Pole Clustering Technique Research Articles

Educational aid for dynamic study of DC converter with Leverrier's and Pole clustering technique using simulation software

Abstract : In this paper, the dynamic analysis of the dc-dc converter is proposed with an educational aid to ease the process in which the study is carried out. This study's primary importance is that it can be added to the curriculum of Master's program in Electrical Engineering. This article mainly focuses on the mathematical modelling of the dc-dc converter with which the dynamic analysis is carried out to regulate the load and line condition. The main problems in the analysis of higher-order dc-dc converter is addressed with techniques available in the literature. A quadratic boost converter with DCL cell is chosen for studying the dynamic analysis with the flow of the technique proposed. The solution to the resolvent matrix of the converter is obtained using Leverrier's algorithm. The higher-order system's transfer function is reduced using the pole clustering technique to ease the controller design. Finally, the PI controller is tuned with Ziegler-Nichols tuning and it is incorporated with the converter using the reduced-order transfer function. The input to output transfer function is analyzed with the step response in MATLAB software and compared with the full order transfer function to validate the reduced-order transfer function. The closed-loop response is also validated both with full order and reduced-order system. Keywords : Bloom's taxonomy, Leverrier's algorithm, Pole clustering, DC-DC converter, dynamic, reduced-order, controller

Reduction of linear dynamic systems using generalized approach of pole clustering method

A new model order abatement method based on the clustering of poles and zeros of a large-scale continuous time system is proposed. The clustering of poles and zeros are used for finding the cluster centres. The abated model is identified from the cluster centres, which reflect the effectiveness of the dominant poles of the clusters. The cluster centre is determined by taking [Formula: see text] root of the sum of the inverse of [Formula: see text] power of poles (zeros) in a particular cluster. It is famous that the magnitude of the pole cluster centre plays an important role in the clustering technique for the simplification of large-scale systems. The magnitude of the cluster centres computed by the modified pole clustering method or some other methods based on the pole clustering techniques is large as compared to the proposed technique. The less magnitude of pole cluster centre reflects the better approximations and proper matching of the abated model with the original system. Therefore, the proposed method offers better approximations matching between actual and abated systems during the transient period compared to some other clustering methods, which supports the replacement of large-scale systems by proposed abated systems. The proposed technique is a generalized version of the standard pole clustering technique. The proposed method guarantees the retention of dominant poles, stability and other fundamental control properties of the actual plant in the abated model. The proposed algorithm is illustrated by the five standard systems taken from the literature. The accuracy and effectiveness of the proposed method are verified by comparing the time responses and various performance error indices.

Computing Dominant Poles of High-Dimensional Transfer Functions Using the Modified Clustering Method

Model order reduction (MOR) solves a high-dimensional problem to its compact representation and plays a key role in the fields where complex simulation studies are always a challenge in terms of simulation time. A new criterion for the dominance of poles has been set out in this paper and its effect on the reduced-order model (ROM) has been observed. Considering the conventional as well as dominant pole-based solutions to ROM, the original system has been reduced to a lower-dimensional state-space and compared with each other. A dominant pole-based strategy incorporated into the modified pole clustering technique has been developed which leads to a proposed novel methodology as a dominant pole-based modified pole clustering method (DPMPCM). The paper also reveals that having applied DPMPCM, an improved approximation to the original system has been achieved as compared to other methods reported to the best of my knowledge in the literature. This method ensures the stability of the ROM with the original system considered as stable. A time delay model has also been presented to approximate the original system well in frequency and time domain. Also, the advantage of the method is that it maintains both transient and steady-state performance. The method proposed has been successfully applied to the linear systems and the results obtained indicate the methodology’s effectiveness. The proposed method, which proves to be an excellent match, efficient and superior as compared to the responses obtained by other methods in the literature concerning the same original system, validating the proposed technique.

