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Journal of Marine Science and Technology–Taiwan

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Articles 1231 - 1260 of 1299

Full-Text Articles in Engineering

The G-Based Jordan Algebra And Lie Algebra With Application To The Model Of Visco-Elastoplasticity, Chein-Shan Liu Jun 2001

The G-Based Jordan Algebra And Lie Algebra With Application To The Model Of Visco-Elastoplasticity, Chein-Shan Liu

Journal of Marine Science and Technology–Taiwan

By a matrix representation the g-based Jordan algebra [1] is proved to form a g-based Lie algebra under the commutator product. Then we derive a new dynamical system based on the composition of the g-based Jordan and Lie algebras, which possesses internal symmetry group DSOo(n,1), and its projection PDSOo(n,1). Utilizing this concept we obtain a linear representation of a constitutive model of visco-elastoplasticity with large deformation. The irreducible representation in the vector space admits of the projective dilation proper orthochronous Lorentz group PDSOo(5,1) in the visco-elastoplastic phase and the dilation special Euclidean group DSE(5) in the viscoelastic phase. The input …

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Resonance Of Continuous Bridges Due To High Speed Trains, Jong-Dar Yau Jun 2001

Resonance Of Continuous Bridges Due To High Speed Trains, Jong-Dar Yau

Journal of Marine Science and Technology–Taiwan

In this paper, the vibration of continuous bridges subjected to the passage of high-speed trains is studied. Only the bridges with uniform spans are considered and the train moving over a bridge is modeled as a series of moving loads. According to the resonant formula of simple beams to moving loads, the effect of multiple resonant peaks for continuous bridges subjected to high-speed trains can be determined by analogy method. Based on the finite element method, the effect of the number of spans on the impact response of the continuous beams is presented. The results show that the more the …

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Design And Preliminary Test On The Integration Of Weather Data In Ecdis For Marine Navigation, Shwu-Jing Chang Jun 2001

Design And Preliminary Test On The Integration Of Weather Data In Ecdis For Marine Navigation, Shwu-Jing Chang

Journal of Marine Science and Technology–Taiwan

The incorporation of marine weather information into Electronic Chart Display and Information System (ECDIS) has become a major issue common to international organizations such as IMO, IHO, and WMO. It is believed that this will further enhance the effectiveness of ECDIS as a tool of decision support to mariners for safe and efficient navigation. This paper first identifies essential items of marine weather information to be integrated into ECDIS. The data structure, formats, and symbology for the display and updating of weather data in ECDIS are then proposed according to related international standards. Potential use of weather data in ECDIS …

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The Design Of Fuzzy Collision-Avoidance Expert System Implemented By H∞ - Autopilot, Cheng-Neng Hwang, Joe-Ming Yang, Chung-Yen Chiang Jun 2001

The Design Of Fuzzy Collision-Avoidance Expert System Implemented By H∞ - Autopilot, Cheng-Neng Hwang, Joe-Ming Yang, Chung-Yen Chiang

Journal of Marine Science and Technology–Taiwan

Collision avoidance is one of the urgent topics on ship voyage at sea. Experts’ experience is still essential when a ship is in the danger of colliding with the others nowadays although a lot of electronic voyage supported apparatuses have been equipped on ships. To include these experts’ experiences to resolve the problems of collision, we design a fuzzy collision-avoidance expert system that includes a knowledge base to store facts and rules, an inference engine to simulate experts’ decision and a fuzzy interface device. Either a quartermaster or an autopilot system can then implement the avoidance action proposed in the …

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Predicting The Integrity Of Existing Prestressed Concrete Bridge Deck Using Sonic Method, Ming-Te Liang, Jyi Wu Jun 2001

Predicting The Integrity Of Existing Prestressed Concrete Bridge Deck Using Sonic Method, Ming-Te Liang, Jyi Wu

Journal of Marine Science and Technology–Taiwan

The principal objective of this paper was provided a general idea for predicting the integrity of existing prestressed concrete bridge decks by using sonic method. The governing equation is a onedimensional wave equation with initial conditions. The method of Fourier transform was adopted for seeking D'Alembert's solution which is an analytical solution of the governing equation. Furthermore, the wave formulae such as displacement, velocity, force and stress waves were derived from the analytical solution. If the viscosity effect of material was neglected, then the elastic wave can be reduced as the sonic wave. Through these sonic wave formulae, the damage …

