A New Technique for the Reduced-Order Modelling of Linear Dynamic Systems and Design of Controller

Prajapati, Arvind Kumar; Rayudu, V G Durgarao; Sikander, Afzal; Prasad, Rajendra

doi:10.1007/s00034-020-01412-y

Cited by 26 publications

(10 citation statements)

References 61 publications

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“…This figure demonstrates that the lower order model (39) acquired by the proposed technique precisely retains the characteristics of the original system (34). In Table 2, it is shown that the performance error indices values of the proposed method are the lowest values compared with some standard methods (Chen et al, 1979; Gu, 2005; Krishnamurthy and Seshadri, 1978; Moore, 1981; Wan, 1981), recently proposed methods (Kranthi et al, 2013; Kumar et al, 2012; Prajapati et al, 2020; Prajapati and Prasad, 2018c) and optimization methods (Desai and Prasad, 2013; Vishwakarma and Prasad, 2009). The accuracy and effectiveness of the proposed scheme to the other popular diminution schemes present in the literature are tabulated in Table 2 by comparing various performance error indices.…”

Section: Controller Design Algorithmmentioning

confidence: 96%

A novel order reduction method for linear dynamic systems and its application for designing of PID and lead/lag compensators

Prajapati

Prasad

2020

Transactions of the Institute of Measurement and Control

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This paper proposes a new model order reduction technology for the simplification of the complexity of large scale models. The proposed technique is focused on the Mihailov stability approach that guarantees the stability of the reduced model constrained that the complex system is stable. In this scheme, the denominator coefficients of the approximated simplified system are computed by using the Mihailov stability algorithm and the truncation method is used for the determination of coefficients of the numerator polynomial. The effectiveness and efficiency of the proposed approach are illustrated by comparing the step responses of the given system and approximated lower order models. The error indices such as integral square error (ISE), relative integral square error (RISE), integral absolute error (IAE) and integral time weighted absolute error (ITAE) are used as performance indices for comparing the proposed scheme with other existing standard reduced order modeling methods. The obtained reduced model is used for the designing of controllers for the original complex system. A new scheme for the determination of controllers is also proposed for the large scale models with help of reduced order modeling. The proposed technique is validated by applying it to an eighth order flexible-missile control system and a third order fuel control system. The simulation results show the dominance of the proposed methodologies over the latest model diminution techniques available in the literature.

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Section: Controller Design Algorithmmentioning

confidence: 96%

A novel order reduction method for linear dynamic systems and its application for designing of PID and lead/lag compensators

Prajapati

Prasad

2020

Transactions of the Institute of Measurement and Control

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“…To examine the effectiveness of the proposed technique with some other standard model abatement algorithms, integral square error (ISE) and relative integral square error (RISE) between the original system and the reduced order models are calculated, which are defined as (Narwal and Prasad, 2016, 2017b; Prajapati et al, 2020)…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…The model diminution techniques have been broadly used in the area of electrical engineering (Ha et al, 2015; Kumar et al, 2018; Prajapati et al, 2020; Prajapati and Prasad, 2021). Fortuna et al (1992) discuss the applications of model order abatement in the different areas of research, such as power systems, transient electromagnetic phenomena, electrical induction machines and Joint European Torus (JET) load and so on.…”

Section: Introductionmentioning

confidence: 99%

“…In Sikander and Prasad (2019), the application of system diminution technique for balancing control of the two-wheeled mobile robot is illustrated. In Gupta and Manocha (2021); Kumari and Vishwakarma (2021); Prajapati and Prasad (2019a, 2020); Tong and Chen (2017); Tong et al (2014), the application of model diminution techniques is discussed in the control systems.…”

Section: Introductionmentioning

confidence: 99%

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

Prajapati

Prasad

2021

Transactions of the Institute of Measurement and Control

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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.

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“…Furthermore, these methods had drawbacks such as non-uniqueness, pole clustering, gain adjustment and difficulty to maintain the dominant roots in the lower order system for non-minimum higher order plants. Ahamed et al (2022a, 2022b), Prajapati and Prasad, 2019, 2020, 2020b, 2022 and Prajapati et al (2020) have presented a number of reduction techniques to overcome these drawbacks, guaranteeing the stability of lower order models in addition to reproducing the behaviour of the original large-scale model for a number of higher order systems. These studies have shown that the reduced-order models produced by Mihailov stability, enhanced Pade approximation and truncation, improved generalized pole clustering, moment matching and salp swarm optimization approaches not only reflect the behaviour of the original large-scale model methods but also ensure the stability of the reduced-order models.…”

Section: Introductionmentioning

confidence: 99%

An effective controller design strategy for higher order systems

Chandramouleeswaran,

Deivanayagam Pillai,

Ramasamy

et al. 2023

Journal of Vibration and Control

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The recent methods that guarantee the stability of the reduced-order models are Mihailov stability, improved Pade approximation and truncation, improved generalized pole clustering, moment matching and salp swarm optimization. Further, these methods could overcome the limitations such as non-uniqueness, pole clustering, gain adjustment and difficulty to maintain the dominant roots in the lower order system for non-minimum higher order plants. This research emphasizes the design of the proposed compensating algorithm by using an additional open loop zero for the stable reduced-order models of large-scale single-input single-output linear time-invariant continuous time systems. The results of the proposed algorithm are compared with the existing compensating methods and the design is validated and illustrated numerically.

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A New Technique for the Reduced-Order Modelling of Linear Dynamic Systems and Design of Controller

Cited by 26 publications

References 61 publications

A novel order reduction method for linear dynamic systems and its application for designing of PID and lead/lag compensators

A novel order reduction method for linear dynamic systems and its application for designing of PID and lead/lag compensators

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

An effective controller design strategy for higher order systems

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