• Korean Journal of Chemical Engineering
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• v.35 no.12
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• pp.2327-2335
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• 2018

Fluid catalytic cracking (FCC) is an important chemical process that is widely used to produce valuable petrochemical products by cracking heavier components. However, many difficulties exist in modeling the FCC process due to its complexity. In this study, a dynamic process model of a FCC process is suggested and its structural observability is analyzed. In the process modeling, yield function for the kinetic model of the riser reactor was applied to explain the product distribution. Hydrodynamics, mass balance and energy balance equations of the riser reactor and the regenerator were used to complete the modeling. The process model was tested in steady-state simulation and dynamic simulation, which gives dynamic responses to the change of process variables. The result was compared with the measured data from operating plaint. In the structural analysis, the system was analyzed using the process model and the process design to identify the structural observability of the system. The reactor and regenerator unit in the system were divided into six nodes based on their functions and modeling relationship equations were built based on nodes and edges of the directed graph of the system. Output-set assignment algorithm was demonstrated on the occurrence matrix to find observable nodes and variables. Optimal locations for minimal addition of measurements could be found by completing the whole output-set assignment algorithm of the system. The result of this study can help predict the state more accurately and improve observability of a complex chemical process with minimal cost.

• Smart Structures and Systems
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• v.30 no.4
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• pp.339-351
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• 2022

Evaluating the current condition of existing structures is of primary importance for economic and safety reasons. This can be addressed by Structural System Identification (SSI). A reliable static SSI depends on well-designed sensor configuration and loading cases, as well as efficient parameter estimation algorithms. Static SSI by the Measurement Error-Minimizing Observability Method (MEMOM) is a model-based deterministic static SSI method that could estimate structural parameters from static responses. In the current state of the art, this method is only applicable when structures are subjected to one loading case. This might lead to lack of information in some local regions of the structure (such as the null curvatures zones). To address this issue, the SSI by MEMOM using multiple loading cases is proposed in this work. Observability equations obtained from different loading cases are concatenated simultaneously and an optimization procedure is introduced to obtain the estimations by minimizing the discrepancy between the predicted response and the measured one. In addition, a Genetic-Algorithm (GA)-based Optimal Sensor Placement (OSP) method is proposed to tackle the OSP problem under multiple static loading cases for the very first time. In this approach, the Fisher Information Matrix (FIM)'s determinant is used as the metric of the goodness of sensor configurations. The numerical examples of a 3-span continuous bridge and a 13-story frame, are analyzed to validate the applicability of the extended SSI by MEMOM and the GA-based OSP method.

• Proceedings of the KIEE Conference
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• 1999.07c
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• pp.1195-1198
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• 1999

This paper presents optimal placement of minimal set of phasor measurement units(PMU's) and observability of measurement system with PMU. By using the incidence matrix symbolic method which directly assigns measurement and pseudo-measurement to incidence matrix, it is much simpler and easier to analyze observability. The optimal PMU set is found through the simulated-annealing(SA) and the direct combinational method. The cooling schedule parameter which is suitable to the property of problem to solve is specified and optimal placement is proven by presented direct combinational method. Search spaces are limited within reasonable feasible solution region to reduce a unnecessary one in the SA implementation based on global search. The proposed method presents to save CPU time and estimate state vectors based on optimal PMU set.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.2
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• pp.144-149
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• 2006

This paper deals with a balanced model reduction for uncertain nonlinear systems via T-S fuzzy approach. We define a generalized controllability/observability gramian and obtain a balanced state space model using generalized gramians which can be obtained from solutions of linear matrix inequalities. We present a balanced model reduction scheme by truncating not only state variables but also uncertain elements. An upper bound of the model reduction error will also be suggested. In order to demonstrate the efficacy of our method, a numerical example will be presented.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.11
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• pp.1621-1628
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• 2004

This paper proposes a design methodology for the robust observer using the eigenstructure assignment in multi-output systems so that the observer is less sensitive to the ill-conditioning factors such as unknown initial estimation error, modeling error and measurement bias in transient and steady-state observer performance. The robustness of the observer can be achieved by selecting the desired eigenvector matrix to have a small condition number that guarantees the small upper bound of the estimation error. So the left singular vectors of the unitary matrix spanned by space of the achievable eigenvectors are selected as a desired eigenvectors. Also, this paper proposes how to select the desired eigenvector based on the measure of observability and designs the observer with small gain. An example of a spindle drive system is simulated to validate the robustness to the ill-conditioning factors in the observer performance.

