Computation of minimal-order realizations of generalized state-space systems (original) (raw)

Model and Controller Order Reduction for Infinite Dimensional Systems

ITB Journal of Engineering Science, 2010

This paper presents a reduced order model problem using reciprocal transformation and balanced truncation followed by low order controller design of infinite dimensional systems. The class of systems considered is that of an exponentially stable state linear systems ( , , ) A B C , where operator A has a bounded inverse, and the operator B and C are of finite-rank and bounded. We can connect the system ( , , ) A B C with its reciprocal system via the solutions of the Lyapunov equations. The realization of the reciprocal system is reduced by balanced truncation. This result is further translated using reciprocal transformation as the reduced-order model for the systems ( , , )

A New Technique For Reduced-Order Modelling of Linear Time-Invariant System

IETE Journal of Research, 2017

In this paper, a new technique for order reduction of linear time-invariant systems is presented. This technique is intended for both single-input single-output (SISO) and multi-input multi-output (MIMO) systems. Motivated by other reduction techniques, the new proposed reduction technique is based on modified pole clustering and factor division algorithm with the objective of obtaining a stable reduced-order system preserving all essential properties of the original system. The new technique is illustrated by three numerical examples which are considered from the literature. To evaluate the superiority and robustness of the new technique, the results of the proposed technique are compared with other well-known and recently developed order-reduction techniques like Routh approximation and Big Bang-Big Crunch algorithm. The comparison of performance indices shows the efficiency and powerfulness of the new technique.

SVD-Krylov based techniques for structure-preserving reduced order modelling of second-order systems

AIMS Mathematical Modelling and Control, 2021

We introduce an efficient structure-preserving model-order reduction technique for the large-scale second-order linear dynamical systems by imposing two-sided projection matrices. The projectors are formed based on the features of the singular value decomposition (SVD) and Krylov-based model-order reduction methods. The left projector is constructed by utilizing the concept of the observability Gramian of the systems and the right one is made by following the notion of the interpolation-based technique iterative rational Krylov algorithm (IRKA). It is well-known that the proficient model-order reduction technique IRKA cannot ensure system stability, and the Gramian based methods are computationally expensive. Another issue is preserving the second-order structure in the reduced-order mode. The structure-preserving model-order reduction provides a more exact approximation to the original model with maintaining some significant physical properties. In terms of these perspectives, the proposed method can perform better by preserving the second-order structure and stability of the system with minimized H2-norm. Several model examples are presented that illustrated the capability and accuracy of the introducing technique.

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.

Model order reduction of linear time invariant systems

Advances in Radio Science, 2008

This paper addresses issues related to the order reduction of systems with multiple input/output ports. The order reduction is divided up into two steps. The first step is the standard order reduction method based on the multipoint approximation of system matrices by applying Krylov subspace. The second step is based on the rejection of the weak part of a system. To recognise the weak system part, Lyapunov equations are used. Thus, this paper introduces efficient solutions of the Lyapunov equations for port to port subsystems.

Order Reduction in Linear Dynamical Systems by Using Improved Balanced Realization Technique

Circuits, Systems, and Signal Processing, 2019

In this article, a new model order reduction scheme is proposed for the simplification of large-scale linear dynamical models. The proposed technique is based on the balanced realization method, in which the steady-state gain problem of the balanced truncation is circumvented. In this method, the denominator coefficients of the reduced system are evaluated by using the balanced realization, and the numerator coefficients are obtained by using a simple mathematical procedure as given in the literature. The proposed technique has been illustrated through some standard large-scale systems. This method gives the least performance error indices compared to some other existing system reduction methods. The time response of the approximated system, evaluated by the proposed method, is also shown which is the excellent matching of the response of the actual model when compared to the responses of other existing techniques.