Comment: Eigenvalue sensitivity method for optimal stabilisation of linear systems

In a letter RauA proposed a new method for designing statefeedback controllers using eigenvalue sensitivity matrices. However, there appears to be a conceptual mistake in the procedure, or else it is unduly restricted in its applicability. In particular the equation — BR~lBTK = A/.I, in which K is a positive-definite symmetric matrix.

Vibrations of a Beam in Variable Contact With a Flat Surface

We study small vibrations of cantilever beams contacting a rigid surface. We study two cases: the first is a beam that sags onto the ground due to gravity, and the second is a beam that sticks to the ground through reversible adhesion. In both cases, the noncontacting length varies dynamically. We first obtain the governing equations and boundary conditions, including a transversality condition involving an end moment, using Hamilton's principle. Rescaling the variable length to a constant value, we obtain partial differential equations with time varying coefficients, which, upon linearization, give the natural frequencies of vibration. The natural frequencies for the first case (gravity without adhesion) match that of a clamped-clamped beam of the same nominal length; frequencies for the second case, however, show no such match. We develop simple, if atypical, single degree of freedom approximations for the first modes of these two systems, which provide insights into the role of the static deflection profile, as well as the end moment condition, in determining the first natural frequencies of these systems. Finally, we consider small transverse sinusoidal forcing of the first case and find that the governing equation contains both parametric and external forcing terms. For forcing at resonance, w find that either the internal or the external forcing may dominate.

Multi-time scale analysis applied to long time simulation of power systems

The results are presented of applying multi-time scale analysis using the singular perturbation technique for long time simulation of power system problems. A linear system represented in state-space form can be decoupled into slow and fast subsystems. These subsystems can be simulated with different time steps and then recombined to obtain the system response. Simulation results with a two-time scale analysis of a power system show a large saving in computational costs.

Economic modelling of grazing systems in the Fitzroy and Burdekin catchments

The Great Barrier Reef (GBR) is the largest reef system in the world; it covers an area of approximately 2,225,000 km² in the northern Queensland continental shelf. There are approximately 750 reefs that exist within 40 km of the Queensland coast. Recent research has identified that poor water quality is having negative impacts on the GBR (Haynes et al. 2007). The Fitzroy Basin covers 143,000 km² and is the largest catchment draining into the GBR as well as being one of the largest catchments in Australia (Karfs et al. 2009). The Burdekin Catchment is the second largest catchment entering into the GBR and covers 133,432 km².The prime determinant for the changes in water quality entering into the GBR have been attributed to grazing, with beef production the largest single land use industry comprising 90% of the land area (Karfs et al. 2009). Extensive beef production contributes over $1 billion dollars to the national economy annually and employs over 9000 people, many in rural communities (Gordon 2007). ‘Economic modelling of grazing systems in the Fitzroy and Burdekin catchments’ was a joint project with the Fitzroy Basin Association and the Queensland Department of Employment Economic Development and Innovation. The project was formed under the federally funded Caring For Our Country and the Reef Rescue programs. The project objectives were as follows; * Quantifying the costs of over-utilising available pasture and the resulting sediment leaving a representative farm for four of the major land systems in the Burdekin or Fitzroy catchments and identifying economically optimal pasture utilisation rates * Estimating the cost of reducing pasture utilisation rates below the determined optimal * Using this information, guide the selection of appropriate tools to achieve reduced utilisation rates e.g. extension process versus incentive payments or a combination of both * Model the biophysical and economic impacts of altering grazing systems to restore land condition e.g. from C condition to B condition for four land systems in the Burdekin or Fitzroy catchments.

Observability for a Class of Nonlinear Systems

t - N m and sufficient computable conditions are obtained for the obsemabii of systems with linear state equations and polgwmIal outputs. Based on these, initial state reconstmctors are also described.

Dynamic Digital Simulation of HVDC Systems Using a Novel Modular Converter Model

This paper describes a method for the dynamic digital simulation of HVDC transmission systems. The method employs a novel modular converter representation during both normal and abnormal conditions.

