix is obtained with respect to the size of a Hankel matrix using a prior finite element model of a shear building. The sizes of the Hankel matrix, which are consistent with a target accuracy level, are chosen through this curve. Among these candidate sizes of the Hankel matrix, more proper one can be determined considering the computational cost of subspace identification. The stiffness matrix and flexural rigidities are estimated using the Hankel matrix with the candidate sizes. The validity of the proposed method is demonstrated through the numerical example of a five-story shear building model with and without damage.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.1018-1023
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• 1992

In this paper we proposed the systematic method of reducing the order of controller with robustness. State space formulae for all controllers is found by solving two coupled J-lossless coprime factorizations and model reduction problem. To reduce the order of controller, balanced truncation and Hankel approximation are used.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.4
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• pp.26-32
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• 2013

The earth reflection effect on the induced voltage by line source such as power line occurring induction inteference is analyzed to scrutinize how much it would reduce the induced voltage. Using hankel transformation including bessel function, directly calculation formulae for extracting a refelction coefficient is a most important technical application in this paper since the reflection coefficient on the earth cannot be deduced by a general coefficient calculation formulae according to a plain wave. The electric field is utilized to transform the electromagnetic field into an induced voltage. The composed efficiency to a source induction voltage by an earth reflection is about a range of 60~70% for the axis constellation of each object like observation point, source position and other material parameters.

• Economic and Environmental Geology
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• v.18 no.1
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• pp.41-47
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• 1985

The filtering ability of $J_0$ and $J_1$ digital linear filters is compared by means of an adaptive linear filter. Any $J_0$ domain Hankel transform integral can be transformed mathematically into its corresponding $J_1$ domain integral. The apparent resistivities for any electrode configuration employed in resistivity soundings can be evaluated with a single $J_1$ filter. The $J_1$ filter usually has similar accuracy to, but shorter length than, the corresponding $J_0$ filter. The domain transformation from $J_0$ to $J_1$ enables us to use effective expressions of apparent resistivity, involving $J_1$ alone, not only for Schlumberger but also for dipole-dipole array.

• International Journal of Internet, Broadcasting and Communication
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• v.4 no.2
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• pp.1-6
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• 2012

Control Theory for continuous-time system has been well developed. Due to the development of computer technology, digital control scheme are employed in many areas. When delays are in control systems, it is hard to control the system efficiently. Delays by controller-to-actuator and sensor-to-controller deteriorate control performance and could possibly destabilize the overall system. In this paper, a new approximated discretization method and digital design for control systems with multiple state, input and output delays and a generalized bilinear transformation method with a tunable parameter are also provided, which can re-transform the integer time-delayed discrete-time model to its continuous-time model. Illustrative examples are given to demonstrate the effectiveness of the developed method.

• Structural Engineering and Mechanics
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• v.85 no.5
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• pp.645-654
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• 2023

Based on first-order shear deformation theory, a wave propagation model of graphene platelets reinforced metal foams (GPLRMFs) circular plates is built in this paper. The expressions of phase-/group- velocities and wave number are obtained by using Laplace integral transformation and Hankel integral transformation. The effects of GPLs pattern, foams distribution, GPLs weight fraction and foam coefficient on the phase and group velocity of GPLRMFs circular plates are discussed in detail. It can be inferred that GPLs distribution have great impacts on the wave propagation problems, and Porosity-I type distribution has the largest phase velocity and group velocity, followed by Porosity-III, and finally Porosity-II; With the increase of the GPLs weight fraction, the phase- and group- velocities for the GPLRMFs circular plate will be increased; With the increase of the foam coefficient, the phase- and group- velocities for the GPLRMFs circular plate will be decreased.