scholarly journals Higher Order Reduction of Uncertain Systems: Affine Arithmeti

2021 ◽  
Vol 08 (1&2) ◽  
pp. 1-4
Author(s):  
H Mallesam Dora ◽  
Keyword(s):  
Uncertain Systems ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Order System ◽  
Effective Algorithm ◽  
Order Model ◽  
Reduced Order ◽  
Numerical Examples ◽  
Rigorous Study ◽  
Lower Order System

In this paper the Modified Routh Approximation (MRA) and Affine Arithmetic (AA) methods are investigates for obtaining the reduced order model (ROM) of SISO, discrete & MIMO uncertain systems into lower order system. Rigorous study and analysis of physical system direct to the outcome of systems with uncertainty instead of certain coefficients. Thus, systems having uncertain but bounded parameters known as uncertain systems are under consideration in this paper. An effective algorithm to determine the reduced order model is proposed here. This proposed methodology is verified using numerical examples available from the literature.

scholarly journals Design of Controller for Large Scale Uncertain Systems via Reduces Order Model

2020 ◽  
Vol 6 (12) ◽  
pp. 262-267
Author(s):  
Vudikala Lalitha and Dr. T Narasimhulu
Keyword(s):  
Uncertain Systems ◽  
Large Scale ◽  
Least Squares Method ◽  
Generalized Least Squares ◽  
High Order ◽  
Reduced Order Model ◽  
Order System ◽  
Order Model ◽  
Reduced Order ◽  
High Order System

In This paper, a method of designing the Controller for large scale uncertain systems. The Controller is designed via a reduced order model for a given high order system. An optimized reduced order model is derived with minimum ISE. The proposed method guarantees stability of the reduced model, if the original high order system is stable system. A PID controller is designed for the high order original systems through its low order model proposed. This paper presents an improvement to generalized least squares method of model order reduction. The improvement enhances the flexibility of the method with very little computational requirement. The reduction procedure is simple, efficient and always generates stable reduced models for the stable high order systems. The proposed method is illustrated with typical numerical examples taken from the literature and the results are compared with the other existing methods to show its superiority.

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.

Model Simplification and Stability Robustness With Elastic Flight Vehicles

1995 ◽  
Vol 117 (3) ◽  
pp. 336-342
Author(s):  
Brett Newman ◽  
David K. Schmidt
Keyword(s):  
Closed Loop ◽  
Order Reduction ◽  
Higher Order ◽  
Reduced Order Model ◽  
Control Law ◽  
Model Simplification ◽  
Closed Loop System ◽  
Order Model ◽  
Reduced Order ◽  
Stability Robustness

Quantitative criteria are presented for model simplification, or order reduction, such that the reduced order model may be used to synthesize and evaluate a control law, and the stability and stability robustness obtained using the reduced order model will be preserved when controlling the higher order system. The error introduced due to model simplification is treated as modeling uncertainty, and some of the results from multivariable robustness theory are brought to bear on the model simplification problem. Also, the importance of the control law itself, in meeting the modeling criteria, is underscored. A weighted balanced order reduction technique is shown to lead to results that meet the necessary criteria. The procedure is applied to an aeroelastic vehicle model, and the results are used for control law development. Critical robustness properties designed into the lower order closed-loop system are shown to be present in the higher order closed-loop system.

Order Reduction of Parametrically Excited Nonlinear Systems Subjected to External Periodic Excitations

2009 ◽  
Author(s):  
Sangram Redkar ◽  
S. C. Sinha
Keyword(s):  
Nonlinear Systems ◽  
Fundamental Solution ◽  
Invariant Manifold ◽  
Large Scale ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
And Control