Analysis of two degrees of freedom systems through weighted mean square linearization approach

In this paper a study of the free, forced and self-excited vibrations of non-linear, two degrees of freedom systems is reported. The responses are obtained by linearizing the nonlinear equations using the weighted mean square linearization approach. The scope of this approach, in terms of the type of non-linearities the method can tackle, is also discussed.

Natural frequencies of rectangular orthotropic plates with a pair of parallel edges simply supported

Solutions of the exact characteristic equations for the title problem derived earlier by an extension of Bolotin's asymptotic method are considered. These solutions, which correspond to flexural modes with frequency factor, R, greater than unity, are expressed in convenient forms for all combinations of clamped, simply supported and free conditions at the remaining pair of parallel edges. As in the case of uniform beams, the eigenvalues in the CC case are found to be equal to those of elastic modes in the FF case provided that the Kirchoff's shear condition at a free edge is replaced by the condition. The flexural modes with frequency factor less than unity are also investigated in detail by introducing a suitable modification in the procedure. When Poisson's ratios are not zero, it is shown that the frequency factor corresponding to the first symmetric mode in the free-free case is less than unity for all values of side ratio and rigidity ratios. In the case of one edge clamped and the other free it is found that modes with frequency factor less than unity exist for certain dimensions of the plate—a fact hitherto unrecognized in the literature.

APSIM – Evolution towards a new generation of agricultural systems simulation

Agricultural systems models worldwide are increasingly being used to explore options and solutions for the food security, climate change adaptation and mitigation and carbon trading problem domains. APSIM (Agricultural Production Systems sIMulator) is one such model that continues to be applied and adapted to this challenging research agenda. From its inception twenty years ago, APSIM has evolved into a framework containing many of the key models required to explore changes in agricultural landscapes with capability ranging from simulation of gene expression through to multi-field farms and beyond. Keating et al. (2003) described many of the fundamental attributes of APSIM in detail. Much has changed in the last decade, and the APSIM community has been exploring novel scientific domains and utilising software developments in social media, web and mobile applications to provide simulation tools adapted to new demands. This paper updates the earlier work by Keating et al. (2003) and chronicles the changing external challenges and opportunities being placed on APSIM during the last decade. It also explores and discusses how APSIM has been evolving to a “next generation” framework with improved features and capabilities that allow its use in many diverse topics.

Analysis of two degrees of freedom systems through weighted mean square linearization approach

In this paper a study of the free, forced and self-excited vibrations of non-linear, two degrees of freedom systems is reported. The responses are obtained by linearizing the nonlinear equations using the weighted mean square linearization approach. The scope of this approach, in terms of the type of non-linearities the method can tackle, is also discussed.

The dynamic stability of degenerate systems under parametric excitation

The parametric resonance in a system having two modes of the same frequency is studied. The simultaneous occurence of the instabilities of the first and second kind is examined, by using a generalized perturbation procedure. The region of instability in the first approximation is obtained by using the Sturm's theorem for the roots of a polynomial equation.

Self-tuning minimum-variance control of nonlinear systems of the Hammerstein model

Self-tuning is applied to the control of nonlinear systems represented by the Hammerstein model wherein the nonlinearity is any odd-order polynomial. But control costing is not feasible in general. Initial relay control is employed to contain the deviations.

Natural frequencies of polar orthotropic annular plates

The classical Rayleigh-Ritz method with simple polynomials as admissible functions has been used for obtaining natural frequencies of transversely vibrating polar orthotropic annular plates. The method in conjunction with transformations introduced in the analysis has been found to be quite effective, particularly for large hole sizes. Estimates of natural frequencies corresponding to modes with one as well as two nodal diameters are obtained for the nine combinations of clamped, simply supported and free edge conditions and for various values of rigidity ratio and hole sizes. Based on the variation of eigenvalue parameter with rigidity ratio, the frequencies of these modes as well as those of axisymmetric modes have been expressed by means of simple formulae in terms of rigidity ratio and the frequencies of corresponding modes in the isotropic case. These formulae have been used in determining the fundamental frequencies of orthotropic plates.