# Students

**Ph.D. Students**

**1.- Vincent Trenchant **(web page), Smart Boundary Control of VibroAcoustic and Elastodynamic Systems, October 2014 - September 2017. FEMTO-ST, Besançon, France. Supervisors: Yann Le Gorrec and Hector Ramirez.

The aim of the thesis is to propose passivity based control strategies for the acoustic or elastic wave attenuation at the output of 2D and 3D acoustic systems. An experimental set-up will be used to validate the developed control approaches. A first approach will use a distributed dissipative port-Hamiltonian representations of the distributed parameter model for the control synthesis. In a second instance, the derivation of a finite dimensional port-Hamiltonian approximation based on k-forms will be developed and used for the control design. In both cases, special attention will be given to the reduction/approximation scheme and the fact that the control will account for the structure of the distributed network of actuators/sensors. More specifically, the robustness of the controllers will be investigated with respect to the structured model error of the finite dimensional approximation of the infinite-dimensional port-Hamiltonian system.

**Keywords: **Distributed parameter system, port-Hamiltionian system, boundary control, acoustic system.

**Master (MT) and professional project (PP) students**

**1.- Harizaka Rakotondratsimba**, Port-Hamiltonian control of a 1-DOF micro-robotic systems (MT), April - August 2014. FEMTO-ST, Besançon, France. Supervisors: Hector Ramirez and Cedric Clevy

In the framework of the robotic microassembly of microsystems (MEMS), many researchers use force control in order to perform microassembly tasks. Robot force control at the macroscale is a well-known topic in the robotic domain. It has been widely investigated in the 80’s and 90’s. However, at the microscale, the difficulty of the control problem increases due to the predominance of the surface forces, the difficulty of integration of sensors, the significant level of noise and the nonlinearities of the system. The microscale specificities increase the complexity of the model which motivates to investigate and develop new model and control strategies, better adapted to micro-applications. In the last decade powerful control techniques based on network models and energy based representations have been developed for electrical, mechanical and electro-mechanical systems. Among these approaches a particularly interesting is the one based on port-Hamiltonian systems. The use of energy based control methods is common in macro-robotic applications, but its use in micro-robotics has not yet been investigated. One of the main objectives of this research project is to use energy based control approaches, and in particular the ones based on the port-Hamiltonian framework, to systematically model and control a 1-DOF typical scenario of interaction between a microrobot manipulator and a flexible environment. This will be performed by developing a port-Hamiltonian model for the interconnected mass-spring-damper systems subject to a non-linear pull-off force. The port-Hamiltonian model will then be instrumental to derive passivity based control strategies, i.e., control laws based on energy balances. The study starts from understanding the behavior of the components at the microscale, modeling the system, developing a control technique and implementing the control technique to test the performances and to stabilize the nonlinear microsystem.

**Keywords: **MEMS, 1-DOF micro-robot, passivity based control, port-Hamiltonian system.

**2.- Yassine Fares**, Modelling and distributed control of an acoustic process (MT), December 2013 - April 2014. FEMTO-ST, Besançon, France. Supervisors: Yann Le Gorrec and Hector Ramirez

The modeling of physical systems based on the representation of the intrinsic energy exchanges between different energetic domains allows a modular description of their (eventually complex) dynamic behavior. This is the aim of the Port Hamiltonian framework that proposes to make the link between the energy of the system and its dynamics through the definition of a geometric structure (named Dirac structure). Such complementary information coming from the modeling step is very valuable for the analysis and the control design in the case of non linear or distributed parameter systems. The aim of the thesis is to propose some passivity based control strategies for the acoustic or elastic wave attenuation at the output of 2D acoustic systems. This is approached using the dissipative Hamiltonian structure of the distributed parameter model for the control design. A particular care is taken on the reduction scheme and the fact that the control will account for the structure of the distributed network of actuators/sensors. In particular the robustness of the controllers is investigated with respect to the structured error model of the Hamiltonian approximation of the infinite-dimensional port-Hamiltonian system.

**Keywords: **Partial differential equations, spatial discretization, port-Hamiltonian systems, passivity based control, acoustic process

**3.- Pablo Zuñiga**, Robust IDA-PBC applied to non-linear processes with singularities (PP), August 2007 - Enero 2008, DIE UDEC, Concepcion, Chile. Supervisors: Daniel Sbarbaro and Hector Ramirez

The Thesis presents a novel nonlinear control strategy based on IDA-PBC for a non-linear process with bidirectional flow. The process was modeled as PH model, and by a proper selection of the process closed-loop matrices. A passivity based strategy was designed, and in order to deal with model uncertainties and unknown disturbances, integral action was also considered in the control law. Since the process exhibits uncontrollable operation conditions; i.e. singular points in the control law, a singular point solution was proposed without compromising the stability conditions of the closed-loop process. A nice feature of the proposed singular point solution is that outside the set of singular points the desired closed-loop interconnection and damping specifications are preserved, hence no special considerations must be taken into account when selecting the desired closed-loop PH system in the IDA-PBC design. The closed-loop behavior of the proposed controller has been illustrated by numerical simulations.

**Keywords: **Bidirectional flow process, non-linear control, port-Hamiltonian systems, IDA-PBC