Isabelle Queinnec

Robust LQR Control for PWM Converters: An LMI Approach

A consistent framework for robust linear quadratic regulators (LQRs) control of power converters is presented. Systems with conventional LQR controllers present good stability properties and are optimal with respect to a certain performance index. However, LQR control does not assure robust stability when the system is highly uncertain. In this paper, a convex model of converter dynamics is obtained taking into account uncertainty of parameters. In addition, the LQR control for switching converters is reviewed. In order to apply the LQR control in the uncertain converter case, we propose to optimize the performance index by using linear matrix inequalities (LMIs). As a consequence, a new robust control method for dc-dc converters is derived. This LMI-LQR control is compared with classical LQR control when designing a boost regulator. Performance of both cases is discussed for load and line perturbations, working at nominal and non nominal conditions. Finally, the correctness of the proposed approach is verified with experimental prototypes.

Brief paper: Control design for a class of nonlinear continuous-time systems

This paper addresses the control design problem for a certain class of continuous-time nonlinear systems subject to actuator saturations. The system under consideration consists of a system with two nested nonlinearities of different type: saturation nonlinearity and cone-bounded nonlinearity. The control law investigated for stabilization purposes depends on both the state and the cone-bounded nonlinearity. Constructive conditions based on LMIs are then provided to ensure the regional or global stability of the system. Different points, like other approaches issued from the literature, are quickly discussed. An illustrative example allows to show the interest of the approach proposed. c 2008 Elsevier Ltd. All rights reserved.

Optimal State-Feedback Control of Bilinear DC–DC Converters With Guaranteed Regions of Stability

This paper deals with the modeling and the robust controller synthesis for nonlinear dc-dc converters. In the first part of this paper, a model for the bilinear dynamics is presented. Such nonlinear dynamics can be included in a convex polytope such that the trajectories of the converter out of the equilibrium are assured to remain inside a guaranteed region of stability despite of the bilinear term. Such a description of the dynamic response of the converter is employed, in the second part of this paper, to propose synthesis algorithms that can guarantee, a priori, the stability and performance requirements of the design. The resulting region of stability can take into account not only the bilinear terms but also the saturation of the control input, which is a topic of major importance in high-performance dc-dc converters. The aim of this paper is to contribute with a robust control framework which allows the designers to deal with the common requirements of regulated dc-dc converters. The correctness of the results has been verified both with numerical simulations and experimental measurements from dc-dc converter prototypes.

Transcriptome and proteome exploration to model translation efficiency and protein stability in Lactococcus lactis.

This genome-scale study analysed the various parameters influencing protein levels in cells. To achieve this goal, the model bacterium Lactococcus lactis was grown at steady state in continuous cultures at different growth rates, and proteomic and transcriptomic data were thoroughly compared. Ratios of mRNA to protein were highly variable among proteins but also, for a given gene, between the different growth conditions. The modeling of cellular processes combined with a data fitting modeling approach allowed both translation efficiencies and degradation rates to be estimated for each protein in each growth condition. Estimated translational efficiencies and degradation rates strongly differed between proteins and were tested for their biological significance through statistical correlations with relevant parameters such as codon or amino acid bias. These efficiencies and degradation rates were not constant in all growth conditions and were inversely proportional to the growth rate, indicating a more efficient translation at low growth rate but an antagonistic higher rate of protein degradation. Estimated protein median half-lives ranged from 23 to 224 min, underlying the importance of protein degradation notably at low growth rates. The regulation of intracellular protein level was analysed through regulatory coefficient calculations, revealing a complex control depending on protein and growth conditions. The modeling approach enabled translational efficiencies and protein degradation rates to be estimated, two biological parameters extremely difficult to determine experimentally and generally lacking in bacteria. This method is generic and can now be extended to other environments and/or other micro-organisms.

Robust Gain-Scheduled Control of Switched-Mode DC–DC Converters

This paper presents a robust control synthesis framework for switched DC-DC converters. The framework is based on an LMI formulation which can be solved automatically by efficient convex optimization algorithms. The method considers parameter-dependent Lyapunov functions such that it can take into account the uncertainty of converter parameters, nonlinear dynamics (such as state-dependence), as well as transient and steady-state performances that can be imposed beforehand. The result of the proposed synthesis method is a gain-scheduled controller that guarantees stability despite the accounted nonlinear dynamics and can provide excellent performances. Two different synthesis examples are shown for a DC-DC boost converter and their performance and robustness are compared with a standard control approach as current-mode control, both in nominal and non-nominal conditions. Finally, the proposed approach is verified with experimental results.

