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

2020 ◽  
pp. 014233122097417
Author(s):  
Arvind Kumar Prajapati ◽  
Rajendra Prasad
Keyword(s):  
Complex System ◽  
Control System ◽  
Large Scale ◽  
Order Reduction ◽  
Absolute Error ◽  
Reduced Order Modeling ◽  
Reduced Order ◽  
Integral Square Error ◽  
Scale Models

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.

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.

Cyclic Breathing Simulations in Large Scale Models of the Lung Airway From the Oronasal Opening to the Terminal Bronchioles

2012 ◽  
Author(s):  
D. Keith Walters ◽  
Greg W. Burgreen ◽  
Robert L. Hester ◽  
David S. Thompson ◽  
David M. Lavallee ◽  
...  
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Large Scale ◽  
Whole Body ◽  
Patient Specific ◽  
Cfd Simulations ◽  
Reduced Order ◽  
Scale Models ◽  
Steady State Simulation ◽  
Conducting Zone

Computational fluid dynamics (CFD) simulations were performed for unsteady periodic breathing conditions, using large-scale models of the human lung airway. The computational domain included fully coupled representations of the orotracheal region and large conducting zone up to generation four (G4) obtained from patient-specific CT data, and the small conducting zone (to G16) obtained from a stochastically generated airway tree with statistically realistic geometrical characteristics. A reduced-order geometry was used, in which several airway branches in each generation were truncated, and only select flow paths were retained to G16. The inlet and outlet flow boundaries corresponded to the oronasal opening (superior), the inlet/outlet planes in terminal bronchioles (distal), and the unresolved airway boundaries arising from the truncation procedure (intermediate). The cyclic flow was specified according to the predicted ventilation patterns for a healthy adult male at three different activity levels, supplied by the whole-body modeling software HumMod. The CFD simulations were performed using Ansys FLUENT. The mass flow distribution at the distal boundaries was prescribed using a previously documented methodology, in which the percentage of the total flow for each boundary was first determined from a steady-state simulation with an applied flow rate equal to the average during the inhalation phase of the breathing cycle. The distal pressure boundary conditions for the steady-state simulation were set using a stochastic coupling procedure to ensure physiologically realistic flow conditions. The results show that: 1) physiologically realistic flow is obtained in the model, in terms of cyclic mass conservation and approximately uniform pressure distribution in the distal airways; 2) the predicted alveolar pressure is in good agreement with previously documented values; and 3) the use of reduced-order geometry modeling allows accurate and efficient simulation of large-scale breathing lung flow, provided care is taken to use a physiologically realistic geometry and to properly address the unsteady boundary conditions.

Order Reduction of Nonlinear Systems Subjected to an External Periodic Excitation

2005 ◽  
Author(s):  
Sangram Redkar ◽  
S. C. Sinha
Keyword(s):  
Nonlinear Systems ◽  
State Space ◽  
Invariant Manifold ◽  
Large Scale ◽  
Order Reduction ◽  
Reduced Order Models ◽  
Periodic Excitation ◽  
External Excitation ◽  
Reduced Order ◽  
Linear Approach

In this work, the basic problem of order reduction nonlinear systems subjected to an external periodic excitation is considered. This problem deserves attention because the modes that interact (linearly or nonlinearly) with the external excitation dominate the response. A linear approach like the Guyan reduction does not always guarantee accurate results, particularly when nonlinear interactions are strong. In order to overcome limitations of the linear approach, a nonlinear order reduction methodology through a generalization of the invariant manifold technique is proposed. Traditionally, the invariant manifold techniques for unforced problems are extended to the forced problems by ‘augmenting’ the state space, i.e., forcing is treated as an additional degree of freedom and an invariant manifold is constructed. However, in the approach suggested here a nonlinear time-dependent relationship between the dominant and the non-dominant states is assumed and the dimension of the state space remains the same. This methodology not only yields accurate reduced order models but also explains the consequences of various ‘primary’ and ‘secondary resonances’ present in the system. Following this approach, various ‘reducibility conditions’ are obtained that show interactions among the eigenvalues, the nonlinearities and the external excitation. One can also recover all ‘resonance conditions’ commonly obtained via perturbation or averaging techniques. These methodologies are applied to some typical problems 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 of large-scale externally excited nonlinear systems.

scholarly journals An evaluation of clouds and radiation in a Large-Scale Atmospheric Model using a Cloud Vertical Structure classification

