Reduced-order modelling of linear discrete-time systems via continued-fraction expansion of a z transfer function about z = 1 and z = a alternately

A new time-domain procedure is suggested for obtaining reduced-order models of linear time-invariant discrete-time systems. The procedure is based on presenting a new form of continued-fraction expansion (CFE) about z = 1 and z = a alternately, and deriving a realization form for the CFE. An algorithm is presented for obtaining the new CFE of the z transfer function of a linear discrete-time system from its state-space model directly, without having to determine the corresponding rational z transfer function. Also presented is a systematic approach to deriving two similarity transformation matrices: one is used to transform a state-space model from a general form to the CFE canonical form, and the other is used to transform a state-space model from the phase-variable canonical form to the CFE canonical form. Finally, an approximate aggregation matrix is constructed to relate the state vector of the original system to that of a reduced model obtained by the present method. The proposed procedure is illustrated with examples.     

Conversion of hydrogen/carbon dioxide into formic acid and methanol over Cu/CuCr2O4 catalyst

Cu/CuCr₂O₄ catalysts were prepared by impregnation method at various calcination temperatures (300, 400, and 500 °C) and then reduced in H₂ stream. The aggregated particles and decreasing surface area/pore volumes of the deactivated catalysts during HCOOH and CH₃OH formations were also observed. Particularly, the EXAFS data showed that first shells of Cu atoms transforms from Cu–O to Cu–Cu after catalytic reactions, their bond distances and coordination numbers are quite different, respectively. It revealed that metallic Cu atoms are one of the important active species over catalyst surface at different reaction temperatures having many unoccupied binding sites for HCOOH and CH₃OH formations. Additionally, the optimal calcination temperature for Cu/CuCr₂O₄ catalysts was demonstrated at 400 °C that attributed to its strongest acidity and basicity. The catalytic reactions in the duration of HCOOH and CH₃OH preparation were proposed that were composed of HCOOH formation, CH₃OH formation, and CH₃OH decomposition happening at CuCr₂O₄, Cu, and CuO active sites, respectively. The highest CO₂ conversion (14.6%), HCOOH selectivity/yield (87.8/12.8%), and TON/TOF values (4.19/0.84) were obtained at 140 °C and 30 bar in 5 h, respectively. Optimal rate constant (2.57 × 10^?2 min^?1) and activation energy (16.24 kJ mol^?1) of HCOOH formation were evaluated by pseudo first-order model and Arrhenius equation, respectively.     

Optimal sensitivity bound estimation and controller design

An explicit computational form is given for the estimation of the smallest upper bound on the sensitivity function over an operating band for a given stability margin in a single right half-plane (RHP) zero scalar system. A stable minimum-phase weighting function is constructed to meet such an infimum and the given stability margin with the H^∞ criterion. A numerical example is presented to demonstrate the optimal sensitivity estimation, weighting function construction and controller design.     

Parameter estimation of discrete systems via Hahn polynomials

This paper presents a procedure for using Hahn polynomials for the analysis and parameter estimation of linear discrete-time single-input/single-output systems described by difference equations. An advantage is gained through transforming a linear difference equation into a set of algebraic equations of the system parameters and the Hahn coefficients of the system variables. The key to the equation conversion is the derivation of a relation between the Hahn coefficients of a function and its time-shifted ones. Examples are provided to show the utilization of the procedure.     

THE COMPUTATION OF WAVELET-GALERKIN APPROXIMATION ON A BOUNDED INTERVAL

This paper describes exact evaluations of various finite integrals whose integrands involve products of Daubechies' compactly supported wavelets and their derivatives and/or integrals. These finite integrals play an essential role in the wavelet-Galerkin approximation of differential or integral equations on a bounded interval.     

INHIBITION STUDIES ON BURDOCK POLYPHENYL OXIDASE (PPO) ACTIVITY

The inhibitory effect of 4-hexylresorcinol (HR), ascorbic acid (AA), citric acid (CA), and bisulfites on polyphenol oxidase (PPO) of burdock roots was studied. HR was an effective inhibitor at low concentrations used in this study for crude PPO from root slices. A binary mixture of HR and AA at 1.0% concentration for 5 min achieved more than 90% inhibition of crude PPO. AA also showed high antibrowning activity for the purified PPO comparable to that of bisulfites, whereas its activity was much lower than that of HR in the crude extract. The inhibitory effect of the combined use of inhibitors was overall in the decreasing order of HR+AA, HR+CA and AA+CA, irrespective of the crude PPO or the purified PPO from burdock slices.