On optimization of structural and control systems using a reduced order model

1990 ◽  
Vol 2 (3) ◽  
pp. 185-191 ◽  
Author(s):  
N. S. Khot
Keyword(s):  
Control Systems ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
And Control

Decentralized Control of a Tower Crane

1999 ◽  
Author(s):  
Kiyoshi Takagi ◽  
Hidekazu Nishimura
Keyword(s):  
Decentralized Control ◽  
Three Dimensional ◽  
Reduced Order Model ◽  
Flexible Structure ◽  
Order Model ◽  
Modeling And Control ◽  
Reduced Order ◽  
Tower Crane ◽  
Three Dimensional Models ◽  
And Control

Abstract This paper deals with modeling and control of a crane mounted on a tower-like flexible structure. A fast transfer of the load causes the sway of the load rope and the vibration of the flexible structure. Our object is to control both the sway and the vibration by the inherent capability of the tower crane. This paper makes its three-dimensional models for simulation and reduced-order-model in order to design the decentralized control system. Then, we design the decentralized H∞ compensator and verify the efficiency by simulations and experiments.

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.

A Reduced Order Model for Spatiotemporal Dynamics and Control of Cardiac Alternans

2018 ◽  
Author(s):  
Xiaopeng Zhao ◽  
Elena G. Tolkacheva
Keyword(s):  
Cardiac Arrest ◽  
Sudden Cardiac Arrest ◽  
Cellular Level ◽  
Reduced Order Model ◽  
Western World ◽  
Order Model ◽  
Reduced Order ◽  
Dynamics And Control ◽  
Cardiac Alternans ◽  
And Control

Sudden cardiac arrest, caused primarily by ventricular fibrillation, is one of the leading causes of mortality in the Western world. There is a compelling need for risk stratification to identify patients at risk for sudden cardiac arrest. Cardiac alternans, a recognized harbinger of sudden cardiac arrest, manifests as a beat-to-beat alternation in action potential duration (cellular level) or in electrocardiogram morphology (whole heart level). Although much progress has been made to understand the mechanisms of alternans, predicting and control of alternans, especially at the heart level, remain great challenges. Current approaches to predict cardiac alternans based on restitution properties of the heart are either too simple to be valid or too complex to be useful. In this work, we developed a reduced order model from the amplitude equation to investigate dynamics and control of alternans in cardiac fiber, i.e. beyond single cell level. Detailed bifurcation and stability analyses were carried out to illustrate complex spatiotemporal patterns of alternans and the limitations in feedback control due to spatial effect.

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