Pole Clustering Research Articles

Designing of 2‐degree of freedom load frequency controller for power system using novel improved pole clustering and genetic method of reduced‐order modelling

Designing of <scp>2‐degree of freedom</scp> load frequency controller for power system using novel improved pole clustering and genetic method of <scp>reduced‐order</scp> modelling

Enabling Rapid Financial Response to Disasters: Knotting and Reknotting Multiple Paradoxes in Interorganizational Systems

While market-based solutions are increasingly being proposed to address major societal and development issues, they are also often considered antithetical to issues such as climate change, poverty alleviation and disaster response. In particular, the interorganizational systems involved in such market solutions gives rise to multiple contradictory tensions, known as paradoxes. We therefore adopt a paradox lens to explain the dynamics through which different actors within these systems navigate the contradictions that are generated. Drawing on a global qualitative study of multi-country risk pools that provide rapid capital in the immediate aftermath of disaster, we advance paradox theory by showing how organizational actors’ interactions i) maintain equilibrium by generating mutually reinforcing balance among paradoxes, whilst ii) the clustering of poles from different paradoxes generates disequilibrium, and iii) the reknotting of poles from different paradoxes restores equilibrium. As our process framework shows, these dynamics form an iterative cycle between equilibrium and disequilibrium that is essential in enhancing the promise of market-based solutions to address development issues; in our study increasing the rapid availability of capital to respond to disasters such as hurricanes, earthquakes and droughts.

LMI-based design of state-feedback controllers for pole clustering of LPV systems in a union of 𝒟 R -regions

This paper introduces an approach for the design of a state-feedback controller that achieves pole clustering in a union of -regions for linear parameter varying systems. The design conditions, obtained using a partial pole placement theorem, are eventually expressed in terms of linear matrix inequalities. In addition, it is shown that the approach can be modified in a shifting sense. Hence, the controller gain is computed such that different values of the varying parameters imply different regions of the complex plane where the closed-loop poles are situated. This approach enables the online modification of the closed-loop performance. The effectiveness of the proposed method is demonstrated by means of simulations.

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.

Resilient Design of Robust Multi-Objectives PID Controllers for Automatic Voltage Regulators: D-Decomposition Approach

Resilient design of robust multi-objectives PID controllers via the D-decomposition method is presented in this paper for automatic voltage regulators (AVRs). The stabilizing interval of derivative gain ( k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> ) is analytically calculated by the Routh-Hurwitz criterion. The k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> domain, for a fixed value of k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> , is decomposed in root invariant regions by mapping the stability boundary from the complex plane. Two regions, described by fixed damping isoclines, are assigned for pole-clustering in the open-left half plane (LHP). Other than regional pole clustering, gain and phase margins, as frequency domain specifications, are considered. Both robust stability and robust performance are considered by stabilizing a set of principle segment plants simultaneously. Optimal pole-placer PID controllers are computed analytically. If a robust control basin does exist for a specific compromise of control objective, the criterion of the maximum inscribed circle is considered to compute the maximum radius of controller resiliency. The merit of the proposed design is the simultaneous consideration of three control concerns, namely performance optimality, stability robustness and controller resiliency. Computation, validation, and simulation results are presented to show the simplicity and efficacy of the suggested method in tracing control basins (CBs) of all admissible PID controllers.

Active control of linear vibrating systems for antiresonance assignment with regional pole placement

This paper proposes a novel method for antiresonance assignment and regional pole placement in linear time-invariant vibrating systems, by means of state feedback control. The method also handles asymmetric systems and unstable ones too. Additionally, it works with both point and cross-receptances and handles the simultaneous assignment of more antiresonances in the same receptance.The method relies on two stages. In the first stage, the desired pairs of closed-loop zeros of a prescribed receptance are exactly assigned. In the second stage, all the closed-loop system poles are placed within the desired region of the complex plane. This feature allows the controller to impose the system stability and to feature the desired dynamic properties through a regional pole placement. Since the gain correction computed in the second stage is obtained as a solution of the homogeneous system related to the zero-assignment problem, it does not cause any spillover on the assigned zeros. The first step exploits the receptance method for gain computing, while the second step uses the first-order model formulation to exploit all the benefits of the Linear Matrix Inequality theory, by formulating a bilinear matrix problem solved as a semidefinite optimization aimed at reducing the control effort.The chief original contribution of the proposed method is that it embeds an a-priori imposition of both the closed-loop stability and the pole clustering in the desired regions, by overcoming the limitations of most of the methods appeared in the literature. The method effectiveness is demonstrated through five meaningful test cases.

Modelling issues and aggressive robust load frequency control of interconnected electric power systems

This article is concerned with modelling, controllability analysis and the design of aggressive robust controllers for interconnected electric power systems. The proposed Load Frequency Control (LFC), relying on methodologies enhanced with integral action and pole clustering, can provide frequency regulation and fast transient response despite the presence of unknown disturbance load application. The inherent saturation constraints are handled by the combination of a controller gain minimisation framework and an anti-windup enhanced controller design which provides stability guarantees, while avoiding frequency and tie-line power oscillations. For this scheme, particular attention should be paid on the modelling and controllability aspects of the power system, where it is shown that due to the singularity of the Laplacian matrix of the network's graph, a reduction of the state vector is necessary. Simulation studies are offered to illustrate the effectiveness of the suggested scheme.