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Coherent Reflection Of Acoustic Plane Wave From Rough Interfaces In A Stratified Random Fluid Medium, Jin-Yuan Liu, Shiahn-Wern Shyue, Chen-Fen Huang Dec 2000

Coherent Reflection Of Acoustic Plane Wave From Rough Interfaces In A Stratified Random Fluid Medium, Jin-Yuan Liu, Shiahn-Wern Shyue, Chen-Fen Huang

Journal of Marine Science and Technology–Taiwan

Coherent reflection of an acoustic plane wave from rough interfaces in a horizontally-stratified medium, within which the sound-speed distribution subject to a small and random perturbation, is considered in this paper. The general formulation based upon the theory for rough-interface scattering in a stratified medium, in conjunction with that for random medium is derived. The Green’s function for a random medium bounded by two surfaces, which serves as generic solution of the problem, is obtained. The formulation is then applied to a simplified seabed environment to study the effects of surface roughness and medium inhomogenieties on the coherent reflection. The …

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Qualitative Modeling For Magnetization Curve, Pei-Hwa Huang, Yu-Shuo Chang Dec 2000

Qualitative Modeling For Magnetization Curve, Pei-Hwa Huang, Yu-Shuo Chang

Journal of Marine Science and Technology–Taiwan

This paper studies the derivation of a qualitative description for the magnetization curve of saturable magnetic materials. From a set of numerical input-output data, a fuzzy model, which is a collection of fuzzy IF-THEN rules for describing the studied system, is first constructed for the magnetization curve. A procedure consisting of a fuzzy clustering method and a rule processing algorithm is then employed for processing the constructed fuzzy modeling rules to extract the qualitative properties of the curve. The proposed approach is objective in that it can yield the system qualitative features without domain experts’ knowledge. An example is demonstrated …

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Effect Of Asymmetric Hydrodynamic Impact On The Dynamic Response, Jianbo Hua, Jeun-Len Wu, Wei-Hui Wang Dec 2000

Effect Of Asymmetric Hydrodynamic Impact On The Dynamic Response, Jianbo Hua, Jeun-Len Wu, Wei-Hui Wang

Journal of Marine Science and Technology–Taiwan

Due to the asymmetric water entry over a submerged part of a ship, the effect of the hydrodynamic impact on the dynamic response of a plate structure is investigated numerically by employing an orthogonal plate theory. The effect is found significant in the calculation. Both the deflection and the stress in the plate increase as the asymmetric degree under water entry of a bottom structure increases. Because of the structural dynamic effect, the maximum deflection at a heel angle of 20 degrees becomes about 50% more than that of the quasi-static approach, and the maximum stress in ydirection 40% more …

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Linearly Unbiased Estimation Combined With Jc Method For The Carbonation Contamination Of Some Concrete Bridges In Taipei, Ming-Te Liang, Guo-Fan Zhao, Yen-Sheng Liao, Chih-Hsin Liang Dec 2000

Linearly Unbiased Estimation Combined With Jc Method For The Carbonation Contamination Of Some Concrete Bridges In Taipei, Ming-Te Liang, Guo-Fan Zhao, Yen-Sheng Liao, Chih-Hsin Liang

Journal of Marine Science and Technology–Taiwan

The main purpose of this investigation was to study the durability evaluations of existing concrete bridges due to carbonation contamination. The linearly unbiased estimation method associated with the JC method developed by the Joint Committee on Structural Safety was adopted to predict the mean value and standard deviation of the normal distribution for the carbonation depths and cover thickness of concrete bridges. The reliability index (β) and failure probability (Pf) of concrete bridges were also evaluated. Since the linearly unbiased estimation method is very suitable for analyzing a small number of specimens obtained from practical engineering problems, the unknown parameters …

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Thermodynamic Aspect And Diffusion Model On Interdiffusion Of Laminate Structure, Shing-Hoa Wang Dec 2000

Thermodynamic Aspect And Diffusion Model On Interdiffusion Of Laminate Structure, Shing-Hoa Wang

Journal of Marine Science and Technology–Taiwan

A non-uniform system such as microsegregation, heterogeneous microstructure and multiple-layer deposition of thin films, always exists in the engineering materials and the electronic materials for solid state devices. As a consequence of interdiffusion under high temperature exposure, The dynamical changes of composition profiles and vacancies could lead to materials in earlier failure and reduce the life time of the component. Several theoretical fundamentals have been proposed on different aspects, including(1) the void formation at the steepest concentration gradient:(2) thermodynamic view points of excess vacancy flux;(3) the model of interdiffusion for dynamic composition profile change; and(4) stress gradient induced strain enhanced …

