5,278 research outputs found
Balanced truncation of perturbative representations of nonlinear systems
The paper presents a novel approach for a balanced truncation style of model reduction of a perturbative representation of a nonlinear system. Empirical controllability and observability gramians for nonlinear systems are employed to define a projection matrix. However, the projection matrix is applied to the perturbative representation of the system rather than directly to the exact nonlinear system. This is to achieve the required increase in efficiency desired of a reduced-order model. Application of the new method is illustrated through a sample test-system. The technique will be compared to the standard approach for reducing a perturbative representation of a nonlinear system
Passivity-preserving parameterized model order reduction using singular values and matrix interpolation
We present a parameterized model order reduction method based on singular values and matrix interpolation. First, a fast technique using grammians is utilized to estimate the reduced order, and then common projection matrices are used to build parameterized reduced order models (ROMs). The design space is divided into cells, and a Krylov subspace is computed for each cell vertex model. The truncation of the singular values of the merged Krylov subspaces from the models located at the vertices of each cell yields a common projection matrix per design space cell. Finally, the reduced system matrices are interpolated using positive interpolation schemes to obtain a guaranteed passive parameterized ROM. Pertinent numerical results validate the proposed technique
Empirical balanced truncation of nonlinear systems
Novel constructions of empirical controllability and observability gramians
for nonlinear systems for subsequent use in a balanced truncation style of
model reduction are proposed. The new gramians are based on a generalisation of
the fundamental solution for a Linear Time-Varying system. Relationships
between the given gramians for nonlinear systems and the standard gramians for
both Linear Time-Invariant and Linear Time-Varying systems are established as
well as relationships to prior constructions proposed for empirical gramians.
Application of the new gramians is illustrated through a sample test-system.Comment: LaTeX, 11 pages, 2 figure
Causal and stable reduced-order model for linear high-frequency systems
With the ever-growing complexity of high-frequency systems in the electronic industry, formation of reduced-order models of these systems is paramount. In this reported work, two different techniques are combined to generate a stable and causal representation of the system. In particular, balanced truncation is combined with a Fourier series expansion approach. The efficacy of the proposed combined method is shown with an example
Circuit Synthesis of Electrochemical Supercapacitor Models
This paper is concerned with the synthesis of RC electrical circuits from
physics-based supercapacitor models describing conservation and diffusion
relationships. The proposed synthesis procedure uses model discretisation,
linearisation, balanced model order reduction and passive network synthesis to
form the circuits. Circuits with different topologies are synthesized from
several physical models. This work will give greater understanding to the
physical interpretation of electrical circuits and will enable the development
of more generalised circuits, since the synthesized impedance functions are
generated by considering the physics, not from experimental fitting which may
ignore certain dynamics
On second-order cone positive systems
Internal positivity offers a computationally cheap certificate for external
(input-output) positivity of a linear time-invariant system. However, the
drawback with this certificate lies in its realization dependency. Firstly,
computing such a realization requires to find a polyhedral cone with a
potentially high number of extremal generators that lifts the dimension of the
state-space representation, significantly. Secondly, not all externally
positive systems posses an internally positive realization. Thirdly, in many
typical applications such as controller design, system identification and model
order reduction, internal positivity is not preserved. To overcome these
drawbacks, we present a tractable sufficient certificate of external positivity
based on second-order cones. This certificate does not require any special
state-space realization: if it succeeds with a possibly non-minimal
realization, then it will do so with any minimal realization. While there exist
systems where this certificate is also necessary, we also demonstrate how to
construct systems, where both second-order and polyhedral cones as well as
other certificates fail. Nonetheless, in contrast to other realization
independent certificates, the present one appears to be favourable in terms of
applicability and conservatism. Three applications are representatively
discussed to underline its potential. We show how the certificate can be used
to find externally positive approximations of nearly externally positive
systems and demonstrated that this may help to reduce system identification
errors. The same algorithm is used then to design state-feedback controllers
that provide closed-loop external positivity, a common approach to avoid over-
and undershooting of the step response. Lastly, we present modifications to
generalized balanced truncation such that external positivity is preserved
where our certificate applies
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