Ramírez, Hector Miguel

This article studies robust output tracking and disturbance rejection for boundary-controlled infinite-dimensional Port– Hamiltonian systems including second-order models such as the Euler–Bernoulli beam equation. The control design is achieved using the internal model principle and the stability analysis using a Lyapunov approach. Contrary to existing works on the same topic, no assumption is made on the external well-posedness of the considered class of PDEs. The results are applied to robust tracking of a piezo actuated tube used in atomic force imaging.

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 this paper, we consider the asymptotic boundary stabilisation of a one-dimensional wave equation subject to anti-damping at its free end and with control at the opposite one. The control action, implemented through a state feedback or a dynamic controller, is derived by using the port-Hamiltonian framework. More precisely, the standard energy-shaping approach plus damping assignment is adapted to cope with infinite dimensional systems with anti-damping boundary conditions. It is shown how to modify the equivalent dynamic controller to account for the instability propagation along the domain.

Irreversible port-Hamiltonian systems (IPHS) are an extension of port-Hamiltonian systems (PHS) for irreversible thermodynamics which encompass a large class of thermodynamic systems that may contain reversible and irreversible phenomena. Energy shaping and damping injection are standard structure preserving passivity based control approaches which have proven to be very successful for the stabilization of PHS. However, in the case of irreversible thermodynamics, the non-linear nature of the systems make it non-trivial to apply these approaches for stabilization. In this paper we propose a systematic procedure to perform, in a first control loop, energy shaping by state modulated interconnection with a controller in IPHS form. Then, a second control loop guarantees asymptotic stability by the feedback of a new closed-loop passive output. The approach allows to stabilize IPHS while preserving the IPHS structure in closed-loop, allowing to interpret the closed-loop system as a desired thermodynamic system. The example of the continuous stirred tank reactor is used to illustrate the approach.

This paper aims to propose a finite-dimensional observer-based state feedback controller to stabilize a class of boundary controlled system. To this end, we propose to use an early-lumping approach, where the infinite-dimensional port-Hamiltonian system is first discretized using a structure-preserving method. Then, we build a passive observed-based controller using a Linear Matrix Inequality (LMI) and finally, the controller is interconnected with the infinite-dimensional system in a passive way. Due to its passivity and Hamiltonian structure, this observer-based controller can stabilize not only the discretized lumped parameter system but also the original distributed parameter system. This approach avoids the intrinsic drawback of early lumping approach and spillover effects. Finally, the boundary controlled undamped wave equation is used to illustrate the effectiveness of the proposed controller.

The linear quadratic regulator is a widely used and studied optimal control technique for the control of linear dynamical systems. It consists in minimizing a quadratic cost functional of the states and the control inputs by the means of solving a linear Riccati equation. The effectiveness of the linear quadratic regulator relies on the cost function parameters hence, an appropriate selection of these parameters is of mayor importance in the control design. Port-Hamiltonian system modelling arise from balance equations, interconnection laws and the conservation of energy. These systems encode the physical properties in their structure matrices, energy function and definition of input and output ports. This paper establishes a relation between two classical passivity based control tools for port-Hamiltonian systems, namely control by interconnection and damping injection, with the linear quadratic regulator. These relations allow then to select the weights of the quadratic cost functional on the base of physical considerations. A simple RLC circuit has been used to illustrate the approach.

We present a port-Hamiltonian system (PHS) model based on the interconnection between basic hydraulic elements equivalent to electrical components such as capacitors, inductors, and resistors to represent the dynamics of a water micro-channel experimental plant. We compare the fluid-structured interconnected PHS model with the data obtained from a micro-channel experimental plant. We then implement a controller using the total hydraulic-mechanical energy as a local Lyapunov function. Finally, we apply an integral action controller (IAC) to correct for modeling errors and load disturbances. The IAC is easy to design given the proposed interconnected model.

The control of a flexible beam using ionic polymer metal composites (IPMCs) is investigated in this paper. The mechanical flexible dynamics are modelled as a Timoshenko beam. The electric dynamics of the IPMCs are considered in the model. The port-Hamiltonian framework is used to propose an interconnected control model of the mechanical flexible beam and IPMC actuator. Furthermore, a passive and Hamiltonian structure-preserving linear quadratic Gaussian (LQG) controller is used to achieve the desired configuration of the system, and the asymptotic stability of the closed-loop system is shown using damping injection. An experimental setup is built using a flexible beam actuated by two IPMC patches to validate the proposed model and show the performance of the proposed control law.

—In this letter, we consider the exponential stabilization of a distributed parameter port-Hamiltonian system interconnected with an unstable finite-dimensional linear system at its free end and control input at the opposite one. The infinite-dimensional system can also have in-domain anti-damping. The control design passes through the definition of a finite-dimensional linear system that “embeds” the response of the distributed parameter model, and that can be stabilized by acting on the available control input. The conditions that link the exponential stability of the latter system with the exponential stability of the original one are obtained thanks to a Lyapunov analysis. Simulations are presented to show the pros and cons of the proposed synthesis methodology.

This paper deals with the finite dimensional modelling and control of an electro-active polymer (EAP) actuated flexible structure. This model reproduces the basic mechanical properties of a class of one dimensional flexible endoscope. The flexible structure and the EAP actuator are both modelled as port-Hamiltonian systems. The EAP actuator is interconnected with the flexible structure in a power preserving manner such that the global system is again a PHS. Using the obtained model, two passivity based control strategies are applied to derive the controllers which achieve a desired equilibrium configuration with desired dynamic behaviour. An experimental benchmark composed of the Ionic Polymer Metal Composites patches glued to a flexible beam is used to validate the proposed model and control law.