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On The Design And Analysis Of Ship Stabilizimg Fin Controller, Ching-Yaw Tzeng, Chung-Yi Wu Dec 2000

On The Design And Analysis Of Ship Stabilizimg Fin Controller, Ching-Yaw Tzeng, Chung-Yi Wu

Journal of Marine Science and Technology–Taiwan

A ship stabilizing fin controller based on the Internal Model Control (IMC) method is described in this paper. The proposed method directly shapes the output sensitivity function which relates the wave disturbance to the ship roll motion to achieve good disturbance rejection. The adopted IMC method gives a controller that depends explicitly on the model parameters and a design parameter that specifies the desired system response. Moreover, under the IMC structure, the sensitivity functions depend linearly on the design transfer function and this makes it easy to satisfy the internal stability condition. A reference conditioning technique is employed in the …

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On The Free Terms Of The Dual Ben For The Two And Three-Dimensional Laplace Problems, Jeng-Tzong Chen, Shyh-Rong Kuo, Wei-Chih Chen, Li-Wei Liu Jun 2000

On The Free Terms Of The Dual Ben For The Two And Three-Dimensional Laplace Problems, Jeng-Tzong Chen, Shyh-Rong Kuo, Wei-Chih Chen, Li-Wei Liu

Journal of Marine Science and Technology–Taiwan

A dual integral formulation for the Laplace problem with a smooth boundary is derived by using the contour approach surrounding the singularity. It is found that using the contour approach the jump terms come half and half from the free terms in the L and M kernel integrations for the two-dimensional case, which is different from the limiting process by approaching an interior point to a boundary point where the jump terms come totally from the L kernel only. The definition of the Hadamard principal value for hypersingular integral at the collocation point of a smooth boundary is extended to …

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The Steady Loops Of Sdof Perfectly Elastoplastic Structures Under Sinusoidal Loadings, Chein-Shan Liu Jun 2000

The Steady Loops Of Sdof Perfectly Elastoplastic Structures Under Sinusoidal Loadings, Chein-Shan Liu

Journal of Marine Science and Technology–Taiwan

The model of single degree of freedom perfectly elastoplastic structures under external loading is treated in this paper. It is analyzed and pointed out that for the perfectly elastoplastic structure the equation of motion is nothing but a two-phase linear system with an on-off switch. Then the exact solutions of the dynamic responses are derived for sinusoidal loadings. For such loading we prove that no matter how large the amplitude is, the structure is impossible undergoing a permanent plastic motion; conversely, the long term behavior exhibits either stable hysteresis loop and limit cycle, or elastic shakedown. A phase plane estimation …

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Applying Fuzzy Mathematics To Evaluating The Membership Of Existing Reinforced Concrete Bridges In Taipei, Ming-Te Liang, Jai-He Wu, Chih-Hsin Liang Jun 2000

Applying Fuzzy Mathematics To Evaluating The Membership Of Existing Reinforced Concrete Bridges In Taipei, Ming-Te Liang, Jai-He Wu, Chih-Hsin Liang

Journal of Marine Science and Technology–Taiwan

In this study, the concept of fuzzy mathematics was applied to the damage evaluation of existing reinforced concrete (RC) bridges. The partition rule of evaluation grade was used to divide the evaluation results. The damage state of existing RC bridges was carried out using a double layer fuzzy synthesis evaluation. Moreover, based on the results of the synthesis evaluation, the damage state of existing RC bridges was thoroughly partitioned. According to the evaluation results, the double-layer synthesis evaluation of fuzzy for the damage of RC bridge is definitely useful. The evaluation results are also offered as the basis for strategy …

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Effect Of Aggregate Volume Fraction On The Elastic Moduli And Void Ratio Of Cement-Based, Shih-Wei Cho, Chung-Chia Yang, Ran Huang Jun 2000

Effect Of Aggregate Volume Fraction On The Elastic Moduli And Void Ratio Of Cement-Based, Shih-Wei Cho, Chung-Chia Yang, Ran Huang

