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This paper is concerned with the modeling and control of a curling Hydraulically Amplified Self-healing Electrostatic (HASEL) actuator using the port-Hamiltonian (PH) approach. For that purpose, we use a modular approach and consider the HASEL actuator as an interconnection of elementary subsystems. Each subsystem is modeled by an electrical component consisting of a capacitor in parallel with an inductor connected through the conservation of volume of the moving liquid to a mechanical structure based on inertia, linear, and torsional springs. The parameters are then identified, and the model is validated on the experimental setup. Position control is achieved by using Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) with integral action (IA) for disturbance rejection. Simulation results show the efficiency of the proposed controller.

This article presents a systematic methodology for modeling a class of flexible multidimensional mechanical structures defined by linear elastic relations that directly allows to obtain their infinite-dimensional port-Hamiltonian representation. The approach is restricted to systems based on a certain class of kinematic assumptions. However this class encompasses a wide range of models currently available in the literature, such as ${\ell}$-dimensional elasticity models (with ${\ell}$ = 1,2,3), vibrating strings, torsion in circular bars, classical beam and plate models, among others. The methodology is based on Hamilton's principle for a continuum medium which allows defining the energy variables of the port-Hamiltonian system, and also on a generalization of the integration by parts theorem, which allows characterizing the skew-adjoint differential operator and boundary inputs and boundary outputs variables. To illustrate this method, the plate modeling process based on Reddy's third-order shear deformation theory is presented as an example. To the best of our knowledge, this is the first time that an infinite-dimensional port-Hamiltonian representation of this system is presented in the literature.

This letter investigates the design of a class of infinite-dimensional observers for one dimensional (1D) boundary controlled port-Hamiltonian systems (BC-PHS) defined by differential operators of order $N \geq 1$. The convergence of the proposed observer depends on the number and location of available boundary measurements. \textcolor{hector}{Asymptotic convergence is assured for $N\geq 1$, and provided that enough boundary measurements are available, exponential convergence can be assured for the cases $N=1$ and $N=2$.} Furthermore, in the case of partitioned BC-PHS with $N=2$, such as the Euler-Bernoulli beam, \textcolor{hector}{it is shown} that exponential convergence can be assured considering less available measurements. The Euler-Bernoulli beam model is used to illustrate the design of the proposed observers and to perform numerical simulations.

An in-domain finite dimensional controller for a class of distributed parameter systems on a one-dimensional spatial domain formulated under the port-Hamiltonian framework is presented. Based on [25] where positive feedback and a late lumping approach are used, we extend the Control by Interconnection method and propose a new energy shaping methodology with an early lumping approach on the distributed spatial domain of the system. Our two main control objectives are to stabilize the closed loop system, as well as to improve the closed loop dynamic performances. With the early lumping approach, we investigate two cases of the controller design, the ideal case where each distributed controller acts independently on the spatial domain (fully-actuated), and the more realistic case where the controller is piecewise constant over certain interval (under-actuated). We then analyze the asymptotic stability of the closed loop system when the infinite dimensional plant system is connected with the finite dimensional controller. Furthermore we provide simulation results comparing the performance of the fully-actuated case and the under-actuated case with an example of an elastic vibrating string., Comment: 13 pages

In this technical note, we consider the stability properties of a viscously damped Timoshenko beam equation with spatially varying parameters. With the help of the port-Hamiltonian framework, we first prove the existence of solutions and show, by an appropriate Lyapunov function, that the system is exponentially stable and has an explicit decay rate. The explicit exponential bound is computed for an illustrative example of which we provide some numerical simulations.

The pinning-depinning phase transitions of interfaces for two classes of discrete elastic-string models are inverstigated numerically. In the (1+1)-dimensions, we revisit these two elastic-string models with slight modification on growth rule, and compare with the previous numerical results. In the (2+1)-dimensional case, we perform extensive simulations on pinning-depinning transitions in these quenched models. For full comparisons in the physically relevant spatial dimensions, we also visit numerically two distinct quenched universality classes, including the quenched Edwards-Wilkinson (QEW) and the quenched Kardar-Parisi-Zhang (QKPZ) equations with and without external driving forces. The critical exponents of these quenched systems are numerically estimated. Our results show that the critical exponents satisfy scaling relations well, and these two discrete elastic-string models do not fall into the existing universality classes. In order to visually comparisons of these quenched systems in (2+1)-dimensional cases, we also exhibit surface morphologies with various external driving forces during the saturated time regimes.

The design of an observer-based state feedback (OBSF) controller with guaranteed passivity properties for port-Hamiltonian systems (PHS) is addressed using linear matrix inequalities (LMIs). The observer gain is freely chosen and the LMIs conditions such that the state feedback is equivalent to control by interconnection with an input strictly passive (ISP) and/or an output strictly passive (OSP) and zero state detectable (ZSD) port-Hamiltonian controller are established. It is shown that the proposed controller exponentially stabilizes a class of infinite-dimensional PHS and asymptotically stabilizes a class of finite-dimensional non-linear PHS. A Timoshenko beam model and a microelectromechanical system are used to illustrate the proposed approach.

An observer-based boundary controller for infinite-dimensional port-Hamiltonian systems defined on 1D spatial domains is proposed. The design is based on an early-lumping approach in which a finite-dimensional approximation of the infinite-dimensional system derived by spatial discretization is used to design the observer and the controller. As long as the finite-dimensional approximation approaches the infinite-dimensional model, the performances also do. The main contribution is a constructive method which guarantees that the interconnection between the controller and the infinite-dimensional system is asymptotically stable. A Timoshenko beam model has been used to illustrate the approach.