Model Order Reduction of Linear Time Interval System Using Stability Equation Method and a Soft Computing Technique

Kumar, Mangipudi Siva; Begum, Gulshad

doi:10.15598/aeee.v14i2.1432

Cited by 6 publications

(4 citation statements)

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“…Various strategies are available for model order reduction of higher order continuous and discrete interval systems. In [24], the low-order interval model is obtained using stability equation technique, Kharitonov's theorem and minimization of integral-square-error (ISE) utilizing differential evolution optimization technique. Singh et al [6] adopted Routh-Pade approximation for order reduction of interval systems and also proposed two simple expressions for computing time moments (TMs) and Markov parameters (MPs).…”

Section: Introductionmentioning

confidence: 99%

Archives of Control Sciences

Bokam¹,

Singh

Devarapalli

et al. 2021

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In recent, modeling practical systems as interval systems is gaining more attention of control researchers due to various advantages of interval systems. This research work presents a new approach for reducing the high-order continuous interval system (HOCIS) utilizing improved Gamma approximation. The denominator polynomial of reduced-order continuous interval model (ROCIM) is obtained using modified Routh table, while the numerator polynomial is derived using Gamma parameters. The distinctive features of this approach are: (i) It always generates a stable model for stable HOCIS in contrast to other recent existing techniques; (ii) It always produces interval models for interval systems in contrast to other relevant methods, and, (iii) The proposed technique can be applied to any system in opposite to some existing techniques which are applicable to second-order and third-order systems only. The accuracy and effectiveness of the proposed method are demonstrated by considering test cases of single-inputsingle-output (SISO) and multi-input-multi-output (MIMO) continuous interval systems. The robust stability analysis for ROCIM is also presented to support the effectiveness of proposed technique.

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Section: Introductionmentioning

confidence: 99%

Archives of Control Sciences

Bokam¹,

Singh

Devarapalli

et al. 2021

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“…Various strategies are available for model order reduction of higher order continuous and discrete interval systems. In [28], the low-order interval model is obtained using the stability equation technique, Kharitonov's theorem and minimization of integral-square-error (ISE) utilizing the differential evolution optimization technique. Singh et al [29] adopted Routh-Pade approximation for order reduction of interval systems and also proposed two simple expressions for computing time moments (TMs) and Markov parameters (MPs).…”

Section: Introductionmentioning

confidence: 99%

Sine Cosine Algorithm Assisted FOPID Controller Design for Interval Systems Using Reduced-Order Modeling Ensuring Stability

Bokam

Patnana

Varshney³

et al. 2020

Algorithms

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The focus of present research endeavor was to design a robust fractional-order proportional-integral-derivative (FOPID) controller with specified phase margin (PM) and gain cross over frequency (ωgc) through the reduced-order model for continuous interval systems. Currently, this investigation is two-fold: In the first part, a modified Routh approximation technique along with the matching Markov parameters (MPs) and time moments (TMs) are utilized to derive a stable reduced-order continuous interval plant (ROCIP) for a stable high-order continuous interval plant (HOCIP). Whereas in the second part, the FOPID controller is designed for ROCIP by considering PM and ωgc as the performance criteria. The FOPID controller parameters are tuned based on the frequency domain specifications using an advanced sine-cosine algorithm (SCA). SCA algorithm is used due to being simple in implementation and effective in performance. The proposed SCA-based FOPID controller is found to be robust and efficient. Thus, the designed FOPID controller is applied to HOCIP. The proposed controller design technique is elaborated by considering a single-input-single-output (SISO) test case. Validity and efficacy of the proposed technique is established based on the simulation results obtained. In addition, the designed FOPID controller retains the desired PM and ωgc when implemented on HOCIP. Further, the results proved the eminence of the proposed technique by showing that the designed controller is working effectively for ROCIP and HOCIP.

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“…20 And some more methods, which use the combination of conventional and stochastic search algorithms for interval systems, are presented in VijayaAnand et al 24 and Sivakumar and Begum. 25 The methods belonging to either of three categories offer the possible user certain advantages and most likely certain disadvantages. In spite of the significant number of MOR methods are available in the literature, still there is a lack of a simple and effective method to give the finest results for all types of systems.…”

Section: Introductionmentioning

confidence: 99%

“…Thereby the numerator coefficients of the ROM are evaluated using equations (22) and (25). The ROM numerator coefficients obtained by this method assure producing optimum value of the error function (E) and also retain the full IRE of the original HOS in the ROM along with matching of initial time response values either for impulse or for step input.…”

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confidence: 99%

A novel model reduction approach for linear time-invariant systems via enhanced PSO-DV algorithm and improved MPPA method

Vasu

Mangipudi²,

Ramalingaraju

2019

Proceedings of the Institution of Mechanical Engineers, Part I:

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In this article, the combination of stochastic search and conventional approaches are used to develop an optimal frequency-domain model order reduction method for determining the stable and accurate reduced-order model for the stable large-scale linear time-invariant systems. The method uses the enhanced particle swarm optimization with differentially perturbed velocity algorithm to determine the denominator polynomial coefficients of the reduced-order model, whereas the numerator polynomial coefficients of the reduced-order model are determined by using an improved multi-point Padé approximation method. The method generates an optimum reduced-order model by minimizing an objective function [Formula: see text], which is formulated using two functions. The first function, [Formula: see text], evaluates the measure of integral squared error between the step responses of the original system and the reduced-order model. And the second function evaluates the measure of retention of full impulse response energy of the original system in the reduced-order model. Therefore, by minimizing the objective function ‘ E’, the proposed method is guaranteed for preserving passivity, stability and the accuracy of the original higher order system in the reduced-order model. The proposed method is extended to the linear time-invariant multi-input multi-output system. In this case, an optimal reduced-order model is determined by minimizing a single objective function [Formula: see text], which is formulated by linear scalarizing of all the objective function [Formula: see text] components. The method is popular for preserving stability, passivity and accuracy of the original system in the reduced-order model. The validation of the method is shown by applying to a sixth-order single-input single-output hydropower system model as well as to the seventh-order two-area multi-input multi-output power system model. The comparison of the simulation results of integral squared error and impulse response energy values of the reduced-order models demonstrates the dominance of the proposed method than the existing reduction methods available in the literature.

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Model Order Reduction of Linear Time Interval System Using Stability Equation Method and a Soft Computing Technique

Cited by 6 publications

References 0 publications

Archives of Control Sciences

Archives of Control Sciences

Sine Cosine Algorithm Assisted FOPID Controller Design for Interval Systems Using Reduced-Order Modeling Ensuring Stability

A novel model reduction approach for linear time-invariant systems via enhanced PSO-DV algorithm and improved MPPA method

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