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.

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.

MICPA: a client-assisted channel assignment scheme for throughput enhancement in WLANs

The emergence of high-density wireless local area network (WLAN) deployments in recent years is a testament to the insatiable demands for wireless broadband services. The increased density of WLAN deployments brings with it the potential of increased capacity, extended coverage, and exciting new applications. However, the corresponding increase in contention and interference can significantly degrade throughputs, unless new challenges in channel assignment are effectively addressed. In this paper, a client-assisted channel assignment scheme that can provide enhanced throughput is proposed. A study on the impact of interference on throughput with multiple access points (APs)is first undertaken using a novel approach that determines the possibility of parallel transmissions. A metric with a good correlation to the throughput, i.e., the number of conflict pairs, is used in the client-assisted minimum conflict pairs (MICPA) scheme. In this scheme, measurements from clients are used to assist the AP in determining the channel with the minimum number of conflict pairs to maximize its expected throughput. Simulation results show that the client-assisted MICPA scheme can provide meaningful throughput improvements over other schemes that only utilize the AP’s measurements.

The institutional antecedents of the assignment of HRM responsibilities to line managers

This article uses large-scale international data to examine how much autonomy organizations have to assign human resource management responsibilities to line managers, as indicated in the prescriptions of the literature. We use data from 11 countries to explore the impact of a variety of internal characteristics of organizations and the kind of economy in which they operate. We find that around half of the organizations assign HRM responsibilities to the line and that organizations appear to have considerable latitude in making choices in this area. Organizations in the Nordic economies are most likely to assign responsibilities for HRM to the line and those in the liberal market economies are the least likely to do so. In any economy, larger organizations, unionized organizations, and those with strategically positioned HRM departments are the least likely to allocate responsibilities for HRM to the line. We discuss the implications of our findings for future research and for practice.

Vibrational spectroscopy of a compound with a CS7 ring

The product of the Asinger reaction between elemental sulfur, n-butylamine and acetophenone is 8-(n-butylaminophenylmethyliden)-1,2,3,4,5,6,7-heptathiocane which contains a CS7 ring. A combination of infrared, Raman and inelastic neutron scattering spectroscopies with periodic density functional theory calculations is used to provide a complete assignment of the vibrational spectra of this unusual species. The similarity between the Raman spectra of the compound and that of elemental sulfur is particularly striking. Copyright (C) 2009 John Wiley & Sons, Ltd.

A refined quartic forcefield for acetylene: accurate calculation of the vibrational spectrum

It is now possible to calculate the nine-dimensional rovibrational wavefunctions of sequentially bonded four-atom molecules variationally without dynamical approximation. In the case of HCCH, the simplest such molecule, many hundreds of rovibrational (J = 0, 1, 2) levels can be converged to better than 1.5 cm −1. Variational calculations of this kind are used here systematically to refine the well-known quartic valence-coordinate forcefleld of Strey and Mills [J.Mol. Spectrosc.59, 103-115 (1976)] against experimental term values up to three C-H stretch quanta for the principal and two deuterated isotopomers, yielding a new surface that reproduces the energies of all the known Σ, Π, and Δ states of these species up to the energy of two C-H stretch quanta with an rms error of 3 cm−1 . The refined forcefield is used to study the resonances associated with the accidental degeneracies (ν2 + ν4 + ν5, ν3) and (ν2 + 2ν5, ν1) in the principal isotopomer, leading to a clarification of the assignment of she experimentally detected states in the 2ν3 and 3ν3, polyads, and to the finding that vibrational Coriolis (kinetic energy) terms, rather than quartic anharmonicities in the potential, are the primary cause of the resonant interactions. Using a new cubic ab initio electric dipole field to calculate IR absorption coefficients, 24 undetected Σ and Π states of 1H12C12C1H and 5 undetected Σ states of D12C12CD are identified as candidates for experimental study, and their calculated energies and assignments are given.

Vibration–rotation variational calculations: precise results on HCN up to 25 000 cm−1

Variation calculations of the vibration–rotation energy levels of many isotopomers of HCN are reported, for J=0, 1, and 2, extending up to approximately 8 quanta of each of the stretching vibrations and 14 quanta of the bending mode. The force field, which is represented as a polynomial expansion in Morse coordinates for the bond stretches and even powers of the angle bend, has been refined by least squares to fit simultaneously all observed data on the Σ and Π state vibrational energies, and the Σ state rotational constants, for both HCN and DCN. The observed vibrational energies are fitted to roughly ±0.5 cm−1, and the rotational constants to roughly ±0.0001 cm−1. The force field has been used to predict the vibration rotation spectra of many isotopomers of HCN up to 25 000 cm−1. The results are consistent with the axis‐switching assignments of some weak overtone bands reported recently by Jonas, Yang, and Wodtke, and they also fit and provide the assignment for recent observations by Romanini and Lehmann of very weak absorption bands above 20 000 cm−1.

Coriolis perturbations in the infrared spectrum of allene

High resolution infrared spectra of the ν9 and ν10 perpendicular fundamentals of the allene molecule are reported, in which the J structure in the sub-bands has been partially resolved. Analysis of the latter shows that the vibrational origin ν9 = 999 cm−1, some 35 cm−1 below previous assignments. The pronounced asymmetry in the intensity distribution of the rotational structure which this assignment implies is shown to be expected theoretically, due to the Coriolis perturbations involved, and it is interpreted in terms of the sign and magnitude of the ratio of the dipole moment derivatives in the two fundamentals. The results of this analysis are shown to be in good agreement with observations on allene-1.1-d2, where similar intensity perturbations are observed, and with an independent analysis of the ν8 band of allene-h4. The A rotational constant of allene-h4 is found to have the value 4.82 ± 0.01 cm−1, and for the molecular geometry we obtain r(CH) = 1.084 A, r(CC) = 1.308 A, and HCH = 118.4°. A partial analysis of the rotational structure of the hot bands (ν9 + ν11 − ν11) and (ν10 + ν11 − ν11) is presented; these provide an example of a strong Coriolis interaction between nearly degenerate A1A2 and B1B2 pairs of vibrational levels. Some localized rotational perturbations in the ν9 and ν10 fundamentals are also noted, and their possible interpretations are discussed.