In this work, some techniques for order reduction of nonlinear systems with periodic coefficients subjected to external periodic excitations are presented. The periodicity of the linear terms is assumed to be non-commensurate with the periodicity of forcing vector. The dynamical equations of motion are transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of the resulting equations become time-invariant while the forcing and/or nonlinearity takes the form of quasiperiodic functions. The techniques proposed here; construct a reduced order equivalent system by expressing the non-dominant states as time-varying functions of the dominant (master) states. This reduced order model preserves stability properties and is easier to analyze, simulate and control since it consists of relatively small number of states in comparison with the large scale system. Specifically, two methods are outlined to obtain the reduced order model. First approach is a straightforward application of linear method similar to the ‘Guyan reduction’, the second novel technique proposed here, utilizes the concept of ‘invariant manifolds’ for the forced problem to construct the fundamental solution. Order reduction approach based on invariant manifold technique yields unique ‘reducibility conditions’. If these ‘reducibility conditions’ are satisfied only then an accurate order reduction via ‘invariant manifold’ is possible. This approach not only yields accurate reduced order models using the fundamental solution but also explains the consequences of various ‘primary’ and ‘secondary resonances’ present in the system. One can also recover ‘resonance conditions’ associated with the fundamental solution which could be obtained via perturbation techniques by assuming weak parametric excitation. This technique is capable of handing systems with strong parametric excitations subjected to periodic and quasi-periodic forcing. These methodologies are applied to a typical problem and results for large-scale and reduced order models are compared. It is anticipated that these techniques will provide a useful tool in the analysis and control system design of large-scale parametrically excited nonlinear systems subjected to external periodic excitations.

scholarly journals Optimal Reduced Order Model of Single- Shaft Heavy Duty Gas Turbine Power Plants

2020 ◽  
Vol 5 (9) ◽  
pp. 1090-1098
Author(s):  
M. Ramasubramanian ◽  
M. Thirumarimurugan ◽  
P. Ananthi
Keyword(s):  
Gas Turbine ◽  
Optimization Technique ◽  
Higher Order ◽  
Reduced Order Model ◽  
Order System ◽  
Heavy Duty ◽  
Order Model ◽  
Reduced Order ◽  
Particle Swarm Optimization Technique ◽  
Heavy Duty Gas Turbine

Design of controller and analyzing the response of higher order system in real time environment would be very complex and expensive. Therefore, an attempt has been made in this paper to obtain the reduced order model of single-shaft Heavy duty gas turbine plants ranging from 18.2 to 106.7 MW by using various model order reduction techniques. The step response of Heavy duty gas turbine model using the reduced order models are compared with that of the original MATLAB/ Simulink model. Various time domain specifications and performance index criteria have been considered for analyzing the responses. The simulation results show that the response obtained by Routh approximation-Pade approximation technique based reduced order model mimics the original, higher order Heavy Duty gas turbine response. It is also proposed in this paper to improve the response by optimizing the co-efficients of reduced order model using Particle Swarm Optimization technique. On comparing the simulation results, Particle Swarm Optimization technique based reduced order model yield better transient and steady state response as close to original higher order system and hence it is identified as an optimal reduced order model for all Heavy Duty gas turbine plants in grid connected operation

scholarly journals Suboptimal Control Using Model Order Reduction

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Avadh Pati ◽  
Awadhesh Kumar ◽  
Dinesh Chandra
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Higher Order ◽  
Reduced Order Model ◽  
Suboptimal Control ◽  
Order Model ◽  
Model Order ◽  
Markov Parameters ◽  
Reduced Order ◽  
Partial Feedback

A Padé approximation based technique for designing a suboptimal controller is presented. The technique uses matching of both time moments and Markov parameters for model order reduction. In this method, the suboptimal controller is first derived for reduced order model and then implemented for higher order plant by partial feedback of measurable states.

Model order reduction for quasi-magnetostatic problems

2017 ◽  
Vol 36 (6) ◽  
pp. 1783-1791
Author(s):  
Yuqing Xie ◽  
Lin Li ◽  
Shuaibing Wang
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Order Method ◽  
Computational Accuracy ◽  
Order Model ◽  
Model Order ◽  
Content Type ◽  
Reduced Order ◽  
Magnetostatic Problem