Journal of Marine Science and Technology–Taiwan

The effects of aggregate volume fraction on the void ratio and the elastic modulus of mortar were studied. Cylindrical specimens with six volume fractions (a/t = 0., 0.05, 0.1, 0.2, 0.3, and 0.4) of fine aggregate and various water/cement ratios (w/c = 0.3, 0.4, and 0.5) were cast and tested. Double inclusion model for three-phase composite (matrix, aggregate, and void) was used to predict the volume of total void based on the properties and quantities of the components and composites. Based on this study, when higher volume fraction of aggregate is used in the mix, the elastic modulus of the …

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Low-Impact Development:An Innovative Alternative Approach To Stormwater Management, Chao-Hsien Liaw, Mow-Soung Cheng, Yao-Lung Tsai Jun 2000

Low-Impact Development:An Innovative Alternative Approach To Stormwater Management, Chao-Hsien Liaw, Mow-Soung Cheng, Yao-Lung Tsai

Journal of Marine Science and Technology–Taiwan

To assist local governments in their efforts to develop more effective stormwater management programs, an innovative comprehensive approach to stormwater management referred to as Low-Impact Development (LID) has been developed. Low-Impact Development technology employs microscale and distributed management techniques. This paper briefly outlines the development of LID technology and discusses its basic hydrological control principles. However, LID's source control techniques are an economical common sense approach that can be used to better manage new development or retrofit existing development. We believe that this new approach is a significant step forward towards advancing the state-of-the-art of stormwater management and will be …

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Machine Vibration Induced Underwater Acoustic Radiation, Wei-Hui Wang, Jia-Horng Liou, Robert Sutton, Ben Dobson Jun 2000

Machine Vibration Induced Underwater Acoustic Radiation, Wei-Hui Wang, Jia-Horng Liou, Robert Sutton, Ben Dobson

Journal of Marine Science and Technology–Taiwan

A coupled FEM/BEM for solving fluid-structure interaction problem in structure-borne noise propagation and underwater acoustic radiation is present in this paper. In order to improve the habitability and stealth low noise condition is required in various types of ships. One of the dominant components is the radiated airborne and underwater noise caused by ship hull vibration. Accordingly, the estimation of structure-borne sound characteristics of a ship is important in the design of a quieter ship-structure. The hull vibration response and pressure distribution on the wetted surface of a ship subjected to excitation sources can be analyzed by utilizing the developed …

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Near-Field Source Localization Using Music With Polynomial Rooting, Hsien-Sen Hung, Shun-Hsyung Chang, Chien-Hsing Wu Jun 1998

Near-Field Source Localization Using Music With Polynomial Rooting, Hsien-Sen Hung, Shun-Hsyung Chang, Chien-Hsing Wu

Journal of Marine Science and Technology–Taiwan

In this paper, the bearing, elevation, and range estimation of near-field narrow-band sources from data observed across an array of sensors is considered. For high-resolution source localization, the multiple signal classification (MUSIC) algorithm is modified and extended to its 3-D version by accounting for spherical curvature and spreading factor in the array manifold. However, the simultaneous estimation of bearing, elevation, and range from 3-D MUSIC spectrum requires exhaustive multidimensional search. As to alleviate computational load, an alternative algorithm is proposed. The proposed algorithm involves search in the range domain combined with polynomial rooting, which replaces the search in the azimuth-elevation …

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Frequency Selection Of Wake Flow Behind A Naca 0012 Wing, Han-Wen Lee, Rong-Fung Huang Jun 1998

Frequency Selection Of Wake Flow Behind A Naca 0012 Wing, Han-Wen Lee, Rong-Fung Huang

Journal of Marine Science and Technology–Taiwan

The oscillating flow modes, frequency selection, and response of periodic frequency to change of characteristic flow modes behind a NACA 0012 wing model are studied experimentally. The functional relationships of the dominant mechanisms in limiting ranges of Reynolds number are justified analytically. The oscillating instabilities in wake region possess four characteristic modes: laminar, subcritical, transitional, and supercritical. In viscous effect dominated regime of laminar mode, Strouhal number is inversely proportional to Reynolds number. In inertial effect or pressure gradient dominated regime of supercritical mode, Strouhal remains constant. In regime between limiting cases, Strouhal number increases nonlinearly with Reynolds number and …

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Investigation Of Longitudinal Elastic Wave At Right-Angle Joint Of Two Rods, Ming-Te Liang, Chiou-Jenn Chen Jun 1998

