Robustness and performance trade-offs in control design for flexible structures

Linear control design models for flexible structures are only an approximation to the “real” structural system. There are always modeling errors or uncertainty present. Descriptions of these uncertainties determine the trade-off between achievable performance and robustness of the control design. In this paper it is shown that a controller synthesized for a plant model which is not described accurately by the nominal and uncertainty models may be unstable or exhibit poor performance when implemented on the actual system. In contrast, accurate structured uncertainty descriptions lead to controllers which achieve high performance when implemented on the experimental facility. It is also shown that similar performance, theoretically and experimentally, is obtained for a surprisingly wide range of uncertain levels in the design model. This suggests that while it is important to have reasonable structured uncertainty models, it may not always be necessary to pin down precise levels (i.e., weights) of uncertainty. Experimental results are presented which substantiate these conclusions

Identification of flexible structures for robust control

Documentation is provided of the authors' experience with modeling and identification of an experimental flexible structure for the purpose of control design, with the primary aim being to motivate some important research directions in this area. A multi-input/multi-output (MIMO) model of the structure is generated using the finite element method. This model is inadequate for control design, due to its large variation from the experimental data. Chebyshev polynomials are employed to fit the data with single-input/multi-output (SIMO) transfer function models. Combining these SIMO models leads to a MIMO model with more modes than the original finite element model. To find a physically motivated model, an ad hoc model reduction technique which uses a priori knowledge of the structure is developed. The ad hoc approach is compared with balanced realization model reduction to determine its benefits. Descriptions of the errors between the model and experimental data are formulated for robust control design. Plots of select transfer function models and experimental data are included

An example of active circulation control of the unsteady separated flow past a semi-infinite plate

Active circulation control of the two-dimensional unsteady separated flow past a semiinfinite plate with transverse motion is considered. The rolling-up of the separated shear layer is modelled by a point vortex whose time-dependent circulation is predicted by an unsteady Kutta condition. A suitable vortex shedding mechanism introduced. A control strategy able to maintain constant circulation when a vortex is present is derived. An exact solution for the nonlinear controller is then obtained. Dynamical systems analysis is used to explore the performance of the controlled system. The control strategy is applied to a class of flows and the results are discussed. A procedure to determine the position and the circulation of the vortex, knowing the velocity signature on the plate, is derived. Finally, a physical explanation of the control mechanism is presented

The wandering weekday effect in major stock markets

This paper reports a wandering weekday effect: the pattern of day seasonality in stock market returns is not fixed, as assumed in the Monday or weekend effects, but changes over time. Analysing daily closing prices in eleven major stock markets during 1993-2007, our results show that the wandering weekday is not conditional on average returns in the previous week (the "twist" in the Monday effect). Nor does it diminish through the period of analysis. The results have important implications for market efficiency, and help to reconcile mixed findings in previous studies, including the reported disappearance of the weekday effect in recent years

On the efficiency of the Trimean and Q123.

A Monte Carlo study showed that, for all but small samples with high levels of contamination, the robust efficiency of Tukey’s trimean may be improved by single-weighting the median

On the Size of Structures in the Solar Corona

Fine-scale structure in the corona appears not to be well resolved by current imaging instruments. Assuming this to be true offers a simple geometric explanation for several current puzzles in coronal physics, including: the apparent uniform cross-section of bright threadlike structures in the corona; the low EUV contrast (long apparent scale height) between the top and bottom of active region loops; and the inconsistency between loop densities derived by spectral and photometric means. Treating coronal loops as a mixture of diffuse background and very dense, unresolved filamentary structures address these problems with a combination of high plasma density within the structures, which greatly increases the emissivity of the structures, and geometric effects that attenuate the apparent brightness of the feature at low altitudes. It also suggests a possible explanation for both the surprisingly high contrast of EUV coronal loops against the coronal background, and the uniform ``typical'' height of the bright portion of the corona (about 0.3 solar radii) in full-disk EUV images. Some ramifications of this picture are discussed, including an estimate (10-100 km) of the fundamental scale of strong heating events in the corona.Comment: To appear in APJ, June 2007; as accepted Feb 200

Robustness of multiloop linear feedback systems

This paper presents a new approach to the frequency-domain analysis of multiloop linear feed-back systems. The properties of the return difference equation are examined using the concepts of singular values, singular vectors and the spectral norm of a matrix. A number of new tools for multiloop systems are developed which are analogous to those for scalar Nyquist and Bode analysis. These provide a generalization of the scalar frequency-domain notions such as gain, bandwidth, stability margins and M-circles, and provide considerable insight into system robustness

A new bound of the ℒ2[0, T]-induced norm and applications to model reduction

We present a simple bound on the finite horizon ℒ2/[0, T]-induced norm of a linear time-invariant (LTI), not necessarily stable system which can be efficiently computed by calculating the ℋ∞ norm of a shifted version of the original operator. As an application, we show how to use this bound to perform model reduction of unstable systems over a finite horizon. The technique is illustrated with a non-trivial physical example relevant to the appearance of time-irreversible phenomena in statistical physics

Coherent-feedback quantum control with a dynamic compensator

I present an experimental realization of a coherent-feedback control system that was recently proposed for testing basic principles of linear quantum stochastic control theory [M. R. James, H. I. Nurdin and I. R. Petersen, to appear in IEEE Transactions on Automatic Control (2008), arXiv:quant-ph/0703150v2]. For a dynamical plant consisting of an optical ring-resonator, I demonstrate ~ 7 dB broadband disturbance rejection of injected laser signals via all-optical feedback with a tailored dynamic compensator. Comparison of the results with a transfer function model pinpoints critical parameters that determine the coherent-feedback control system's performance.Comment: 4 pages, 4 EPS figure