Order reduction of linear time invariant large-scale system by preserving the impact of dominant poles in the reduced model

2021 ◽  
pp. 1-12
Author(s):  
Pragati Shrivastava Deb ◽  
Leena G
Keyword(s):  
Large Scale ◽  
Linear Time ◽  
Order Reduction ◽  
Reduced Model ◽  
Large Scale System ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
The Impact

scholarly journals Reduction of Large-Scale Dynamical Systems by Extended Balanced Singular Perturbation Approximation

2020 ◽  
Vol 5 (5) ◽  
pp. 939-956 ◽  
Author(s):  
Santosh Kumar Suman ◽  
Awadhesh Kumar
Keyword(s):  
Singular Perturbation ◽  
Large Scale ◽  
Linear Time ◽  
Order Reduction ◽  
Original System ◽  
Simplified Approach ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
Time Systems ◽  
Perturbation Approximation

A simplified approach for model order reduction (MOR) idea is planned for better understanding and explanation of large- scale linear dynamical (LSLD) system. Such approaches are designed to well understand the description of the LSLD system based upon the Balanced Singular Perturbation Approximation (BSPA) approach. BSPA is tested for minimum / non-minimal and continuous/discrete-time systems valid for linear time-invariant (LTI) systems. The reduced-order model (ROM) is designed to preserved complete parameters with reasonable accuracy employing MOR. The Proposed approach is based upon retaining the dominant modes (may desirable states) of the system and eliminating comparatively the less significant eigenvalues. As the ROM has been derived from retaining the dominant modes of the large- scale linear dynamical stable system, which preserves stability. The strong aspect of the balanced truncation (BT) method is that the steady-state values of the ROM do not match with the original system (OS). The singular perturbation approximation approach (SPA) has been used to remove this drawback. The BSPA has been efficaciously applied on a large-scale system and the outcomes obtained show the efficacy of the approach. The time and frequency response of an approximated system has been also demonstrated by the proposed approach, which proves to be an excellent match as compared to the response obtained by other methods in the literature review with the original system.

scholarly journals Order Reduction based on Coulomb’s and Franklin’s laws Algorithm

2021 ◽  
Author(s):  
Ram Kumar ◽  
Afzal Sikander
Keyword(s):  
Large Scale ◽  
Linear Time ◽  
Order Reduction ◽  
Absolute Error ◽  
Search Space ◽  
Engineering Problem ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Linear Time Invariant

Abstract The Coulomb and Franklin laws (CFL) algorithm is used to construct a lower order model of higher-order continuous time linear time-invariant (LTI) systems in this study. CFL is quite easy to implement in obtaining reduced order model of large scale system in control engineering problem as it employs the combined effect of Coulomb’s and Franklin’s laws to find the best values in search space. The unknown coefficients are obtained using the CFLA methodology, which minimises the integral square error (ISE) between the original and proposed ROMs. To achieve the reduced order model, five practical systems of different orders are considered. Finally, multiple performance indicators such as the ISE, integral of absolute error (IAE), and integral of time multiplied by absolute error were calculated to determine the efficacy of the proposed methodology. The simulation results were compared to previously published well-known research.

scholarly journals Frequency Weighted Discrete-Time Controller Order Reduction Using Bilinear Transformation

2011 ◽  
Vol 62 (1) ◽  
pp. 44-48 ◽  
Author(s):  
Paknosh Karimaghaee ◽  
Navid Noroozi
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Linear Time ◽  
Order Reduction ◽  
Bilinear Transformation ◽  
Reduced Order ◽  
Linear Time Invariant ◽  
The Stability ◽  
Controllability And Observability ◽  
Time Invariant

Frequency Weighted Discrete-Time Controller Order Reduction Using Bilinear TransformationThis paper addresses a new method for order reduction of linear time invariant discrete-time controller. This method leads to a new algorithm for controller reduction when a discrete time controller is used to control a continuous time plant. In this algorithm, at first, a full order controller is designed ins-plane. Then, bilinear transformation is applied to map the closed loop system toz-plane. Next, new closed loop controllability and observability grammians are calculated inz-plane. Finally, balanced truncation idea is used to reduce the order of controller. The stability property of the reduced order controller is discussed. To verify the effectiveness of our method, a reduced controller is designed for four discs system.

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