Model reduction of weakly nonlinear systems

In general, model reduction techniques fall into two categories — moment —matching and Krylov techniques and balancing techniques. The present contribution is concerned with the former. The present contribution proposes the use of a perturbative representation as an alternative to the bilinear representation [4]. While for weakly nonlinear systems, either approximation is satisfactory, it will be seen that the perturbative method has several advantages over the bilinear representation. In this contribution, an improved reduction method is proposed. Illustrative examples are chosen, and the errors obtained from the different reduction strategies will be compared

Krylov subspaces from bilinear representations of nonlinear systems

Purpose – The paper is aimed at the development of novel model reduction techniques for nonlinear systems. Design/methodology/approach – The analysis is based on the bilinear and polynomial representation of nonlinear systems and the exact solution of the bilinear system in terms of Volterra series. Two sets of Krylov subspaces are identified which capture the most essential part of the input-output behaviour of the system. Findings – The paper proposes two novel model-reduction strategies for nonlinear systems. The first involves the development, in a novel manner compared with previous approaches, of a reduced-order model from a bilinear representation of the system, while the second involves reducing a polynomial approximation using Krylov subspaces derived from a related bilinear representation. Both techniques are shown to be effective through the evidence of a standard test example. Research limitations/implications – The proposed methodology is applicable to so-called weakly nonlinear systems, where both the bilinear and polynomial representations are valid. Practical implications – The suggested methods lead to an improvement in the accuracy of nonlinear model reduction, which is of paramount importance for the efficient simulation of state-of-the-art dynamical systems arising in all aspects of engineering. Originality/value – The proposed novel approaches for model reduction are particularly beneficial for the design of controllers for nonlinear systems and for the design and analysis of radio-frequency integrated circuits

Variable domain transformation for linear PAC analysis of mixed-signal systems

This paper describes a method to perform linear AC analysis on mixed-signal systems which appear strongly nonlinear in the voltage domain but are linear in other variable domains. Common circuits like phase/delay-locked loops and duty-cycle correctors fall into this category, since they are designed to be linear with respect to phases, delays, and duty-cycles of the input and output clocks, respectively. The method uses variable domain translators to change the variables to which the AC perturbation is applied and from which the AC response is measured. By utilizing the efficient periodic AC (PAC) analysis available in commercial RF simulators, the circuit’s linear transfer function in the desired variable domain can be characterized without relying on extensive transient simulations. Furthermore, the variable domain translators enable the circuits to be macromodeled as weakly-nonlinear systems in the chosen domain and then converted to voltage-domain models, instead of being modeled as strongly-nonlinear systems directly

Automating Dynamic Decoupling in Object-Oriented Modelling and Simulation Tools

Abstract This manuscript presents a technique that allows Equationbased Object-Oriented Modelling Tools (EOOMT) to exploit Dynamic Decoupling (DD) for partitioning a complex model into "weakly coupled" submodels. This enhances simulation efficiency, and is naturally keen to parallel integration or co-simulation. After giving an overview of the problem and of related work, we propose a method to automate DD by means of a novel structural analysis of the system -called "cycle analysis" -and of a mixed-mode integration method. Also, some considerations are exposed on how the presented technique can be integrated in EOOMT, considering as representative example a Modelica translator. Simulation tests demonstrate the technique, and the realised implementation is released as free software

An Efficient Reduced-Order Approach for Nonaffine and Nonlinear Partial Differential Equations

In the presence of nonaffine and highly nonlinear terms in parametrized partial differential equations, the standard Galerkin reduced-order approach is no longer efficient, because the evaluation of these terms involves high computational complexity. An efficient reduced-order approach is developed to deal with “nonaffineness” and nonlinearity. The efficiency and accuracy of the approach are demonstrated on several test cases, which show significant computational savings relative to classical numerical methods and relative to the standard Galerkin reduced-order approach.Singapore-MIT Alliance (SMA

Automated nonlinear Macromodelling of output buffers for high-speed digital applications

We present applications of a recently developed automated nonlin-ear macromodelling approach to the important problem of macro-modelling high-speed output buffers/drivers. Good nonlinear macro-models of such drivers are essential for fast signal-integrity and timing analysis in high-speed digital design. Unlike traditional black-box modelling techniques, our approach extracts nonlinear macromodels of digital drivers automatically from SPICE-level de-scriptions. Thus it can naturally capture transistor-level nonlinear-ities in the macromodels, resulting in far more accurate signal in-tegrity analysis, while retaining significant speedups. We demon-strate the technique by automatically extracting macromodels for two typical digital drivers. Using the macromodel, we obtain about 8 × speedup in average with excellent accuracy in capturing differ-ent loading effects, crosstalk, simultaneous switching noise (SSN), etc.