2019 ◽  
Author(s):  
Dongmin Lee ◽  
Lazaros Oreopoulos ◽  
Nayeong Cho
Keyword(s):  
Large Scale ◽  
Vertical Structure ◽  
Climate Model ◽  
Global Climate ◽  
Global Climate Model ◽  
Atmospheric Model ◽  
Cloud Radiative Effect ◽  
Scale Models ◽  
High Clouds

Abstract. We revisit Cloud Vertical Structure (CVS) classes we have previously employed to classify the planet’s cloudiness. The CVS classification reflects simple combinations of simultaneous cloud occurrence in the three standard layers traditionally used to separate low, middle, and high clouds and was applied to a dataset derived from active lidar and cloud radar observations. This classification is now introduced in an Atmospheric Global Climate Model (AGCM), specifically NASA’s GEOS-5, in order to evaluate the realism of its cloudiness and of the radiative effects associated with the various CVS classes. Determination of CVS and associated radiation in the model is possible thanks to the implementation of a subcolumn cloud generator which is paired with the model’s radiative transfer algorithm. We assess GEOS-5 cloudiness in terms of the statistics and geographical distributions of the CVS classes, as well as features of their associated Cloud Radiative Effect (CRE). We decompose the model’s CVS-specific CRE errors into component errors stemming from biases in the frequency of occurrence of the CVSs, and biases in their internal radiative characteristics. Our framework sheds additional light into the verisimilitude of cloudiness in large scale models and can be used to complement cloud evaluations that take advantage of satellite simulator implementations.

scholarly journals A Broadband Enhanced Structure-Preserving Reduced-Order Interconnect Macromodeling Method for Large-Scale Equation Sets of Transient Interconnect Circuit Problems

Energies ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 5746
Author(s):  
Ning Wang ◽  
Huifang Wang ◽  
Shiyou Yang
Keyword(s):  
Large Scale ◽  
Krylov Subspace ◽  
Equivalent Circuit Model ◽  
Order Reduction ◽  
Wide Band ◽  
Circuit Model ◽  
Band Frequency ◽  
Reduced Order ◽  
Structure Preserving ◽  
Expansion Point

In the transient analysis of an engineering power electronics device, the order of its equivalent circuit model is excessive large. To eliminate this issue, some model order reduction (MOR) methods are proposed in the literature. Compared to other MOR methods, the structure-preserving reduced-order interconnect macromodeling (SPRIM) based on Krylov subspaces will achieve a higher reduction radio and precision for large multi-port Resistor-Capacitor-Inductor (RCL) circuits. However, for very wide band frequency transients, the performance of a Krylov subspace-based MOR method is not satisfactory. Moreover, the selection of the expansion point in this method has not been comprehensively studied in the literature. From this point of view, a broadband enhanced structure-preserving reduced-order interconnect macromodeling (SPRIM) method is proposed to reduce the order of equation sets of a transient interconnect circuit model. In addition, a method is introduced to determine the optimal expansion point at each frequency in the proposed method. The proposed method is validated by the numerical results on a transient problem of an insulated-gate bipolar transistor (IGBT)-based inverter busbar under different exciting conditions.

scholarly journals A Reduced Order Modeling Technique for Mistuned Bladed Disks

1997 ◽  
Vol 119 (3) ◽  
pp. 439-447 ◽  
Author(s):  
M. P. Castanier ◽  
G. O´ttarsson ◽  
C. Pierre
Keyword(s):  
Monte Carlo ◽  
Degrees Of Freedom ◽  
Order Reduction ◽  
Reduced Order Modeling ◽  
Modeling Technique ◽  
Mode Analysis ◽  
Bladed Disks ◽  
Engineering Structures ◽  
Element Analysis ◽  
Reduced Order

The analysis of the response statistics of mistuned turbomachinery rotors requires an expensive Monte Carlo simulation approach. Simple lumped parameter models capture basic localization effects but do not represent well actual engineering structures without a difficult parameter identification. Current component mode analysis techniques generally require a minimum number of degrees of freedom which is too large for running Monte Carlo simulations at a reasonable cost. In the present work, an order reduction method is introduced which is capable of generating reasonably accurate, very low order models of tuned or mistuned bladed disks. This technique is based on component modes of vibration found from a finite element analysis of a single disk-blade sector. It is shown that the phenomenon of mode localization is well captured by the reduced order modeling technique.

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.

Sign in / Sign up

Export Citation Format

Share Document