Renovation in the Modified Pole Clustering Technique for the Linear Dynamic Systems

The authors propose a new mixed order reduction technique for large-scale linear dynamic systems (LSLDSs). The denominator of the original LSLDS is reduced by the proposed renovated pole clustering technique, whereas the reduced numerator is obtained by using the Pade approximations technique. The proposed technique is an improved form of the modified pole clustering technique suggested by Vishwakarma. It is well known that the low value of pole cluster centres, provides better matching of original LSLDS with low order reduced system (LORS). So by small modifications in the modified pole clustering technique, provides a lower value of pole cluster centres in comparison to all the techniques based on pole cluster. The proposed technique guarantees the preservation of stability and steady-state value of the Original LSLDS into a LORS with a deficient value of integral square error (ISE). Its supremacy is justified by taking two LSLDSs from the literature. The time and frequency responses of the proposed LORS are obtained by using MATLAB/Simulink and compared with other popular reduction techniques from the literature. The step time qualitative properties and performance index (ISE) of the proposed LORS is also compared with a few recent famous techniques which support the goodness and simplicity of the proposed technique. The proposed technique is also applicable to multi-input multi-output (MIMO) LSLDSs.

Order Abatement of Linear Dynamic Systems Using Renovated Pole Clustering and Cauer Second Form Techniques

A mixed-method for the order abatement of large-scale linear dynamic systems (LSLDSs) into desired low order systems is proposed. The denominator of the abated system (AS) is obtained by the renovated pole clustering technique, while the numerator is obtained by Cauer second form technique. The AS is stable if the original system (OS) is stable and retains all the essential time and frequency response specifications of the OS. The proposed mixed method is an improved version of the modified pole clustering technique. As we know, the magnitude of the pole cluster center plays an important role in the clustering technique for the abatement of LSLDS. Less magnitude of pole cluster center, better approximations matching of AS with the OS has occurred. The magnitude of dominated pole cluster centers obtained by the modified pole clustering technique or other pole clustering techniques is large compared to the proposed technique. Hence the proposed technique provides better approximations matching between OS and AS during the transient period compared to other clustering techniques, which supports the replacement of OS with better AS. The efficacy of the proposed technique is verified by taking three numerical examples and compared with other recent and famous techniques available in the literature.

A novel method based on pole clustering technique and differential evolution for model order reduction

This paper strives to present a model order reduction (MOR) method for complex high order linear time-invariant (LTI) single input-single output (SISO) systems. The recommended method utilises the benefits of pole clustering method and differential evolution algorithm. In this suggested method, approximated denominator polynomial is obtained by pole clustering method whereas; approximated numerator is obtained using differential evolution algorithm. To indicate the effectiveness of the suggested method over existing MOR techniques, a comparison on the basis of a performance index known as integral square error (ISE) is depicted in this paper by using simulation graphs and in tabular form. Further, the suggested method is extended for MIMO systems also. Numerical examples are solved to give better understanding of the propound technique for SISO and MIMO systems. The recommended method derives and guarantees a stable approximated ROM if the original higher order system (HOS) is stable.

System reduction using modified inverse distance measure and modified Cauer continued fraction method

A useful technique for obtaining the stable approximated model is proposed by combining modified inverse distance measure and modified Cauer continued fraction method. Modified inverse distance measure is based on pole clustering technique used to get the suitable dominant poles of the approximated model and modified Cauer continued fraction method has the advantages of approximation at the steady state as well as initial transient situations. Effectiveness of the proposed method is validated through considering numerical cases. The suggested method is computer oriented and simple in calculation.

Strain Accommodation in the Daliangshan Mountain Area, Southeastern Margin of the Tibetan Plateau

AbstractThe Xianshuihe‐Xiaojiang fault system (XXFS) plays a crucial role in accommodating relative motions of the south China block and the expanding Tibetan Plateau. Compared to the narrow southern and northern segments of the XXFS, the central section (also referred to as the Daliangshan mountain area) is broader and dissected by a network of faults. Geologic studies suggest that three major NNW trending faults may dominate slip partitioning of more recent faults in this region. However, due to accessibility issues, sparse geodetic studies have constrained geodetic fault slip rates with contradictory results. In this study, we use 17 new Global Navigation Satellite System sites combined with existing solutions to investigate slip partitioning of the region. We derive a tectonic velocity solution, develop a block kinematic model constrained by Euler pole clustering technique, and calculate geodetic fault slip rates to compare with geologic fault slip rates. We confirm that the Anninghe‐Daliangshan sliver (ADS) is a distinct, rigid block, and we resolve a new, rigid Daliangshan‐Yingjing‐Mabian block (DYB). Kinematic modeling predicts long‐term slip rates that suggest both the ADS and the DYB partition (~10.0–12.0 mm/year) relative motion between the Tibetan Plateau and south China block in the central XXFS, reconciling geologic observations. We suggest that both the continuum and microplate deformation patterns are present in our study area, of which the local tectonics is better explained by the microplate model, but scale of the kinematics makes its motion more consistent with the continuum model.

