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8th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (LHMNC)

作者： Risse, Thomas Helie, Thomas Silva, Fabrice Falaize, Antoine IRCAM Paris France Aix Marseille Univ Cent Marseille CNRS LMA UMR 7031 Marseille France LaSIE La Rochelle France

Voice production results from the interaction between expelled airflow and soft tissues in the larynx and the vocal tract. Among the large literature on this topic over the last fifty years, a few nonlinear fluid-structure interaction models have been proposed in the port-Hamiltonian framework for passivity purposes. In this paper, we examine, compare and discuss two lumped-element port-Hamiltonian models from the literature, both derived from distributed parameter descriptions and simplifying assumptions chosen to integrate the minimal relevant phenomena involved in the larynx (for self-oscillations) or the vocal tract (during articulation). These models are recalled and reformulated using common terminology and notations. This leads to equivalent circuit representations, the components and the structure of which allow direct comparison (about causality, dimension, nonlinear laws, coupling) and physical interpretation. These results highlight important properties to consider and provide guidelines for future modelling improvement to be used in simulation. Copyright (C) 2024 The Authors.

关键词： Modelling Port-Hamiltonian systems distributed parameter systems Fluid-structure interaction Vocal apparatus

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Numerical Diffusion and its Impact on System-Identification for an Industrial Heating Process 11

Numerical Diffusion and its Impact on System-Identification ...

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11th Vienna International Conference on Mathematical Modelling (MATHMOD)

作者： Weiss, Ruven Diehl, Moritz Reuter, Johannes HTWG Konstanz Inst Syst Dynam Constance Germany Univ Freiburg Dept Microsyst Engn Freiburg Germany

This paper deals with system-identification for a distributed parameter heating process where a solid substrate is moving through a spatially extended heating zone and heated up by applying hot air to its surface. The temperature distribution inside the substrate is modeled in a spatial plane, where heat conduction is considered in the direction, perpendicular to the direction of movement. In contrast to previous work, where scalar model parameters (e.g. the thermal parameters of the substrate) have been identified, here, the quantities for the heat transfer (heat transfer coefficient and air temperature) are identified as functions yielding a significantly improved fit to the measurement data. This improved system-identification is performed for two early-lumping modeling approaches, which differ in the way the advection term in the governing Partial Differential Equation is discretized: one uses Eulerian coordinates, where the computational grid is stationary, whereas the second employs Lagrangian coordinates where the grid is moving with the substrate. The differences of the two approaches are discussed with the main focus on numerical diffusion. Especially its impact on the system-identification is investigated: although the fit to the measurement is comparably good in both cases, very different solutions are obtained for the identified functions which, we argue, is due to the optimizer counteracting the smoothing effect of numerical diffusion. Copyright (c) 2025 The Authors. This is an open access article under the CC BY-NC-ND license (https://***/licenses/by-nc-nd/4.0/)

关键词： System-Identification Numerical Diffusion Thermal Dynamics distributed parameter systems Transportation Heat Conduction

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Port-Hamiltonian Macroscopic Modelling based on the Homogenisation Method: case of an acoustic pipe with a porous wall 8

Port-Hamiltonian Macroscopic Modelling based on the Homogeni...

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8th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (LHMNC)

作者： Thibault, Alexis Helie, Thomas Boutin, Henri Chabassier, Juliette Modartt 9 Ave EuropeBat B18 F-31520 Ramonville St Agne France Sorbonne Univ Lab STMS UMR 9912 IRCAMCNRSMinist Culture 1 Pl Igor Stravinsky F-75004 Paris France

This paper addresses linear propagation in an acoustic pipe with a porous wall, a common scenario in wooden wind instruments. First, a scale separation technique is proposed for dissipative propagation within the wall: the material is modelled as a periodic assembly of identical microscopic cells, forming a network of channels filled with air. It is shown that the resulting PDE admits a port-Hamiltonian formulation, of which the state, flow, effort, Hamiltonian, and differential connection operator are structured using powers of the scale parameter. The resulting macroscopic description, derived from the governing equations at the two lowest orders, manifests as a constrained port-Hamiltonian system involving a Lagrange multiplier. As an example, using an academic cell geometry, we determine the effective wavenumber and dissipation coefficient of a straight tube with a porous wall. Copyright (C) 2024 The Authors.

关键词： Modelling Homogenisation method Port-Hamiltonian systems distributed parameter systems Acoustics

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Folding Bilateral Backstepping Output-Feedback Control Design for an Unstable Parabolic PDE

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2022年第5期67卷 2389-2404页

作者： Chen, Stephen Vazquez, Rafael Krstic, Miroslav Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA Univ Seville Dept Ingn Aeroespacial Seville 41092 Spain

We present a novel methodology for designing output-feedback backstepping bilateral boundary controllers for an unstable 1D diffusion-reaction partial differential equation (PDE) with spatially varying reaction. Using folding transforms the parabolic PDE into a 2 x 2 coupled PDE system with coupling through compatibility conditions. We apply a two-tiered backstepping approach, where the invertibility of the transformations guarantees the state-feedback controllers exponentially stabilize the trivial solution of the PDE system. A state observer is also designed for two collocated measurements at an arbitrary interior point, generating exponentially stable state estimates. The output feedback control law is formulated by composing the independently designed state-feedback controller with the observer, and the resulting dynamic feedback is shown to stabilize the trivial solution. Some numerical analysis on how the selection of these points affect the responses of the controller and observer are discussed, with simulations illustrating various choices of folding points and their effect on the stabilization in different performance indexes.

