Robust pole assignment in systems subject to structured perturbations

The problem of robust pole assignment by feedback in a linear, multivariable, time-invariant system which is subject to structured perturbations is investigated. A measure of robustness, or sensitivity, of the poles to a given class of perturbations is derived, and a reliable and efficient computational algorithm is presented for constructing a feedback which assigns the prescribed poles and optimizes the robustness measure.

Robust pole assignment and optimal stability margins

A robust pole assignment by linear state feedback is achieved in state-space representation by selecting a feedback which minimises the conditioning of the assigned eigenvalues of the closed-loop system. It is shown here that when this conditioning is minimised, a lower bound on the stability margin in the frequency domain is maximised.

Comments, with reply, on "Computational algorithms for pole assignment" by N.K. Nichols

Some points of the paper by N.K. Nichols (see ibid., vol.AC-31, p.643-5, 1986), concerning the robust pole assignment of linear multiinput systems, are clarified. It is stressed that the minimization of the condition number of the closed-loop eigenvector matrix does not necessarily lead to robustness of the pole assignment. It is shown why the computational method, which Nichols claims is robust, is in fact numerically unstable with respect to the determination of the gain matrix. In replying, Nichols presents arguments to support the choice of the conditioning of the closed-loop poles as a measure of robustness and to show that the methods of J Kautsky, N. K. Nichols and P. VanDooren (1985) are stable in the sense that they produce accurate solutions to well-conditioned problems.

Robustness in partial pole placement

The robustness of state feedback solutions to the problem of partial pole placement obtained by a new projection procedure is examined. The projection procedure gives a reduced-order pole assignment problem. It is shown that the sensitivities of the assigned poles in the complete closed-loop system are bounded in terms of the sensitivities of the assigned reduced-order poles, and the sensitivities of the unaltered poles are bounded in terms of the sensitivities of the corresponding open-loop poles. If the assigned poles are well-separated from the unaltered poles, these bounds are expected to be tight. The projection procedure is described in [3], and techniques for finding robust (or insensitive) solutions to the reduced-order problem are given in [1], [2].

On computational algorithms for pole assignment

A number of computationally reliable direct methods for pole assignment by feedback have recently been developed. These direct procedures do not necessarily produce robust solutions to the problem, however, in the sense that the assigned poles are insensitive to perturbalions in the closed-loop system. This difficulty is illustrated here with results from a recent algorithm presented in this TRANSACTIONS and its causes are examined. A measure of robustness is described, and techniques for testing and improving robustness are indicated.

Algorithms for Robust Pole Assignment in Singular Systems

The solution of the pole assignment problem by feedback in singular systems is parameterized and conditions are given which guarantee the regularity and maximal degree of the closed loop pencil. A robustness measure is defined, and numerical procedures are described for selecting the free parameters in the feedback to give optimal robustness.

Equator-to-pole temperature differences and the extra-tropical storm track responses of the CMIP5 climate models

This paper aims to understand the physical processes causing the large spread in the storm track projections of the CMIP5 climate models. In particular, the relationship between the climate change responses of the storm tracks, as measured by the 2–6 day mean sea level pressure variance, and the equator-to-pole temperature differences at upper- and lower-tropospheric levels is investigated. In the southern hemisphere the responses of the upper- and lower-tropospheric temperature differences are correlated across the models and as a result they share similar associations with the storm track responses. There are large regions in which the storm track responses are correlated with the temperature difference responses, and a simple linear regression model based on the temperature differences at either level captures the spatial pattern of the mean storm track response as well explaining between 30 and 60 % of the inter-model variance of the storm track responses. In the northern hemisphere the responses of the two temperature differences are not significantly correlated and their associations with the storm track responses are more complicated. In summer, the responses of the lower-tropospheric temperature differences dominate the inter-model spread of the storm track responses. In winter, the responses of the upper- and lower-temperature differences both play a role. The results suggest that there is potential to reduce the spread in storm track responses by constraining the relative magnitudes of the warming in the tropical and polar regions.

