A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions

A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one important contribution of this paper. Once the NLDI representation of the nonlinear system is obtained, the paper proposes the application of a linear control design method to this representation. The design is based on quadratic Lyapunov functions and formulated as search problem over a set of bilinear matrix inequalities (BMIs), which is solved using a two-step separation procedure that maps the BMIs into a set of corresponding linear matrix inequalities. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.

Modeling the growth rate and lag time of different strains of Salmonella enterica and Listeria monocytogenes in ready-to-eat lettuce

The growth parameters (growth rate, mu and lag time, lambda) of three different strains each of Salmonella enterica and Listeria monocytogenes in minimally processed lettuce (MPL) and their changes as a function of temperature were modeled. MPL were packed under modified atmosphere (5% O-2, 15% CO2 and 80% N-2), stored at 7-30 degrees C and samples collected at different time intervals were enumerated for S. enterica and L monocytogenes. Growth curves and equations describing the relationship between mu and lambda as a function of temperature were constructed using the DMFit Excel add-in and through linear regression, respectively. The predicted growth parameters for the pathogens observed in this study were compared to ComBase, Pathogen modeling program (PMP) and data from the literature. High R-2 values (0.97 and 0.93) were observed for average growth curves of different strains of pathogens grown on MPL Secondary models of mu and lambda for both pathogens followed a linear trend with high R2 values (>0.90). Root mean square error (RMSE) showed that the models obtained are accurate and suitable for modeling the growth of S. enterica and L monocytogenes in MP lettuce. The current study provides growth models for these foodborne pathogens that can be used in microbial risk assessment. (C) 2011 Elsevier Ltd. All rights reserved.

Robust and optimal adjustment of Power System Stabilizers through Linear Matrix Inequalities

This work presents the application of Linear Matrix Inequalities to the robust and optimal adjustment of Power System Stabilizers with pre-defined structure. Results of some tests show that gain and zeros adjustments are sufficient to guarantee robust stability and performance with respect to various operating points. Making use of the flexible structure of LMI's, we propose an algorithm that minimizes the norm of the controllers gain matrix while it guarantees the damping factor specified for the closed loop system, always using a controller with flexible structure. The technique used here is the pole placement, whose objective is to place the poles of the closed loop system in a specific region of the complex plane. Results of tests with a nine-machine system are presented and discussed, in order to validate the algorithm proposed. (C) 2012 Elsevier Ltd. All rights reserved.

Modeling and identification of freeplay nonlinearity

A nonlinear analysis is performed for the purpose of identification of the pitch freeplay nonlinearity and its effect on the type of bifurcation of a two degree-of-freedom aeroelastic system. The databases for the identification are generated from experimental investigations of a pitch-plunge rigid airfoil supported by a nonlinear torsional spring. Experimental data and linear analysis are performed to validate the parameters of the linearized equations. Based on the periodic responses of the experimental data which included the flutter frequency and its third harmonics, the freeplay nonlinearity is approximated by a polynomial expansion up to the third order. This representation allows us to use the normal form of the Hopf bifurcation to characterize the type of instability. Based on numerical integrations, the coefficients of the polynomial expansion representing the freeplay nonlinearity are identified. Published by Elsevier Ltd.

Robust statistical modeling using the Birnbaum-Saunders-t distribution applied to insurance

In this paper, we carry out robust modeling and influence diagnostics in Birnbaum-Saunders (BS) regression models. Specifically, we present some aspects related to BS and log-BS distributions and their generalizations from the Student-t distribution, and develop BS-t regression models, including maximum likelihood estimation based on the EM algorithm and diagnostic tools. In addition, we apply the obtained results to real data from insurance, which shows the uses of the proposed model. Copyright (c) 2011 John Wiley & Sons, Ltd.

BEM modeling of saturated porous media susceptible to damage

This paper deals with the numerical analysis of saturated porous media, taking into account the damage phenomena on the solid skeleton. The porous media is taken into poro-elastic framework, in full-saturated condition, based on Biot's Theory. A scalar damage model is assumed for this analysis. An implicit boundary element method (BEM) formulation, based on time-independent fundamental solutions, is developed and implemented to couple the fluid flow and two-dimensional elastostatic problems. The integration over boundary elements is evaluated using a numerical Gauss procedure. A semi-analytical scheme for the case of triangular domain cells is followed to carry out the relevant domain integrals. The non-linear problem is solved by a Newton-Raphson procedure. Numerical examples are presented, in order to validate the implemented formulation and to illustrate its efficacy. (C) 2011 Elsevier Ltd. All rights reserved.

Fatigue crack growth assessments in welded components including crack closure effects: Experiments and 3-D numerical modeling

This work provides a numerical and experimental investigation of fatigue crack growth behavior in steel weldments including crack closure effects and their coupled interaction with weld strength mismatch. A central objective of this study is to extend previously developed frameworks for evaluation of crack clo- sure effects on FCGR to steel weldments while, at the same time, gaining additional understanding of commonly adopted criteria for crack closure loads and their influence on fatigue life of structural welds. Very detailed non-linear finite element analyses using 3-D models of compact tension C ( T ) fracture spec- imens with center cracked, square groove welds provide the evolution of crack growth with cyclic stress intensity factor which is required for the estimation of the closure loads. Fatigue crack growth tests con- ducted on plane-sided, shallow-cracked C ( T ) specimens provide the necessary data against which crack closure effects on fatigue crack growth behavior can be assessed. Overall, the present investigation pro- vides additional support for estimation procedures of plasticity-induced crack closure loads in fatigue analyses of structural steels and their weldments