Extracting second-order structures from single-input state-space models: Application to model order reduction (original) (raw)
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Time-limited Gramians-based model order reduction for second-order form systems
Transactions of the Institute of Measurement and Control, 2018
A new scheme for model order reduction of large-scale second-order systems in time-limited intervals is presented. Time-limited Gramians that are solutions of continuous-time algebraic Lyapunov equations for second-order form systems are introduced. Time-limited second-order balanced truncation procedures with provision of balancing position and velocity Gramians are formulated. Stability conditions for reduced-order models are stated and algorithms that preserve stability in reduced-order models are discussed. Numerical examples are presented to validate the superiority of the proposed scheme compared with the infinite-time Gramians technique for time-limited applications.
International Journal of Control, 2018
A new technique for frequency limited model order reduction of discrete time second-order systems is presented. Discrete time frequency limited Gramians (DFLGs) and corresponding discrete algebraic Lyapunov equations are developed. An efficient technique for the computation of DFLGs and their Cholesky factors is presented. Computed DFLGs are partitioned to obtain position and velocity Gramians. These Gramians are balanced with different combinations to obtain various balanced transformations that yield Hankel singular values (HSVs) for order reduction. Frequency limited discrete time balanced truncation framework is proposed and truncation based on magnitudes of HSVs is applied to obtain the reduced order model. Moreover, stability conditions for reduced order models are stated. Results of the proposed technique are compared with infinite Gramians balancing scheme in order to certify the usefulness of the presented technique for frequency limited applications.
Asian Journal of Control, 2017
A new structure preserving model order reduction technique for second order systems in limited frequency interval is presented. Frequency limited Gramians (FLGs) and corresponding continuous time algebraic lyapunov equations (CALEs) are developed. For solution of CALEs and Cholesky factorization of FLGs, computationally efficient approximation scheme is proposed. Multiple transformations based on balancing of frequency limited position or velocity Gramians are defined in order to compute Hankel singular values (HSVs). Frequency limited second order balanced truncation based on magnitudes of HSVs is performed for order reduction. Moreover, stability conditions for reduced order models (ROMs) are stated and algorithms for achieving stability in ROMs are proposed. Results are compared with existing technique to certify the usefulness of the proposed technique.
A transformation approach for model order reduction of nonlinear systems
… Electronics Society, 1990. …, 1990
In this paper, a new technique for nonlinear model order reduction is developed. A transformation matrix is devised from a "representative model!' of the original nonlinear system and applied to the nonlinear model to provide a reduced order nonlinear model. ...
Finite Element Model Reduction and Model Updating of Structures for Control
Proceedings of the 19th IFAC World Congress, 2014
Estimation and control of unmeasurable performance variables in complex large-scale systems is an important issue in systems and control. The preferred solution to this problem is to have a relatively low-order and accurate standard plant model which can be used for control purposes. For this purpose, a two-step procedure is proposed. The first step is to generate a reduced Finite Element (FE) model based on the selection of desired Degrees Of Freedom (DOFs), resulting in reduced-order mass, damping, and stiffness matrices. The second step is updating of the reduced-order FE model that is carried out to minimize the differences between the model and the measurements from the structure with the focus on input-output behavior. The presented approach helps to create sufficiently accurate reduced-order dynamic models which can be used for control purposes. The approach will be examined on a planar plate FE model.
Reducing second order systems by an integrated state space and back conversion procedure
Proceedings of the 16th IFAC World Congress, 2005, 2005
The Arnoldi algorithm is modified to match the first Markov parameter and some of the first moments in order reduction of large scale systems while preserving the properties of the standard Arnoldi algorithm: an upper Hessenberg matrix as a coefficient ofẋ r , the identity matrix as a coefficient of x r and a multiple of the first unit vector as the input vector. These properties are then used for the reduction of large scale second order models by first reducing in state space and then converting into second order form by introducing a numerical algorithm.