Investigation Of Longitudinal Elastic Wave At Right-Angle Joint Of Two Rods, Ming-Te Liang, Chiou-Jenn Chen

Journal of Marine Science and Technology–Taiwan

The right-angle welded joint is usefully and frequently used in the welded type for the steel structures. The present study is focused on the longitudinal elastic waves propagating through the right-angle welded joint of two rods. One uses the theory and numerical calculation to identify the consequence of the problems of reflection and transmission. The present study indicates that the incident longitudinal elastic waves are almost reflected in the horizontal rod while the values of 3% of the generated pulse are transmitted in the vertical rod.

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Routing And Broadcasting Algorithms For The Root-Folded Petersen Etworks, Ming-Bo Lin, Grene-Eu Jan Jun 1998

Routing And Broadcasting Algorithms For The Root-Folded Petersen Etworks, Ming-Bo Lin, Grene-Eu Jan

Journal of Marine Science and Technology–Taiwan

Petersen networks have been proposed as the alternatives for interconnecting highly parallel computers. The main advantages of Petersen networks are: regular topology, high scalability, and smaller diameters. In this paper, we propose a new node naming scheme for Petersen networks. Based on this scheme, two Petersen graph related networks, called root-folded Petersen network in type-I and type-II, are constructed. Furthermore, both O(1ogio N) routing and broadcasting algorithms for the proposed networks are developed, where N is the number of nodes.

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The Estimation Of Direction-Of-Arrivals Of Wideb And Sources By Signal Subspace Focusing Approach, Lena Chang, Chung-Fan Twu Jun 1998

The Estimation Of Direction-Of-Arrivals Of Wideb And Sources By Signal Subspace Focusing Approach, Lena Chang, Chung-Fan Twu

Journal of Marine Science and Technology–Taiwan

A novel signal subspace focusing (SSF) approach for the wideband array processing is proposed in this paper. The method is based on the transformation of the signal subspaces by using focusing matrices. The focusing matrix is designed to align the signal subspaces for different frequencies in the bandwidth of the sources, and is constructed without the preliminary angle estimation. Hence, the SSF can avoid the inherent sensitivity to focusing error. Simulation results validate the effectiveness of the SSF in the estimation of the direction-of-arrivals (DOAs) of wideband sources.

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Complete Solution Of The Five-Position Synthesis For Spherical Four-Bar Mechanisms, Chen-Chou Lin Jun 1998

Complete Solution Of The Five-Position Synthesis For Spherical Four-Bar Mechanisms, Chen-Chou Lin

Journal of Marine Science and Technology–Taiwan

The objective of this paper is to synthesis spherical four-bar motion and path generators using continuation method (homotopy method). Using continuation method, we may obtain a complete set of the solutions to the problems, and provide mechanism designers with all possible choices which meet the kinematic specifications. In contrast to other local numerical schemes such as Newton method and Powell method which are sensitive to initial guess, continuation method is a global convergence method that guarantee to find all solutions to the equations. In this paper, the problems with four and five precision points will be formulated, solved, and compared …

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Analysis Of The Pivot Point For A Turning Ship, Ching-Yaw Tzeng Jun 1998

Analysis Of The Pivot Point For A Turning Ship, Ching-Yaw Tzeng

Journal of Marine Science and Technology–Taiwan

An approximate method based on the steady state linearized sway-yaw equations is proposed to estimate the pivot point of a turning ship. The location of the pivot point is directly related to the ratio of the "sway-rudder" and "yaw-rudder" gain coefficients. which can be readily computed from six linear hydrodynamic coefficients. Hence, estimation of the pivot point for a ship at the design stage is made possible with minimum hydrodynamic coefficients information required. Numerical results indicate that based on the proposed method, the estimated pivot point position for a turning ship correlates well with the solution obtained from a full …

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A Unified Approach For The Robust Spr Property Of A Parametric Uncertainty System, Chih-Yung Cheng, Chao-Fong Chang Jun 1998

A Unified Approach For The Robust Spr Property Of A Parametric Uncertainty System, Chih-Yung Cheng, Chao-Fong Chang

Journal of Marine Science and Technology–Taiwan

In this paper, we adopt a unified approach based on the concept of value set to analyze the robust strict positive real (SPR) property of uncertain systems with interval, affine linear or multilinear uncertainty structures.

