Systematic LFT Derivation of Uncertain Electrical Circuits for the Worst-Case Tolerance Analysis

Abstract

In line with the trend towards continuous miniaturization and price reduction, it is crucial to analyze the impact of uncertainties on the performance of electrical circuits. Performance is evaluated for the worst-case scenario and in the frequency domain, by computing upper and lower bounds. The purpose is not only to propose a method for the worst-case tolerance analysis but also to provide an efficient and a suitable tool for electrical engineers that can be easily applied to realistic electrical engineering problems. The proposed method is based on the robust analysis method (so called µ-analysis) for which well-known and efficient algorithms exist. However in order to apply it, the problem under consideration has to be transformed in a standard minimal so called LFT representation. Its derivation is a difficult task even for control systems engineers. Our paper proposes a transparent and systematic LFT derivation procedure for users based only on their knowledge of electrical engineering. At the end of the paper, an industrial example is provided which reveals the benefits and the efficiency of the proposed approach and how it can be applied to any linear electrical circuit.

Robust Stability Analysis of a DC/DC Buck Converter Under Multiple Parametric Uncertainties

“…Following the LFT operation, the structure of the uncertainty matrix, of size 351 × 351, is obtained as (31).…”

“…Although the strength of the µ tool lies in the fact that it can be applied to system models with multiple uncertainties, the benefits of this powerful feature have been utilised or examined in a limited number of studies [21], [31]. This may be due to a few limitations that tend to make the approach hard to apply.…”

Efficient worst‐case analysis of electronic networks in intervals of frequency

“…There has been a lot of effort from the scientific community to tackle the problem of uncertainty analysis in electrical engineering, as it can be verified by the growing number of publications in this field …”

“…Finally, in Ferber et al, a completely different approach to the uncertainty analysis problem has been proposed to the electrical engineering community. This proposed approach is well suited to uncertain linear circuit models in the frequency domain, and it focuses on the worst‐case tolerance analysis.…”

“…In this paper, we propose an alternative modeling technique, in the context of Ferber et al, to compute upper and lower bounds of the frequency response of uncertain electronic networks. Here, we use intervals of frequency instead of fixed values of frequency.…”