关键词： Backstepping distributed parameter systems multiple input partial differential equations (PDE)

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Numerical Implementation of Deep Neural PDE Backstepping Control of Reaction -Diffusion PDEs with Delay 4

Numerical Implementation of Deep Neural PDE Backstepping Con...

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4th Modeling, Estimation, and Control Conference (MECC)

作者： Wang, Shanshan Diagne, Mamadou Krstic, Miroslav Univ Shanghai Sci & Technol Dept Control Sci & Engn Shanghai Peoples R China Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA

Deep neural networks that approximate nonlinear function -to-function mappings, i.e., operators, which are called DeepONet, have been demonstrated in recent articles to be capable of encoding entire PDE control methodologies, such as backstepping, so that, for each new functional coefficient of a PDE plant, the backstepping gains are obtained through a simple function evaluation. These initial results have been limited to single PDEs from a given class, approximating the solutions of only single-PDE operators for the gain kernels. In this paper, we expand this framework by numerically illustrating the approximation of multiple (cascaded) nonlinear operators. Multiple operators arise in the control of PDE systems from distinct PDE classes, such as the system in this paper: a reaction -diffusion plant, which is a parabolic PDE, with input delay, which is a hyperbolic PDE. The DeepONet-approximated nonlinear operator is a cascade/composition of the operators defined by one hyperbolic PDE of the Goursat form and one parabolic PDE on a rectangle, both of which are bilinear in their input functions and not explicitly solvable. For the delay-compensated PDE backstepping controller, which employs the learned control operator, namely, the approximated gain kernel, exponential stability is guaranteed in our companion manuscript, in the L2 norm of the plant state and the H1 norm of the input delay state. In this paper, learning of a neural operator is presented, along with PDE backstepping simulations that illustrate closed-loop stabilization.

关键词： PDE backstepping deep learning neural networks distributed parameter systems delay systems

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Disturbance-decoupling observers for a class of second order distributed parameter systems

Disturbance-decoupling observers for a class of second order...

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American Control Conference (ACC)

作者： Demetriou, Michael A. Worcester Polytech Inst Dept Mech Engn Worcester MA 01609 USA

ISBN: (纸本)9781479901784

This work is concerned with the construction of disturbance-decoupling observers for a class of second order distributed parameter systems. The observer design relies on the knowledge of the operator associated with the spatial distribution of the disturbances. Following the finite dimensional results on disturbance-decoupling observers, a disturbance decoupling observer is proposed for a class of second order distributed parameter systems. Conditions for the solvability of the disturbance-decoupling observer are provided and Lyapunov-based convergence of the position and velocity errors is summarized. Simulations studies for the one-dimensional wave equation with two position measurements are included to illustrate the benefits of the disturbance-decoupling observer.

关键词： distributed parameter systems unknown input observers natural observers disturbance-decoupling observers second order systems

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Jet space extensions of infinite-dimensional Hamiltonian systems 8

Jet space extensions of infinite-dimensional Hamiltonian sys...

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8th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (LHMNC)

作者： Preuster, Till Maschke, Bernhard Schaller, Manuel Tech Univ Ilmenau Inst Math Ilmenau Germany Univ Claude Bernard Lyon 1 CNRS LAGEPP UMR 5007 Villeurbanne France

We analyze infinite-dimensional Hamiltonian systems corresponding to partial differential equations on one-dimensional spatial domains formulated with formally skew-adjoint Hamiltonian operators and non-quadratic Hamiltonian density. In various applications, the Hamiltonian density can depend on spatial derivatives of the state such that these systems can not straightforwardly be formulated as boundary port-Hamiltonian system using a Stokes-Dirac structure. In this work, we show that any Hamiltonian system of the above class can be reformulated as a Hamiltonian system on the jet space, in which the Hamiltonian density only depends on the extended state variable itself and not on its derivatives. Consequently, well-known geometric formulations with Stokes-Dirac structures are applicable. Additionally, we provide a similar result for dissipative systems. We illustrate the developed theory by means of the the Boussinesq equation, the dynamics of an elastic rod and the Allen-Cahn equation. Copyright (C) 2024 The Authors.

