Nonlinear Modeling & Robust Control of Electro-active Polymer Actuators
Scientific context of the thesis
The port-Hamiltonian (pH) framework, originally introduced in [1], offers an energy-based approach for modeling dynamical systems. This is achieved by incorporating energy and co-energy variables together with an intrinsic geometric structure, namely the Dirac structure, which reflects maximality and ensures power preservation between conservative and dissipative phenomena.
Two passivity-based control (PBC) strategies exploit the pH framework [2]: Control by Interconnection (CBI) that consists in shaping the closed-loop energy through a power-preserving coupling between plant and controller, while Interconnection and Damping Assignment PBC (IDA-PBC) assigns a target interconnection matrix Jd and damping Rd so that the closed-loop Hamiltonian Hd has its minimum at the desired equilibrium.
The extension to infinite-dimensional systems governed by partial differential equations (PDEs), introduced in [3], uses a Stokes-Dirac structure defined on spaces of differential forms over a spatial domain Ω with boundary ∂Ω. This formulation has been widely studied for one-dimensional (1D) linear distributed parameter systems, leading to important advances in both analysis and controller design: for example in [4] for boundary control, and in [5] for in-domain distributed control. Nevertheless, the modelling and control of flexible structures undergoing large deformations and nonlinear material behavior, leading to inherently nonlinear PDEs, remain largely unexplored in the literature, with multiphysical coupling posing an additional challenge that has received even less attention.
The objective of this Ph.D. thesis is twofold: first, to develop a nonlinear infinite-dimensional portHamiltonian (pH) model for flexible structures undergoing large deformations with strongly nonlinear (electro-)mechanical behavior; and second, to synthesize robust controllers with clear physical interpretations to stabilize such structures at desired configurations and to follow desired trajectories. The proposed theoretical framework will be applied to the modeling and control of a cardiac assist device based on dielectric elastomer technology. Dielectric elastomer actuators (DEAs) have attracted considerable interest in biomedical robotics over the past two decades, owing to their large deformation capacity, fast response, high compliance, low power consumption, and biocompatibility. As the electric field induces membrane thinning via Maxwell stress, the resulting reduction in thickness further intensifies the field, leading to a positive feedback loop [7]. Recent studies have investigated the modeling and stabilization of this instability within finitedimensional pH systems, under the restrictive assumption that the deformation field is spatially homogeneous [8]. However, this lumped-parameter hypothesis fails to capture the non-homogeneous deformations that DEAs exhibit in practice, and cannot accurately predict the true instability threshold. To overcome these limitations, and to lay the groundwork for future work accounting for fluid-structure interaction between the DEA and the surrounding flow, modeling DEAs as nonlinear infinite-dimensional pH systems is required. The DEA structure considered here is weakly electromechanically coupled and will be a 1D infinite-dimensional pH system. Its nonlinearity arises in both the interconnection operator J (x) and the gradient of the Hamiltonian, related to geometric nonlinearity, material nonlinearity, and electro-mechanical coupling. The input operator is distributed in space, while the input voltage remains finite-dimensional, which gives rise to instability under changes in deformation. The controller design for such DEAs naturally leads to the problem of in-domain distributed control of 1D infinite-dimensional pH systems. In-domain control of linear infinite-dimensional pH systems via CBI has been investigated in [5]. However, owing to the dissipation obstacle in electromechanical systems, extending IDA-PBC to the nonlinear infinite-dimensional setting remains a necessary step, which this thesis proposes to address.
Ph.D. thesis activities and time planing
The PhD will be carried out in MOCOPHYS team at the AS2M department of FEMTO-ST institute (CNRS UMR 6174, Besan¸con, France), internationally recognized for micro-nano robotics, smart materials, and automatic control. The candidate will have access to DEA experiment setup, real-time control hardware (dSPACE), and high-voltage equipment. The primary goals of this thesis include:
- 1. Develop a nonlinear, multi-physical, infinite dimensional pH model of DEAs. Perform structure-preserving spatial discretization and numerical simulation.
- 2. Design robust passivity control for 1D nonlinear infinite-dimensional pH systems.
- 3. Validate the proposed model identification and test the designed controllers against the electromechanical instability.
Administrative information
ANR funding ensures a full 3-year doctoral contract, with support for international conferences, and research visits. The candidate will be under the supervision of Prof. Yann Le Gorrec, and Dr. Ning Liu. The Ph.D. thesis will start in September 2026 or by arrangement.
Candidate profile
Required:
- MSc in Control Engineering, Mechanical Engineering, Applied Mathematics, or equivalent.
- Solid background in dynamical systems theory, numeric simulation, Lyapunov stability, and mathematical analysis.
- Scientific programming skills (MATLAB or Python).
- Good written and oral English.
Appreciated:
- Knowledge of continuum mechanics, or PDEs analysis.
- Familiarity with passivity-based control or energy-based methods.
- Experience with dSPACE, smart materials, soft actuators, or experimental platforms.
How to apply
List of documents to be provided:
- Detailed CV (including publications, if any).
- A concise cover letter describing your interest in the topic, written without LLM assistance.
- An academic transcript and ranking of (Bachelor’s and Master’s)
- Recommendation letters.
For more information and application, please contact: [email protected].
Deadline : 2026/06/15 - early applications strongly encouraged .
References
[1] B. Maschke, A. V. D. Schaft, and P. Breedveld, “An intrinsic hamiltonian formulation of network dynamics: nonstandard poisson structures and gyrators,” Journal of the Franklin Institute, vol. 329, pp. 923–966, 9 1992.
[2] R. Ortega, A. J. Van der Schaft, I. Mareels, and B. Maschke, “Putting energy back in control,” IEEE Control Systems, vol. 21, no. 2, pp. 18–33, apr 2001.
[3] A. van der Schaft and B. Maschke, “Hamiltonian formulation of distributed-parameter systems with boundary energy flow,” Journal of Geometry and Physics, vol. 42, pp. 166–194, 5 2002.
[4] A. Macchelli, Y. L. Gorrec, H. Ramirez, and H. Zwart, “On the synthesis of boundary control laws for distributed port-hamiltonian systems,” IEEE Transactions on Automatic Control, vol. 62, pp. 1700–1713, 4 2017.
[5] N. Liu, Y. Wu, Y. L. Gorrec, L. Lef`evre, and H. Ramirez, “Reduced order in domain control of distributed parameter port-hamiltonian systems via energy shaping,” Automatica, vol. 161, p. 111500, 3 2024.
[6] M. Almanza, F. Clavica, J. Chavanne, D. Moser, D. Obrist, T. Carrel, Y. Civet, and Y. Perriard, “Feasibility of a dielectric elastomer augmented aorta,” Advanced Science, vol. 8, 3 2021.
[7] N. Liu, T. Martinez, A. Walter, Y. Civet, and Y. Perriard, “Control-oriented modeling and analysis of tubular dielectric elastomer actuators dedicated to cardiac assist devices,” IEEE Robotics and Automation Letters, vol. 7, no. 2, pp. 4361–4367, 2022.
[8] A. Hammoud, N. Liu, Y. L. Gorrec, Y. Civet, and Y. Perriard, “Energy-based control of a dielectric elastomer cardiac assist device,” Mechatronics, vol. 117, p. 103515, 7 2026
Job Type: Contract
Contract length: 36 months
Pay: 2,071.41€ - 2,300.00€ per month
Work Location: In person
