Yuz Eissmann, Juan Ignacio

In this paper we consider general port-Hamiltonian formulations of multidimensional Maxwell’s viscoelastic fluids. Two different cases are considered to describe the energy fluxes in isentropic compressible and incompressible fluids. In the compressible case, the viscoelastic effects of shear and dilatational strains on the stress tensor are described individually through the corresponding constitutive equations. In the incompressible case, an approach based on the bulk modulus definition is proposed in order to obtain an appropriate characterization, from the port-Hamiltonian point of view, of the pressure and nonlinear terms in the momentum equation, associated with both dynamic pressure and vorticity of the flow.

In-flame optical characterization of soot is of vital importance to understand soot formation mechanisms as well as to develop and validate accurate soot models. The present work introduces an unconventional methodology adapted to laminar axisymmetric flames that avoids the issue of variable measurement volume with varying scattering angle in the existing light scattering techniques and thus enables the determination of aggregate size with a higher spatial resolution. Coupled with multi-wavelength line-of-sight attenuation measurements, the proposed Horizontal Planar Angular Light Scattering at 532 nm was found able to provide radial profiles of aggregate size, number and diameter of primary spheres, soot volume fraction, and number density in a laminar axisymmetric coflow ethylene/air diffusion flame established over a Gülder burner. The spatial variation of soot optical properties associated with soot maturity was considered in data analysis.

We consider the discretization of continuous-time nonlinear systems described by normal forms. In particular, we consider the case when the input to the system is generated by a B-spline hold device to obtain an approximate discrete-time model. It is shown that the corresponding sampled-data model and its accuracy (measured in terms of the local truncation error) depend on the smoothness of the input and on the applied integration strategy, namely, the truncated Taylor series expansion. Moreover, the sampling zero dynamics of the discrete-time model are asymptotically characterized as the sampling period goes to zero, and it is shown that these zero dynamics converge to the asymptotic sampling zeros of the linear case.

In this paper we consider the physical-based modeling of 3D and 2D Newtonian fluids including thermal effects in order to cope with the first and second principles of thermodynamics. To describe the energy fluxes of non-isentropic fluids we propose a pseudo port-Hamiltonian formulation, which includes the rate of irreversible entropy creation by heat flux. For isentropic fluids, the conversion of kinetic energy into heat by viscous friction is considered as an energy dissipation associated with the rotation and compression of the fluid. Then, a dissipative port-Hamiltonian formulation is derived for this class of fluids. In the 2D case we modify the vorticity operators in order to preserve the structure of the proposed models. Moreover, we show that a description for inviscid or irrotational fluids can be derived from the proposed models under the corresponding assumptions leading to a pseudo or dissipative port-Hamiltonian structures.

A new high gain control law is proposed for stably invertible linear systems. The continuous-time case is first studied to set ideas. The extension to the sampled-data case is made difficult by the presence of sampling zeros. For continuous-time systems having relative degree greater than or equal to two, these zeros converge, as the sampling rate approaches zero, to either marginally stable or unstable locations. A methodology which specifically addresses the sampling zero issue is developed. The methodology uses an approximate model which includes, when appropriate, the asymptotic sampling zeros. The core idea is supported by simulation studies. Also, a preliminary theoretical analysis is provided for degree two, showing that the design based on the approximate model stabilizes the true system for the continuous and sampled-data cases

Models of the human body are key in bio-engineering and medical applications. This study presents the identification, in time and frequency domains, of linear time invariant models of the human subglottal system, for the clinical assessment of vocal function. For time domain identification, the input-output data corresponds to the glottal volume velocity and the acceleration registered by a sensor on the neck skin of the patient. For frequency domain identification, the frequency response of the subglottal tract module is used. Maximum likelihood and prediction error methods are applied. Additionally, the Akaike and Bayes Information Criteria are used to select the models order.

A new high gain control law is proposed for stably invertible linear systems. The continuous-time case is first studied to set ideas. The extension to the sampled-data case is made difficult by the presence of sampling zeros. For continuous-time systems having relative degree greater than or equal to two, these zeros converge, as the sampling rate approaches zero, to either marginally stable or unstable locations. A methodology which specifically addresses the sampling zero issue is developed. The methodology uses an approximate model which includes, when appropriate, the asymptotic sampling zeros. The core idea is supported by simulation studies. Also, a preliminary theoretical analysis is provided for degree two, showing that the design based on the approximate model stabilizes the true system for the continuous and sampled-data cases.

In this paper, the servo control design methodologies based on Feedback Linearization (FL) and Linear Algebra Based (LAB) are applied to nonlinear systems with and without zero dynamics, analysing the case of unstable zero dynamics. Their advantages and drawbacks are discussed. Some examples are developed to illustrate the results.

Some nonlinear systems can be represented through linear parameter varying models. In this work, we address the estimation of continuous-time linear parameter varying models in output error form, using a refined instrumental variable method. A distinguished feature of a linear parameter varying model is that it has parameters that depend on an external signal called the scheduling variable. In this paper, we assume that the scheduling variable is noisy, a condition which is often met in practice, but not frequently considered in the literature. On the other hand, there are applications in which the noise-free version of the scheduling variable is smooth. Under such scenario we can simply filter the scheduling variable before estimating the linear parameter model. Nonetheless, there are cases where special smoothing techniques are required. In this study, we consider one of these special cases, and we use the well-known local regression method as smoothing technique. A numerical example based on a Monte Carlo simulation shows the benefits of the proposed approach.

A simple and scalable finite-dimensional model based on the port-Hamiltonian framework is proposed to describe the fluid–structure interaction in tubes with time-varying geometries. For this purpose, the moving tube wall is described by a set of mass-spring-damper systems while the fluid is considered as a one-dimensional incompressible flow described by the average momentum dynamics in a set of incompressible flow sections. To couple these flow sections small compressible volumes are defined to describe the pressure between two adjacent fluid sections. The fluid-structure coupling is done through a power-preserving interconnection between velocities and forces. The resultant model includes external inputs for the fluid and inputs for external forces over the mechanical part that can be used for control or interconnection purposes. Numerical examples show the accordance of this simplified model with finite-element models reported in the literature.