• Journal of Institute of Control, Robotics and Systems
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• v.5 no.6
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• pp.647-655
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• 1999

For linear time-varying systems described by the triple (A(t),B(t),C(t)) where A(t),B(t),C(t) are the system, the input, and the output matrices, respectively, we propose concepts for measures of modal and gross controllability /observability. We introduce a differential algebraic eigenbvalue theory for linear time-varying systems to calculate the PD-eigenvalues and left and right PD-eigenvectors of the system matrix A(t) which will be used to derive the concepts for the measures. The time-dependent angle between the left PD-eigenvectors of the system matrix A(t) and the columns of the input matrix B(t), and the magnitude of the each element of the input matrix B(t) are used to propose the modal controllability measure. Similarly, the time-dependent angle between the right PD-eigenvectors of the system matrix A(t) and the rows of the output matrix C(t) are used to propose the madal observability measure. Gross measure of controllability of a mode from all inputs and its gross measure of observability in all outputs for the linear time-varying systems are also proposed. Numerical examples are presented to illustrate the proposed concepts.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.63-70
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• 2008

In this paper, we propose a bearing redundant coordinates and decoupled PD controller for 5-axes active magnetic bearing system, which consists of two bearing parts such as three-pole hybrid active magnetic bearing for stabilize the radial direction and ring-type permanent magnetic bearing stabilizing in axial and tilting motion. Based on derived system equation with decoupled control scheme, we conduct the modal analysis and measure of modal controllability and observability.

• Smart Structures and Systems
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• v.8 no.2
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• pp.191-204
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• 2011

A technique for damage localization and assessment based on measurements of both eigenvectors curvatures and eigenfrequencies is proposed. The procedure is based on two successive steps: a model independent localization, based on changes of modal curvatures, and the solution of a one-dimensional minimization problem to evaluate damage intensity. The observability properties of damage parameters is discussed and, accordingly, a suitable change of coordinates is introduced. The proposed technique is illustrated with reference to a cantilever Euler beam endowed with a set of piezoelectric transducers. To assess the robustness of the algorithm, a parametric study of the identification errors with respect to the number of transducers and to the number of considered modal quantities is carried out with both clean and noise-corrupted data.

• Journal of Mechanical Science and Technology
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• v.17 no.1
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• pp.11-22
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• 2003

In this paper, a method for optimal placement of sensors and actuators is presented by using new measures of modal controllability and observability defined in a balanced coordinate system. The proposed new measures are shown to have a great advantage in practical use when they are used as criteria for selecting the locations of sensors and actuators, since the most controllable and observable locations can be obtained to be identical. In addition, they are more accurate than the measures of Hamdan and Nayfeh in that the effects of the eigenvector norm are considered into the magnitude of measures. In simulations, to verify the effectiveness of the proposed measures and optimal placement method, the closed-loop response of a simply supported flexible beam, in which the number and locations of actuators are determined by using the proposed measures and optimal placement method, has been examined and compared with the case of Hamdan and Nayfeh’s measures.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.461-468
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• 2004

Modal participation factor(MPF) is essential to analyze structural response under earthquake load. MPF of real structure differs from that of analytic mathematical model due to the error induced from analytical assumption and construction. In this study, a identification method is proposed to calculate the MPF of real structure based on H∞ optimal model reduction. The MPF is obtained from the relationship between observability, controllability matrix of realized from S.I. and typical 2-degree state space model. The proposed method is verified thorough examples.

• Journal of the Earthquake Engineering Society of Korea
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• v.9 no.1 s.41
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• pp.25-32
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• 2005

Seismic load is distributed to modes of a structure through the modal participation factor(MPF). The modal participation factor is essential to analyze structural response under earthquake load. MPF of a real structure differs from that of analytical mathematical model due to the error induced from analytical assumptions and during the construction. In this study, an identification method is proposed to calculate the 1st MPF of real structure based on $H^{\infty}$ optimal model reduction. The MPF is obtained from the relationship between observability and controllability matrices realized from system identification and those of a prototype 2-degree state space model. The proposed method is verified thorough numerical examples.

• Smart Structures and Systems
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• v.10 no.4_5
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• pp.353-373
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• 2012

The instrumented Canton Tower is a 610 m high-rise structure, which has been considered as a benchmark problem for structural health monitoring (SHM) research. In this paper, an improved automatic modal identification method is presented based on a natural excitation technique in conjunction with the eigensystem realization algorithm (NExT/ERA). In the proposed modal identification method, damping ratio, consistent mode indicator from observability matrices (CMI_O) and modal amplitude coherence (MAC) are used as criteria to distinguish the physically true modes from spurious modes. Enhanced frequency domain decomposition (EFDD), the data-driven stochastic subspace identification method (SSI-DATA) and the proposed method are respectively applied to extract the modal parameters of the Canton Tower under different environmental conditions. Results of modal parameter identification based on output-only measurements are presented and discussed. User-selected parameters used in those methods are suggested and discussed. Furthermore, the effect of environmental conditions on the dynamic characteristics of Canton tower is investigated.

• Journal of KSNVE
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• v.9 no.4
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• pp.703-713
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• 1999

A side mirror is an important safety tool with which the driver can observe objects out of sight. This paper presents an organized design technology for the side mirror of improved vibration characteristics. Resonance response to forced vibration is critical to observability through the mirror to be designed. This study aims at the reduction of vibration level by the modification of mirror structures and consequent effects are predicted by computer simulations. We used a three-dimensional solid modeling and the modal and frequency analysis ; Pro/Engineer is used as a solid modeler; Pro/Mechanica for vibration analysis. The simulation results are compared with those obtained in experiemnts to check the validity by the three-dimensional modeling. The design technique of side mirror has been established and found to be effective in vibration analysis of redesigned parts.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.1
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• pp.12-20
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• 2002

To control the noise of an enclosed sound field, we built a state space model using the acoustic modal parameter description. Using the state space model, we can investigate the controllability and observability, and find an appropriate position of control speaker and microphone to control sound field of the enclosed space. We implemented LQR(linear quadratic regulator) controller and reduced order observer to reduce the first acoustic mode. Experiments showed satisfactory results of 4∼10 dB reduction of magnitude of the first acoustic mode, and support the feasibility of the proposed scheme to lightly damped acoustic field.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.49 no.3
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• pp.136-141
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• 2000

This paper presents the design of an H$\infty$ based robust Static Synchronous Compensator (STATCOM) supplementary controller to suppress the subsynchronous resonance (SSR) in the series-compensated system. The IEEE second benchmark, System-l model is employed for this study. In order to design the effective controller, the modal controllability and observability indices to the oscillation modes are considered. Comprehensive time domain simulations using a nonlinear system model that the proposed STATCOM supplementary controller can suppress the SSR efficiently in spite of the variations of power system operating conditions.