关键词： port-Hamiltonian systems jet spaces distributed parameter systems

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State estimation of the Stefan PDE: A tutorial on design and applications topolar ice and batteries

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ANNUAL REVIEWS IN CONTROL 2022年 53卷 199-223页

作者： Kogaa, Shumon Krstic, Miroslav Univ Calif San Diego Dept Elect & Comp Engn 9500 Gilman Dr La Jolla CA 92093 USA Univ Calif San Diego Dept Mech & Aerosp Engn 9500 Gilman Dr La Jolla CA 92093 USA

The Stefan PDE system is a representative model for thermal phase change phenomena, such as melting andsolidification, arising in numerous science and engineering processes. The mathematical description is givenby a Partial Differential Equation (PDE) of the temperature distribution defined on a spatial interval with amoving boundary, where the boundary represents the liquid-solid interface and its dynamics are governed byan Ordinary Differential Equation (ODE). The PDE-ODE coupling at the boundary is nonlinear and creates asignificant challenge for state estimation with provable convergence and *** tutorial article presents a state estimation method based on PDE backstepping for the Stefan system,using measurements only at the moving boundary. PDE backstepping observer design generates an observergain by employing a Volterra transformation of the observer error state into a desirable target system, solvinga Goursat-form PDE for the transformation's kernel, and performing a Lyapunov analysis of the target observererror *** observer is applied to models of problems motivated by climate change and the need for renewableenergy storage: a model of polar ice dynamics and a model of charging and discharging in lithium-ion *** numerical results for polar ice demonstrate a robust performance of the designed estimator with respect tothe unmodeled salinity effect in sea ice. The results for an electrochemical PDE model of a lithium-ion batterywith a phase transition material show the elimination of more than 15 % error in State-of-Charge estimatewithin 5 min even in the presence of sensor noise.

关键词： Stefan system State estimation distributed parameter systems Backstepping Nonlinear observer Sea ice Lithium-ion batteries

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Model-order reduction for nonlinear distributed parameter systems with application to internal combustion engine modeling and simulation

Model-order reduction for nonlinear distributed parameter sy...

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作者： Stockar, Stephanie The Ohio State University

学位级别：Ph.D.

In recent years, difficult challenges have been faced by the automotive industry to meet the increasingly ambitious fuel economy objectives without sacrificing the vehicle performance, hence remaining appealing to the market. In this sense, the automotive industry is moving toward the implementation of advanced powertrain technologies aiming at improving the efficiency of breathing and combustion in Internal Combustion Engines (ICEs). With the advancements in engine design, the air path systems have become more sophisticated and advanced control techniques are needed in order to fully exploit the potential of existing technologies. This has pushed the automotive industry to adopt more efficient procedures for modeling, system simulation and model-based control. Such procedures require accurate and computationally efficient engine system simulation models that are able to predict the cylinder charge composition and the thermodynamic conditions with limited calibration effort. To this extent, reduced-order models for unsteady compressible flow systems, namely models derived from the fundamental conservation laws without over-simplifying the topology of the engine air path, are receiving considerable interest for performance simulation and control design. These models have high predictive abilities and maintain a relatively simple structure, namely, implementable as low-order systems of linear or nonlinear Differential and Algebraic Equations (DAEs). In this scenario, a novel mathematical modeling methodology is presented in this dissertation for the solution of non-linear hyperbolic partial differential equation describing the wave propagation in compressible fluids. The proposed approach combines an integral representation of the conservation laws for compressible fluids with a projection onto a pre-determined basis, which capture and solve the spatially-dependent nature of the system separately from its time evolution. This allows one to describe propagatory-type ph

关键词： Mechanical Engineering model-order reduction internal combustion engine system dynamics engine modeling distributed parameter systems

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Actuator and Sensor Fault Detection and Failure Prediction for systems with Multi-dimensional Nonlinear Partial Differential Equations

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INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND systems 2022年第3期20卷 789-802页

作者： Ferdowsi, Hasan Cai, Jia Jagannathan, Sarangapani Northern Illinois Univ Dept Elect Engn 590 Garden Rd De Kalb IL 60115 USA Missouri Univ Sci & Technol Elect & Comp Engn Dept 301 W 16th St Rolla MO 65409 USA

This paper presents a new model-based fault detection and failure prediction framework for a class of multi-input and multi-output (MIMO) nonlinear distributed parameter systems (DPS) described by partial differential equations (PDE) with actuator and sensor faults. The fault functions cover both abrupt and incipient faults. A Luenberger type observer is used to monitor the health of the DPS as a detection observer on the basis of the nonlinear PDE representation of the system and by utilizing only the measured output vector. By taking the difference between measured and estimated outputs, a residual signal is generated for fault detection. If the detection residual exceeds a predefined threshold, a fault is claimed to be active. Once an actuator or a sensor fault is detected, an appropriate fault parameter update law is developed to learn the fault dynamics online with the help of an additional measurement. Later, an explicit formula is introduced to estimate the time-to-failure in the presence of an actuator/sensor fault by utilizing the limiting values of the output vector along with the estimated fault parameter vector. Eventually, the effectiveness of the proposed detection and prediction framework is demonstrated on a nonlinear process.

关键词： distributed parameter systems estimation and detection fault detection and diagnosis nonlinear systems

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