Frequency domain stability and relaxed convergence conditions for filtered error adaptive feedforward

The convergence of filtered error and filtered reference adaptive feedforward is limited by three effects: model mismatch, unintended input-disturbance interaction and too fast parameter adaptation. In this article, the first two effects are considered for MIMO systems under the slow parameter adaptation assumption. The convergence with model mismatch is conventionally guaranteed using a strictly positive-real condition. This condition can be easily verified in the frequency domain, but due the high-frequency parasitic dynamics of real systems, it is hardly ever satisfied. Nevertheless, filtered error and filtered reference adaptive feedforward have successfully been implemented in numerous applications without satisfying the strictly positive-real condition. It is shown in this article that the strictly positive-real condition can be relaxed to a power-weighted integral condition, that is less conservative and provides a practical check for the convergence of filtered error adaptive feedforward for real systems in the frequency domain. The effects of input-disturbance interaction are analysed and conditions for the stability are given in the frequency domain. Both conditions give clear indicators for frequency domain filter tuning, and are verified on an experimental active vibration isolation system.</p

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PMID = 2773580

In Bacillus subtilis LutR is part of the global complex regulatory network governing the adaptation to the transition from exponential growth to stationary phase

The lutR gene, encoding a product resembling a GntR-family transcriptional regulator, has previously been identified as a gene required for the production of the dipeptide antibiotic bacilysin in Bacillus subtilis. To understand the broader regulatory roles of LutR in B. subtilis, we studied the genome-wide effects of a lutR null mutation by combining transcriptional profiling studies using DNA microarrays, reverse transcription quantitative PCR, lacZ fusion analyses and gel mobility shift assays. We report that 65 transcriptional units corresponding to 23 monocistronic units and 42 operons show altered expression levels in lutR mutant cells, as compared with lutR+ wild-type cells in early stationary phase. Among these, 11 single genes and 25 operons are likely to be under direct control of LutR. The products of these genes are involved in a variety of physiological processes associated with the onset of stationary phase in B. subtilis, including degradative enzyme production, antibiotic production and resistance, carbohydrate utilization and transport, nitrogen metabolism, phosphate uptake, fatty acid and phospholipid biosynthesis, protein synthesis and translocation, cell-wall metabolism, energy production, transfer of mobile genetic elements, induction of phage-related genes, sporulation, delay of sporulation and cannibalism, and biofilm formation. Furthermore, an electrophoretic mobility shift assay performed in the presence of both SinR and LutR revealed a close overlap between the LutR and SinR targets. Our data also revealed a significant overlap with the AbrB regulon. Together, these findings reveal that LutR is part of the global complex, interconnected regulatory systems governing adaptation of bacteria to the transition from exponential growth to stationary phase.