Robustness Analysis of Voltage Control Strategies of Smart Transformer

The increasing penetration of Distributed Generators (DG) in the modern electric distribution network poses high priority on the problem of the stability. In this article the Harmonic Stability of a Smart Transformer-fed microgrid is investigated under different control strategies. The considered microgrid is composed by a Smart Transformer and three Distributed Generators, considering the bandwidth of the DGs unknown. The robustness is evaluated analysing the eigenvalues as a consequence of a variation of the DGs bandwidth. The system is modelled as a Multi Input Multi Output System (MIMO); the eigenvalue based analysis is carried out to assess the stability and compare the robustness of the traditional double-loop PI and a state-feedback (SF) integral controller. The results show that the SF controller ensures a higher robustness than the traditional PI controller with respect to increasing bandwidths of the DGs

Robustness analysis for real parametric uncertainty

Some key results in the literature in the area of robustness analysis for linear feedback systems with structured model uncertainty are reviewed. Some new results are given. Model uncertainty is described as a combination of real uncertain parameters and norm bounded unmodeled dynamics. Here the focus is on the case of parametric uncertainty. An elementary and unified derivation of the celebrated theorem of Kharitonov and the Edge Theorem is presented. Next, an algorithmic approach for robustness analysis in the cases of multilinear and polynomic parametric uncertainty (i.e., the closed loop characteristic polynomial depends multilinearly and polynomially respectively on the parameters) is given. The latter cases are most important from practical considerations. Some novel modifications in this algorithm which result in a procedure of polynomial time behavior in the number of uncertain parameters is outlined. Finally, it is shown how the more general problem of robustness analysis for combined parametric and dynamic (i.e., unmodeled dynamics) uncertainty can be reduced to the case of polynomic parametric uncertainty, and thus be solved by means of the algorithm

Probabilistic Robustness Analysis of Stochastic Jump Linear Systems

In this paper, we propose a new method to measure the probabilistic robustness of stochastic jump linear system with respect to both the initial state uncertainties and the randomness in switching. Wasserstein distance which defines a metric on the manifold of probability density functions is used as tool for the performance and the stability measures. Starting with Gaussian distribution to represent the initial state uncertainties, the probability density function of the system state evolves into mixture of Gaussian, where the number of Gaussian components grows exponentially. To cope with computational complexity caused by mixture of Gaussian, we prove that there exists an alternative probability density function that preserves exact information in the Wasserstein level. The usefulness and the efficiency of the proposed methods are demonstrated by example.Comment: 2014 ACC(American Control Conference) pape

Quantitative Robustness Analysis of Quantum Programs (Extended Version)

Quantum computation is a topic of significant recent interest, with practical advances coming from both research and industry. A major challenge in quantum programming is dealing with errors (quantum noise) during execution. Because quantum resources (e.g., qubits) are scarce, classical error correction techniques applied at the level of the architecture are currently cost-prohibitive. But while this reality means that quantum programs are almost certain to have errors, there as yet exists no principled means to reason about erroneous behavior. This paper attempts to fill this gap by developing a semantics for erroneous quantum while-programs, as well as a logic for reasoning about them. This logic permits proving a property we have identified, called $\epsilon$-robustness, which characterizes possible "distance" between an ideal program and an erroneous one. We have proved the logic sound, and showed its utility on several case studies, notably: (1) analyzing the robustness of noisy versions of the quantum Bernoulli factory (QBF) and quantum walk (QW); (2) demonstrating the (in)effectiveness of different error correction schemes on single-qubit errors; and (3) analyzing the robustness of a fault-tolerant version of QBF.Comment: 34 pages, LaTeX; v2: fixed typo

Robustness Analysis for Value-Freezing Signal Temporal Logic

In our previous work we have introduced the logic STL*, an extension of Signal Temporal Logic (STL) that allows value freezing. In this paper, we define robustness measures for STL* by adapting the robustness measures previously introduced for Metric Temporal Logic (MTL). Furthermore, we present an algorithm for STL* robustness computation, which is implemented in the tool Parasim. Application of STL* robustness analysis is demonstrated on case studies.Comment: In Proceedings HSB 2013, arXiv:1308.572

Mind the (approximation) gap: a robustness analysis

This note continues the discussion of the results reported by Ricardo Caballero and Eduardo Engel (1993), hereafter CE, and Ricardo Caballero, Eduardo Engel, and John Haltiwanger (1997), hereafter CEH, by responding to the results reported in Christian Bayer (2008). Russell Cooper and Jonathan Willis (2004), hereafter CW, find that the aggregate nonlinearities reported in CE and CEH may be the consequence of mismeasurement of the employment gap rather than nonlinearities in plant-level adjustment. Bayer reassesses this finding in the context of the CE model in the case where static employment gaps are observed and concludes that the CW result is not robust to alternative shock processes. We concur with Bayer's assessment that the nonlinearity finding is sensitive to the aggregate profitability shock process. We argue, however, that Bayer's finding does not imply that the mismeasurement problem goes away. Instead, the nonlinearity created by mismeasurement is directly related to the level of the aggregate shock. Once the empirical specification properly incorporates the aggregate shock, the nonlinearity test is robust to alternative shock processes and confirms the results in CW. More importantly, we demonstrate that the CW findings are robust to alternative shock processes for the natural case of unobserved gaps as examined by CE and CEH.

Robustness analysis of magnetic torquer controlled spacecraft attitude dynamics

This paper describes a systematic approach to the robustness analysis of linear periodically time-varying (LPTV) systems. The method uses the technique known as Lifting to transform the original time-varying uncertain system into linear fractional transformation (LFT) form. The stability and performance robustness of the system to structured parametric uncertainty can then be analysed non-conservatively using the structured singular value μ. The method is applied to analyse the stability robustness of an attitude control law for a spacecraft controlled by magnetic torquer bars, whose linearised dynamics can naturally be written in linear periodically time-varying form. The proposed method allows maximum allowable levels of uncertainty, as well as worst-case uncertainty combinations to be computed. The destabilising effect of these uncertain parameter combinations is verified in time-domain simulations