In vitro osteogenesis on fluorcanasite glass-ceramic with three different chemical compositions

This study aimed at investigating in vitro osteogenesis on three fluorcanasite glass-ceramic compositions with different solubilities (K3, K5, and K8). Osteoblastic cells were obtained from human alveolar bone fragments and cultured under standard osteogenic condition until subconfluence. First passage cells were cultured on K3, K5, and K8 and on Bioglass (R) 45S5 (45S5-control). Cell adhesion was evaluated at 24 h. For proliferation and viability, cells were cultured for 1, 4, and 10 days. Total protein content and alkaline phosphatase (ALP) activity were measured at 7, 14, and 21 days. Cultures were stained with Alizarin red at 21 days, for detection of mineralized matrix. Data were compared by ANOVA followed by Duncan`s test. Cell adhesion, cell proliferation, viability, total protein content, and ALP activity were not affected by fluorcanasite glass-ceramic composition and solubility. Bone-like formation was similar on all fluorcanasite-glass ceramics and was reduced compared to 45S5. The changes in the chemical composition and consequently solubility of the fluorcanasite glass-ceramics tested here did not significantly alter the in vitro osteogenesis. Further modifications of the chemical composition of the fluorcanasite glass-ceramic would be required to improve bone response, making this biomaterial a good candidate to be employed as a bone substitute.

Virtual Pole from Magnetic Anomaly (VPMA): A procedure to estimate the age of a rock from its magnetic anomaly only

Virtual Pole from Magnetic Anomaly (VPMA) is a new multi-disciplinary methodology that estimates the age of a source rock from its magnetic anomaly, taken directly from available aeromagnetic data. The idea is to use those anomalies in which a strong remanent magnetic component is likely to occur. Once the total magnetization of the anomaly is computed through any of the currently available methods, the line that connects all virtual paleogeographic poles is related with the position, on a paleogeographic projection, of the appropriate age fragment of the APWT curve. We applied this procedure to five (5) well-known magnetic anomalies of the South American plate in SE Brazil, all of them associated to alkaline complexes of Mesozoic age. The apparent ages obtained from VPMA on three of the anomalies where the radiometric age of the source rock is known - Tapira, Araxa and Juquia were inside the error interval of the published ages. The VPMA apparent ages of the other two, where the age of the source rock is not known (Registro and Pariqueracu magnetic anomalies) were geologically coherent. We expect that the application of the VPMA methodology as a reconnaissance geochronological tool may contribute to geological knowledge over continental areas, especially when the source rocks of the magnetic anomalies am unknown or buried below superficial sediments. (C) 2009 Elsevier B.V. All rights reserved.

A late Neoproterozoic paleomagnetic pole for the Congo craton: Tectonic setting, paleomagnetism and geochronology of the Nola dike swarm (Central African Republic)

New structural, geochronological and paleomagnetic data were obtained on dolerite dikes of the Nola region (Central African Republic) at the northern border of the Congo craton. In this region metavolcanic, successions were thrust southward onto the craton during the Panafrican orogenic events. Our structural data reveal at least two structural klippes south of the present-day limits of the Panafrican nappe suggesting that it has once covered the whole Nola region, promoting the pervasive hydrothermal green-schist metamorphism observed in the underlying cratonic basement and also in the intrusive dolerite dikes. Paleomagnetic measurements revealed a stable dual-polarity low-inclination magnetization component in nine dikes (47 samples), carried by pyrrhotite and magnetite. This component corresponds to a paleopole at 304.8 degrees E and 61.8 degrees S (dp = 5.4, dm = 10.7) graded at 2 = 6. Both metamorphism and magnetic resetting were dated by the Ar-40/Ar-39 method on amphibole grains separated from the dikes at 571 +/- 6 Ma. The Nola pole is the first well-dated paleomagnetic pole for the Congo craton between 580 and 550 Ma. It marks a sudden change in direction of the Congo craton apparent polar wander path at the waning stages of the Panafrican orogenic events. (c) 2008 Elsevier B.V. All rights reserved.