• Proceedings of the KIEE Conference
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• 1999.07c
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• pp.1049-1053
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• 1999

It is important to measuring and monitoring about state vectors of power system for precise operation control. All state vectors cannot be measured because it is economically disadvantageous, so that some state vectors are determined using state estimator. Determination of observability is a important precondition of power system state estimation because state estimation can be performed when given power system is observable. Recently as time-synchronization technique progress, using the PMU(Phasor Measurement Unit), state vector can be measured directly so that voltage phasor and current phasor measurements can be used for power system estimation. In this paper, observability algorithm is proposed to determinate the observability with real/reactive injection power measurements and real/reactive lineflow power measurements of existing measurement system and with phasor measurements of PMU. The jacobian matrix is newly composed for state estimation with measurements of added PMU, and state estimation is performed with least square estimatior. Comparison between state estimation result of existing measurement system and that of measurement system added PMU is presented.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.49 no.7
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• pp.313-322
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• 2000

This paper presents optimal placement of minimal set of Phasor Measurement Units (PMU's) and observability analysis of the network with PMU's. In order to find a observable system, a symbolic method which directly assigns an appropriate symbol for measurement or pseudo-measurement to every entry of node-branch incidence matrix is proposed. It is much simpler and easier to analyze the observability of the network with PMU's than the conventional ones. For the optimal PMU placement problem, two approaches which are based on a modified Simulated-Annealing (SA) method and a Direct Combination method are proposed. Some case studies with IEEE sample system are made to show the performance of the proposed methods are almost alike and more effective than the conventional simulated-annealing method. It is also shown that the Direct Combination method is more effective than the modified simulated-annealing one in the sense of computation burden. The results of this study showed also that the accuracy of power system estimation and system observability can be improved the proposed PMU placements.

• Journal of Advanced Navigation Technology
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• v.22 no.3
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• pp.220-227
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• 2018

The most widely used method for constructing an inertial navigation system (INS)/global navigation satellite system (GNSS) coupling system is to construct an integrated navigation system using a Kalman filter. However, depending on the trajectory, non-observable state variables may be generated. In this case, the state variables are not estimated. To solve this problem, a integrated navigation system is constructed and then an observability analysis is performed. In this paper, a 24th order position-matched Kalman filter is defined to design an INS/GNSS integrated navigation system for vehicles moving with a large pitch angle change. To verify the appropriateness of the error state variables applied to the Kalman filter, an observability analysis was performed. The trajectory was divided into five segments, and the piece-wise constant system (PWCS) was assumed for each segment, and the results were analytically analyzed. The analytical results and the simulation results confirm that the error state parameters of the Kalman filter are well-designed to the estimation side.

• Journal of Electrical Engineering and Technology
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• v.12 no.3
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• pp.996-1006
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• 2017

Phasor Measurement Unit (PMU) placement is a crucial problem for State Estimation (SE) of the power system, which can ensure that the power network is fully observed. Further, the observation reliability problem of the system has been concerned in the operation conditions. In this paper, based on modified weighted adjacent matrix ($A_w$), an optimal placement method is proposed to solve simultaneously two problems involving the optimal PMU placement problem and the observation reliability enhancement problem of the system. The purpose of the proposed method is to achieve both the minimum total cost and the maximum observation reliability, with a focus on increasing the security of observability, strengthening the observation reliability of buses as well as enhancing the effectiveness of redundancy. Simulations on IEEE 14, 24, 30 and 57 bus test systems are presented to justify the methodology. The results of this study show that the proposed method is not only ensuring the power network having the observability effectively but also enhancing significantly the observation reliability. Therefore, it can be a useful tool for SE of the power system.

• Journal of Mechanical Science and Technology
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• v.15 no.12
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• pp.1609-1615
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• 2001

This paper presents the characteristics of a general structured observer and presents an estimation algorithm for a system with external disturbances which are added to the input of the system. By using a disturbance model, the general structured observer can estimate the states of the system is spite of disturbances, where the system is affected from external disturbances. Also, the general structured observer can include the function of a PI observer or high gain observer by properly adjusting the observer's gain matrices. The existence condition for the observer is derived, which can be checked by the system's observability condition and the pole-zero cancellation of the system's polynomial matrix. Through a numerical example, it is verified that the proposed observer is effective estimating the system and the input disturbance.