Purpose To reduce the computational scale for quasi-magnetostatic problems, model order reduction is a good option. Reduced-order modelling techniques based on proper orthogonal decomposition (POD) and centroidal Voronoi tessellation (CVT) have been used to solve many engineering problems. The purpose of this paper is to investigate the computational principle, accuracy and efficiency of the POD-based and the CVT-based reduced-order method when dealing with quasi-magnetostatic problems. Design/methodology/approach The paper investigates computational features of the reduced-order method based on POD and CVT methods for quasi-magnetostatic problems. Firstly the construction method for the POD and the CVT reduced-order basis is introduced. Then, a reduced model is constructed using high-fidelity finite element solutions and a Galerkin projection. Finally, the transient quasi-magnetostatic problem of the TEAM 21a model is studied with the proposed reduced-order method. Findings For the TEAM 21a model, the numerical results show that both POD-based and CVT-based reduced-order approaches can greatly reduce the computational time compared with the full-order finite element method. And the results obtained from both reduced-order models are in good agreement with the results obtained from the full-order model, while the computational accuracy of the POD-based reduced-order model is a little higher than the CVT-based reduced-order model. Originality/value The CVT method is introduced to construct the reduced-order model for a quasi-magnetostatic problem. The computational accuracy and efficiency of the presented approaches are compared.

Reduced-Order Model-Based Feedback Control of Flow Over an Obstacle Using Center Manifold Methods

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Coşku Kasnakoğlu ◽  
R. Chris Camphouse ◽  
Andrea Serrani
Keyword(s):  
Boundary Control ◽  
Center Manifold ◽  
Controller Design ◽  
Tracking Error ◽  
Reduced Order Model ◽  
Order System ◽  
Linear Quadratic ◽  
Order Model ◽  
Control Effort ◽  
Reduced Order

In this paper, we consider a boundary control problem governed by the two-dimensional Burgers’ equation for a configuration describing convective flow over an obstacle. Flows over obstacles are important as they arise in many practical applications. Burgers’ equations are also significant as they represent a simpler form of the more general Navier–Stokes momentum equation describing fluid flow. The aim of the work is to develop a reduced-order boundary control-oriented model for the system with subsequent nonlinear control law design. The control objective is to drive the full order system to a desired 2D profile. Reduced-order modeling involves the application of an L2 optimization based actuation mode expansion technique for input separation, demonstrating how one can obtain a reduced-order Galerkin model in which the control inputs appear as explicit terms. Controller design is based on averaging and center manifold techniques and is validated with full order numerical simulation. Closed-loop results are compared to a standard linear quadratic regulator design based on a linearization of the reduced-order model. The averaging∕center manifold based controller design provides smoother response with less control effort and smaller tracking error.

scholarly journals Model Order Reduction Technique Applied on Harmonic Analysis of a Submerged Vibrating Blade

2019 ◽  
Vol 24 (1) ◽  
pp. 131-142 ◽  
Author(s):  
E. Tengs ◽  
F. Charrassier ◽  
M. Holst ◽  
Pål-Tore Storli
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Reduction Technique ◽  
Reduced Order Model ◽  
Order Model ◽  
Model Order ◽  
Reduced Order ◽  
Speed Up ◽  
Speedup Factor ◽  
Fully Coupled

Abstract As part of an ongoing study into hydropower runner failure, a submerged, vibrating blade is investigated both experimentally and numerically. The numerical simulations performed are fully coupled acoustic-structural simulations in ANSYS Mechanical. In order to speed up the simulations, a model order reduction technique based on Krylov subspaces is implemented. This paper presents a comparison between the full ANSYS harmonic response and the reduced order model, and shows excellent agreement. The speedup factor obtained by using the reduced order model is shown to be between one and two orders of magnitude. The number of dimensions in the reduced subspace needed for accurate results is investigated, and confirms what is found in other studies on similar model order reduction applications. In addition, experimental results are available for validation, and show good match when not too far from the resonance peak.

scholarly journals Model Order Reduction for Lumped RC Transmission Lines

2020 ◽  
Author(s):  
Farid N. Najm
Keyword(s):  
Transmission Lines ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Order Model ◽  
Model Order ◽  
Reduced Order ◽  
Detailed Review ◽  
Circuit Description ◽  
Rc Networks

<div>We start with a detailed review of the PACT approach for model order reduction of RC networks. We then develop a method that uses PACT as a preprocessing step to transform a generic lumped RC transmission line of some nominal order, based on a nominal (r,c) setting, into a parameterized circuit captured in a SPICE sub-circuit description. Then, given any other lumped RC line of the same order, we pass its (r,c) setting as parameters to this sub-circuit so as to automatically transform and reduce the line into a reduced order model without having to rerun PACT. In this way, we effectively characterize lumped RC transmission lines in a way that allows them to be reduced on-the-fly without any expensive processing.</div>

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