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A Study Of Along Wind Speed Power Spectrum For Taiwan Area, Jing-Jong Jang, Yu-Lin Lee Jun 1998

A Study Of Along Wind Speed Power Spectrum For Taiwan Area, Jing-Jong Jang, Yu-Lin Lee

Journal of Marine Science and Technology–Taiwan

The Purpose of this paper is to formulate the wind speed power spectrum by time history data of strong wind speed in Taiwan area. By utilizing random vibration theory and statistical regression analysis, a systematic analysis and discussions of along wind turbulence effects for wind speed power spectrum is performed. This study includes the time history data collection of along wind speed for typhoon in Taiwan and the regression analysis of wind speed spectral formulas. The strong wind speed data was first transformed from time domain to frequency domain. Then, the statistical analysis methods were applied for spectrum formulation and …

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Robust Multiple Constrained State Feedback Controller Design With Minimum Auxiliary Entropy For Linear Discrete Systems, Wen-Jer Chang Jun 1998

Robust Multiple Constrained State Feedback Controller Design With Minimum Auxiliary Entropy For Linear Discrete Systems, Wen-Jer Chang

Journal of Marine Science and Technology–Taiwan

Existence of a state feedback controller with minimized auxiliary entropy design problem will be explained in this paper. This state feedback controller will achieve multiple performance constraints for linear discrete systems. These constraints include individual state variance constraints. H.. norm constraints and regional pole assignment constraints. By achieving the previous three requirements, the state feedback controller can then be solved through use of the singular value decomposition (SVD) techniques and the theory of generalized inverses. An example will be provided to demonstrate the effectiveness of the present methodology.

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Analysis Of Design Wind Speed Distribution Of Taiwan Area, Jing-Jong Jang, Jeng-Ru Lee Jun 1997

Analysis Of Design Wind Speed Distribution Of Taiwan Area, Jing-Jong Jang, Jeng-Ru Lee

Journal of Marine Science and Technology–Taiwan

This paper thoroughly examines the basic design wind speed according to wind loading of building codes in Taiwan. The first part of this study contains Chi-Square test and K-S (Kolmogorov Smirnov) test on four common wind speed probability distribution models. The data to be tested are sampled from the annual maximum 10-minute average wind speed recorded by 25 weather stations of Taiwan Central Weather Bureau during the period from 1951 to 1990. The Type I Extreme Value model is determined and recommended as the best wind speed probability distribution model for Taiwan area. This paper then explores the probability of …

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On The Rigid-Ideally Plastic Deformation Of Cantilever Bean Subjected To Tip Impact, Ming-Te Liang, Bon-Jofei Lee, Sen-Shyang Yang Jun 1997

On The Rigid-Ideally Plastic Deformation Of Cantilever Bean Subjected To Tip Impact, Ming-Te Liang, Bon-Jofei Lee, Sen-Shyang Yang

Journal of Marine Science and Technology–Taiwan

This paper presents to study the resemblance and discrepancy between the rigid-plastic and elastic-plastic deformation of cantilever beams subjected to tip impact. For this, the theory of Ting's analysis [3] and calculation parameter obtained from Parkes [1] and Symonds and Fleming [4] are used for numerical computation. These results obtained from rigid-plastic deformation are compared with those results calculated by Reid and Gui [8] who used the non-linear finite-clement code ABAQUS for presenting the numerical solution of the elastic-plastic deformation of cantilever beams. No matter what rigid-plastic or elastic-plastic deformation, the kink phenomena of the plastic hinge arrest mechanism is …

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On Parametric Pole-Placement For A Class Of Linear Systems, Jeng Yih Juang Jun 1997

On Parametric Pole-Placement For A Class Of Linear Systems, Jeng Yih Juang

Journal of Marine Science and Technology–Taiwan

This paper presents an innovative approach for parametrizing a class of state-feedback pole-placement controllers through the minimum number of effective free parameters. The approach is based on the theory of hypothetical loop-decoupling. Linear and nonlinear functions of parameter coupling in the feedback gain matrices are disclosed to the problem of generic parametric poleplacement for a linear time-invariant controllable system. With the class depicted by the controllability indices for the hypothetical control loops, parametrization for state-feedback design can be achieved. The flexibility in loop pole-assignment for a multi-input system also affects the choice for the gain matrix. The excellence of the …

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