Robust multi-objective PSSs design via complex Kharitonov's theorem

This paper represents a step toward shooting an optimal robust three-parameter power system stabilizer (PSS) with the common form of (x1+x2s)/(1+x3s). The whole set of stabilizing PSSs is graphically characterized using d-decomposition with which the controller-parameter space is subdivided into root-invariant regions. Design is accomplished using the bench mark model of single machine-infinite bus system (SMIB). Rather than Hurwitz stability, d-decomposition is extended to consider d-stability where D refers to a pre-specified damping cone in the open left half of the complex s-plane to enhance time-domain specifications. Pole clustering in damping cone is inferred by enforcing Hurwitz stability of a complex polynomial accounting for the geometry of such cone. Parametric uncertainties of the model imposed by continuous variation in load patterns is captured by an interval polynomial. As a result, computing the set of all robust d-stabilizing PSSs calls for Hurwitz stability of a complex interval polynomial. The latter is tackled by a complex version of Kharitonov's theorem. A less-conservative and computationally effective approach based on only two extreme plants is concluded from the geometry of the stability region in the controller parameter plane. Simulation results affirm the robust stability and performance with the proposed PSSs over wide range of operating points.

Orbital Precession in the Distant Solar System: Further Constraining the Planet Nine Hypothesis with Numerical Simulations

Abstract The longitudes of perihelia and orbital poles of the solar system’s dozen or so most remote detected objects are clustered in a manner inconsistent with that of a random sample of uniformly distributed orbits. While small number statistics and observational biases may explain these features, the statistical significance of the clustering has led to the recent development of the “Planet Nine hypothesis.” In the proposed scenario, orbits in the distant solar system are shepherded via secular perturbations from an undetected massive planet on an eccentric orbit. However, the precession of perihelia and nodes in the outer Kuiper Belt and inner Oort cloud are also affected by the giant planets, passing stars, and the galactic tide. We perform a large suite of numerical simulations designed to study the orbital alignment of extreme trans-Neptunian objects (ETNOs) and inner Oort cloud objects (IOCOs). In our various integrations that include Planet Nine, we consistently find that ≳60% of ETNOs and IOCOs that are detectable after 4 Gyr are also anti-aligned in perihelia with the distant massive perturber. However, when we randomly select 17 objects from this sample of remaining orbits, there is significant scatter in the degree of longitude of perihelion and orbital pole clustering that might be observed. Furthermore, we argue that, in the absence of Planet Nine, 17 randomly drawn orbits should still exhibit some clustering even if the underlying distribution is uniform. Thus, we find that still more ETNO and IOCO detections are required to confidently infer the presence of Planet Nine.

Pole Clustering-based Modified Reduced-Order Model for Boiler System

ABSTRACT A modified reduction order is proposed for the LTI boiler system from the pole clustering method to reduce the higher-order system which yields an exact system model also to minimize the complexity involved in traditional methods. This approach is used to compute the reduced-order system from the combined method of cluster and Routh-Padé approximation techniques that are to achieve the effective formulated reduced-order system, and the method is explained through a numerical example. To evaluate the higher-order system from the new technique, the results of the proposed method are compared with other recently developed order reduction techniques like pole clustering, optimization algorithm, minimum variance, least square and recursive least square. The comparison results show that the proposed method is a powerful and stable method for linear time invariant boiler system.

Automated Harmonic Signal Removal Technique Using Stochastic Subspace-Based Image Feature Extraction.

This paper presents automated harmonic removal as a desirable solution to effectively identify and discard the harmonic influence over the output signal by neglecting any user-defined parameter at start-up and automatically reconstruct back to become a useful output signal prior to system identification. Stochastic subspace-based algorithms (SSI) methods are the most practical tool due to the consistency in modal parameters estimation. However, it will be problematic when applied to structures with rotating machines and the presence of harmonic excitations. Difficulties arise when automating this procedure without any human interaction and the problem is still unresolved because stochastic subspace-based algorithms (SSI) methods still require parameters (the maximum within-cluster distance) that are compulsory to be defined at start-up for each analysis of the dataset. Thus, the use of image-based feature extraction for clustering and classification of harmonic components and structural poles directly from a stabilization diagram and for modal system identification is the focus of the present paper. As a fundamental necessary condition, the algorithm has been assessed first from computed numerical responses and then applied to the experimental dataset with the presence of harmonic excitation. Results of the proposed approach for estimating modal parameters demonstrated very high accuracy and exhibited consistent results before and after removing harmonic components from the response signal.

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.