A Novel Method Based on Pole Clustering Technique and Differential Evolution for Model Order Reduction

This paper strives to present a model order reduction (MOR) method for complex high order linear time-invariant (LTI) single input-single output (SISO) systems. The recommended method utilises the benefits of pole clustering method and differential evolution algorithm. In this suggested method, approximated denominator polynomial is obtained by pole clustering method whereas; approximated numerator is obtained using differential evolution algorithm. To indicate the effectiveness of the suggested method over existing MOR techniques, a comparison on the basis of a performance index known as integral square error (ISE) is depicted in this paper by using simulation graphs and in tabular form. Further, the suggested method is extended for MIMO systems also. Numerical examples are solved to give better understanding of the propound technique for SISO and MIMO systems. The recommended method derives and guarantees a stable approximated ROM if the original higher order system (HOS) is stable.

Biased reduction method by combining improved modified pole clustering and improved Pade approximations

This paper presents a mixed method to reduce the order of the linear high order dynamic systems by combining improved modified pole clustering technique and improved Pade approximations. The denominator of the reduced order model is computed by improved modified pole clustering while the numerator coefficients are obtained by improved Pade approximations. The proposed method is competent in generating ‘k’ number of reduced order models from the original high order system. The superiority of the proposed method is concluded through numerical examples taken from literature and compared with existing well- known order reduction methods.

MIMO System Reduction Using Modified Pole Clustering and Genetic Algorithm

A new mixed method for reducing the order of the large-scale linear dynamic multi-input-multi-output (MIMO) systems has been presented. In this method, the common denominator polynomial of the reduced-order transfer function matrix is synthesized by using modified pole clustering while the coefficients of the numerator elements are computed by minimizing the integral square error between the time responses of the original and reduced system element using Genetic Algorithm. The modified pole clustering generates more dominant cluster centres than cluster centres obtained by pole clustering technique already available in literature. The proposed algorithm is computer-oriented and comparable in quality. This method guarantees stability of the reduced model if the original high-order system is stable. The algorithm of the proposed method is illustrated with the help of an example and the results are compared with the other well-known reduction techniques.

Robust pole placement in LMI regions

Discusses analysis and synthesis techniques for robust pole placement in linear matrix inequality (LMI) regions, a class of convex regions of the complex plane that embraces most practically useful stability regions. The focus is on linear systems with static uncertainty on the state matrix. For this class of uncertain systems, the notion of quadratic stability and the related robustness analysis tests are generalized to arbitrary LMI regions. The resulting tests for robust pole clustering are all numerically tractable because they involve solving linear matrix inequalities (LMIs) and cover both unstructured and parameter uncertainty. These analysis results are then applied to the synthesis of dynamic output-feedback controllers that robustly assign the closed-loop poles in a prescribed LMI region. With some conservatism, this problem is again tractable via LMI optimization. In addition, robust pole placement can be combined with other control objectives, such as H/sub 2/ or H/sub /spl infin// performance, to capture realistic sets of design specifications. Physically motivated examples demonstrate the effectiveness of this robust pole clustering technique.

On the Shape and Orientation Control of Orbiting Shallow Spherical Shell Structure

The dynamics of orbiting shallow flexible spherical shell structures under the influence of control actuators is studied. Control laws are developed to provide both attitude and shape control of the structure. It is seen that the elastic modal frequencies for the fundamental and lower modes are closely grouped due to the effect of the shell curvature. The shell is also assumed to be gravity stabilized by a spring-loaded dumbbell type damper attached at its apex. Control laws are developed based on the pole clustering technique and it is assumed that the dumbbell state information may not be directly observable. Numerical results verify that a significant savings in fuel consumption can be realized by using the hybrid shell-dumbbell system together with point actuators. Other results indicate that for the less robust systems instability may result by not including the orbital and first order gravity-gradient effects in the plant prior to control law design.