Control design for bilinear systems with a guaranteed region of stability: An LMI-based approach

This paper deals with the problem of stabilizing a bilinear system with unstable open-loop part by means of state feedback control. The implicit objective is to provide an estimate of the region of stability of the closed-loop system. The proposed procedure can be decomposed into two convex optimization problems described in terms of LMIs: i) Given a polytope which bounds the values of the state, containing the origin, find a stabilizing state feedback control law and an associate region of stability as large as possible inside the polytope. ii) For a solution of the first problem, find the largest polytope containing the ellipsoid such that the stability conditions hold. By iterating these two steps, constructive conditions are given to compute a state feedback control that maximizes the estimate of the region of stability. The results are illustrated by means of examples.

A two pathway model for N2O emissions by ammonium oxidizing bacteria supported by the NO/N2O variation

In this work, a new model for nitritation combining two N2O emission pathways was confronted with both NO and N2O measurements during nitrification. The model was calibrated with batch experiments and validated with long-term data collected in a sequencing batch reactor (SBR). A good prediction of the evolution of N2O emissions for a varying level of nitrite was demonstrated. The NO/N2O ratio was shown to vary during nitritation depending on the nitrite level. None of the models based on a single pathway could describe this variation of the NO/N2O ratio. In contrast, the 2 pathway model was capable of describing the trends observed for the NO/N2O ratio and gave better predictions of N2O emission factors. The model confirmed that the decrease of the NO/N2O ratio can be explained by an increase of the ND pathway to the detriment of the NN pathway. The ND pathway was systematically the predominant pathway during nitritation. The combined effect of nitrite (or free nitrous acid) and dissolved oxygen (DO) on the contribution of each pathway was in agreement with practical observations and the literature.

A Reduced Nonlinear Model of an Activated Sludge Process

Abstract A linear model of an alternating-phase activated sludge process is presented in this paper. Two linear sub-models are derivated from the ASM No. 1, one specific to the aerobic phase and another one for the anoxic phase. Main concerned variables (ammonia and nitrate concentrations, oxygen concentration and readily biodegradable concentration) are the most important for ammonia removal achieved by sequential alternance of nitrification and denitrification phases. Model identification and validation is done by using both experimental and simulated data. Identified parameters match realistic values under applied operating conditions. Model performance is satisfactory, and it has been conceived to be used for online estimation and control purposes

Stability region enlargement through anti-windup strategy for linear systems with dynamics restricted actuator

This paper addresses the problem of determination of stability regions for linear systems with amplitude and successive dynamics restricted actuator through anti-windup strategies. Considering a linear dynamic output feedback designed with respect to the linear system (without saturation), an anti-windup design method is investigated to guarantee both the stability of the closed-loop system and the respect of the controlled output constraints for a region of admissible initial states as large as possible. Based on the modelling of the closed-loop system resulting from the controller plus the anti-windup loop as a linear system with dead-zone and dynamics restricted nonlinearities, LMI stability conditions are formulated. Numerical optimization procedures are discussed.

Role of mRNA stability during bacterial adaptation.

Bacterial adaptation involves extensive cellular reorganization. In particular, growth rate adjustments are associated with substantial modifications of gene expression and mRNA abundance. In this work we aimed to assess the role of mRNA degradation during such variations. A genome-wide transcriptomic-based method was used to determine mRNA half-lives. The model bacterium Lactococcus lactis was used and different growth rates were studied in continuous cultures under isoleucine-limitation and in batch cultures during the adaptation to the isoleucine starvation. During continuous isoleucine-limited growth, the mRNAs of different genes had different half-lives. The stability of most of the transcripts was not constant, and increased as the growth rate decreased. This half-life diversity was analyzed to investigate determinants of mRNA stability. The concentration, length, codon adaptation index and secondary structures of mRNAs were found to contribute to the determination of mRNA stability in these conditions. However, the growth rate was, by far, the most influential determinant. The respective influences of mRNA degradation and transcription on the regulation of intra-cellular transcript concentration were estimated. The role of degradation on mRNA homeostasis was clearly evidenced: for more than 90% of the mRNAs studied during continuous isoleucine-limited growth of L. lactis, degradation was antagonistic to transcription. Although both transcription and degradation had, opposite effects, the mRNA changes in response to growth rate were driven by transcription. Interestingly, degradation control increased during the dynamic adaptation of bacteria as the growth rate reduced due to progressive isoleucine starvation in batch cultures. This work shows that mRNA decay differs between gene transcripts and according to the growth rate. It demonstrates that mRNA degradation is an important regulatory process involved in bacterial adaptation. However, its impact on the regulation of mRNA levels is smaller than that of transcription in the conditions studied.