Robust pole-placer power system stabilisers design via complex Kharitonov's theorem

In this paper, the synthesis of robust three-parameter power system stabilisers (PSSs) is presented. Graphical characterisation of the set of stabilising PSSs is carried out using D-decomposition. Dynamic model of single-machine infinite-bus system (SMIB) is considered to accomplish the design. D-decomposition is extended to consider D-stability where D refers to a pre-specified damping cone in the open left half of the complex plane to enhance time-domain specifications. Pole clustering in a damping cone is inferred by enforcing Hurwitz stability of a complex polynomial accounting for the geometry of such cone. Parametric uncertainties of the model are captured by an interval polynomial. Hence, performance enhancement calls for Hurwitz stability of a complex interval polynomial. The latter is tackled by the complex version of Kharitonov's theorem. A less-conservative and computationally effective approach is concluded from the geometry of the stability region. Simulation results affirm robust stability and performance over a wide range of operating points.

Performance enhancements of physical systems by reduced-order modelling and simulation

It is a matter of great concern to simplify the large-scale physical systems for obtaining a better understanding of the behaviour more accurately at a faster rate. The proposed method focuses on the designing of a method of model order reduction of real time physical systems based on the mixed approach. Improved pole clustering is preferred to reduce the denominator and genetic algorithm to reduce the numerator equation. These techniques are implemented in Matlab simulation environment. The proposed order reduction technique is compared with previously designed methods. The performance comparison is done based on the calculated parameters viz. ISE, rise time, percentage overshoot, steady-state error, settling time as well gain margin and phase margin. The research work reveals that the proposed method provides an improved approximation of a large order system as compared to previous techniques with improved accuracy and better transient and steady-state response.

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.

Identification of a Synergistic Multi-Drug Combination Active in Cancer Cells via the Prevention of Spindle Pole Clustering.

A major limitation of clinically used cancer drugs is the lack of specificity resulting in toxicity. To address this, we performed a phenotypically-driven screen to identify optimal multidrug combinations acting with high efficacy and selectivity in clear cell renal cell carcinoma (ccRCC). The search was performed using the Therapeutically Guided Multidrug Optimization (TGMO) method in ccRCC cells (786-O) and nonmalignant renal cells and identified a synergistic low-dose four-drug combination (C2) with high efficacy and negligible toxicity. We discovered that C2 inhibits multipolar spindle pole clustering, a survival mechanism employed by cancer cells with spindle abnormalities. This phenotype was also observed in 786-O cells resistant to sunitinib, the first line ccRCC treatment, as well as in melanoma cells with distinct percentages of supernumerary centrosomes. We conclude that C2-treatment shows a high efficacy in cells prone to form multipolar spindles. Our data suggest a highly effective and selective C2 treatment strategy for malignant and drug-resistant cancers.

H-infinity controller with graphical LMI region profile for liquid slosh suppression

This paper presents a H-infinity synthesis with pole clustering based on LMI region schemes for liquid slosh control. Using LMI approach, the regional pole placement known as LMI region combined with design objective in H-infinity controller guarantee a fast input tracking capability and very minimal liquid slosh. A graphical profile of the transient response of liquid slosh suppression system with respect to pole placement is very useful in giving more flexibility to the researcher in choosing a specific LMI region. With the purpose to confirm the design of control scheme, a liquid slosh model is considered to represent the lateral slosh movement. Supremacy of the proposed approach is shown by comparing the results with hybrid model-free fuzzy-PID controller with derivative filter. The performance of the control schemes is examined in terms of time response specifications of lateral tank tracking capability and level of liquid slosh reduction.

A new model order reduction method for the design of compensator by using moment matching algorithm

The aim of this paper is the construction of a new model reduction technique for large scale stable linear dynamic systems. It is principally focused on the dominant modes and time moments retention. This reduction implicates the translation of the overall important features confined in the large scale complete order model into the lower order system, allowing the computation of approximant denominator by using generalized pole clustering method. The approximant numerator is obtained by means of the factor division algorithm. As a result, a lower order system is obtained. To demonstrate its effectiveness, to highlight some fundamental of its features, and to accomplish its accuracy, a comparative study is done. Two standard numerical examples are taken, where approximant model computed by the proposed method is compared with the reduced order models computed from the recently proposed methods as well as well-known model reduction schemes. The paper is also emphasized on the design of compensator by using moment matching algorithm with the help of the reduced model. The design of compensator is validated and illustrated with the help of a standard numerical example taken from the literature.

A New Model Reduction Method for the Linear Dynamic Systems and Its Application for the Design of Compensator

A new model reduction method for the simplification and design of a controller for the linear time-invariant systems is proposed. An improved generalized pole clustering algorithm is employed in the proposed technique for obtaining the denominator of the reduced model. The numerator is computed with a simple mathematical technique available in the literature. The proposed method guarantees the stability in the reduced plant given that the full-order plant is stable and also retains the fundamental characteristics of the original model in the approximated one. This reduced model has been used for the design of compensator for the large-scale original plant by using a new algorithm. The compensator obtained by using the reduced model gives the approximately same time domain specification as compensator obtained by using large-scale original system, and the design of compensator by using the reduced model is comparatively easier. The results of the proposed algorithm are compared with existing methods of reduced-order modeling which show improvement in the performance error indices, time response characteristics and time domain specifications. The validity, effectiveness and superiority of the proposed technique have been demonstrated through some standard numerical examples.