Sensitivity reduction in modal control systems

The conventional modal control theory is concerned with the problem of determining a state feedback matrix-valued gain which drives the system eigenvalues to prescribed positions. When the parameters of the open-loop system involve certain variations, the closed-loop eigenvalues, obtained by using a feedback gain determined as above, also contain variations. In the present paper the problem of choosing an additional state feedback gain such as to reduce the closed-loop eigenvalue variations as much as desired is solved. Specifically, upon the assumption that a nominal set of parameter values is given, and that a feedback modal control law which drives the eigenvalues of the nominal closed-loop system to the desired positions is known, two alternative expressions for the required additional reduced eigenvalue sensitivity feedback controller are derived. Both cases of known and unknown system state vector are considered. The theory is illustrated by several examples.     

Exact Model-Matching of 2-D Systems via State Feedback

This paper considers the problem of matching the transfer function matrix of a given two-dimensional (2-D) system to that of a desired 2-D model using state feedback. The approach followed refers to systems having square transfer function matrices and reduces the problem to that of solving a linear system of equations. Furthermore, necessary and sufficient conditions are established for exact matching. An example is included to illustrate the proposed method.     

A post-Byzantine icon of St Nicholas painted on a leather support. Microanalysis and characterisation of technique

The pigments, organic materials and techniques used on a post-Byzantine icon of St Nicholas were determined by means of several micro-analytical techniques. The icon painter covered the leather support with silver leaf about 3 μm thick to create a smooth working surface. Animal glue was used to secure the leaf to the leather, and FTIR spectroscopy has identified another layer, 30–60 μm thick, of the same material applied as a primer above the silver. Above that, a layer of lead white covering the entire surface creates a white substratum serving the same purpose as the gesso on a wood panel. The colour palette, determined by means of scanning electron microscopy and FTIR spectroscopy, is very simple. Only seven colours were identified: lead white, caput mortuum, red and yellow ochre, cinnabar, carbon black and smalt. As far as we know, this is the first time that smalt has been found on a Byzantine icon. Since smalt was chemically synthesised only after 1500 AD, it may be concluded that this icon was painted after the end of the 15th century. Beeswax was used as a protective varnish.     

The effect of nature documentaries on students’ environmental sensitivity: a case study

Despite the potential educational value of nature documentaries, the contribution of such films to environmental education is largely unknown. In the present study, we attempt to delineate the role of nature documentaries to the environmental sensitivity of students when the films are simply introduced to the class. More specifically, the present study experimentally checks whether students who have been exposed to a nature documentary on insects develop a greater level of environmental sensitivity towards those animals compared to students who have not. Moreover, we explore whether nature documentaries of a distinct type (i.e., verbal vs. non‐verbal) have a different effect on the students’ sensitivity. The results suggest that traditional nature documentaries have a positive effect on students’ sensitivity, while the non‐verbal, less conventional documentary is more effective in the development of environmental knowledge and feelings about insects. However, the non‐conventional approach is equally effective in the change in attitudes and beliefs as the verbal, ‘traditional’ one. Finally, the study discloses that students in general report more positive emotional reactions to insects than perceived knowledge and understanding. Although nature documentaries seem to improve all components of environmental sensitivity, they do not subvert the predominance of emotion over knowledge about insects.     

State feedback uniform decoupling problem of linear time-varying analytic systems

A new approach to the input-output uniform decoupling problem of linear time-varying analytic systems via proportional state feedback is presented. A major feature of the proposed approach is that it reduces the solution of the uniform decoupling problem to that of solving a linear algebraic system of equations. This system of equations greatly facilitates the solution of the three major aspects of the decoupling problem: the necessary and sufficient conditions, the general analytical expressions for the controller matrices, and the structure of the uniformly decoupled closed-loop system.     

On the computation of the transfer function matrix of singular systems

For singular systems, i.e. for systems of the form E[xdot] = Ax + Bu, with E singular, the problem of computing the transfer function matrix has been studied. An algorithm is developed which is similar to the corresponding algorithm proposed by Faddeev or Leverrier for regular systems. The present results involve the Drazin inverse and yield an expression for the transfer function matrix suitable for computer use.     

Chebyshev series approach to system identification,analysis and optimal control

The problems of identification, analysis and optimal control have been recently studied via orthogonal functions. The particular orthogonal functions used up to now are the Walsh, the block-pulse and the Laguerre functions. In this paper, the Chebyshev functions are introduced and solutions for the aforementioned problems are established. The algorithms proposed are analogous to those already derived for the Walsh, block-pulse and Laguerre functions. The Chebyshev series approach presented here appears to have certain advantages over other orthogonal series, and they may therefore be more suitable for the study of the problems of identification, analysis and optimal control.