The paper recapitulates recently conducted investigations of non-proportional Luenberger observers, applied to reconstruction of state variables of induction motors. Three structures of non-proportional observers are analyzed, a proportional-integral observer, modified integral observer and observer with integrators. Criteria for gain selection of the observer are described, classical ones based on poles, as well as additional, increasing observer’s robustness. Fulfilment of the presented criteria can be ensured with the three proposed methods for gain selection, two analytical, based on dyadic transformation and one based on optimization.
A hybrid method is presented for the integration of low-, mid-, and high-frequency driver filters in loud-speaker crossovers. The Pascal matrix is exploited to calculate denominators; the locations of minimum values in frequency magnitude responses are associated with the forms of numerators; the maximum values are used to compute gain factors. The forms of the resulting filters are based on the physical meanings of low-pass, band-pass, and high-pass filters, an intuitive idea which is easy to be understood. Moreover, each coefficient is believed to be simply calculated, an advantage which keeps the software-implemented crossover running smoothly even if crossover frequencies are being changed in real time. This characteristic allows users to efficiently adjust the bandwidths of the driver filters by subjective listening tests if objective measurements of loudspeaker parameters are unavailable. Instead of designing separate structures for a low-, mid-, and high-frequency driver filter, by using the proposed techniques we can implement one structure which merges three types of digital filters. Not only does the integration architecture operate with low computational cost, but its size is also compact. Design examples are included to illustrate the effectiveness of the presented methodology
The paper addresses the problem of constrained pole placement in discrete-time linear systems. The design conditions are outlined in terms of linear matrix inequalities for the Dstable ellipse region in the complex Z plain. In addition, it is demonstrated that the D-stable circle region formulation is the special case of by this way formulated and solved pole placement problem. The proposed principle is enhanced for discrete-lime linear systems with polytopic uncertainties.