Gou Nishida

Formal Distributed Port-Hamiltonian Representation of Field Equations

The purpose of this study is to establish a unified modeling procedure of distributed port-Hamiltonian formulations for field equations. First, higher order Stokes-Dirac structures on variational complexes of jet bundles are introduced. Next, a one-to-one correspondence between Euler-Lagrange equations and distributed port-Hamiltonian systems is presented. Finally, in the case that the Lagrangian is given, the concrete transformation procedure for distributed port-Hamiltonian systems is explained by using two examples.

Multi-Scale Distributed Port-Hamiltonian Representation of Ionic Polymer-Metal Composite

This paper shows that one of soft actuators, Ionic Polymer-Metal Composite (IPMC) can be modeled in terms of distributed port-Hamiltonian systems with multi-scale. The physical structure of IPMC consists of three parts. The first part is an electric double layer at the interface between the polymer and the metal electrodes. The frequency response of the polymer-metal interface shows a fractal degree of gain slope. Then we adopt a black-box circuit model to this part and give considerations for distributed impedance parameters. The second part is an electrostress diffusion coupling model with bending and relaxation dynamics. This part is represented by an electro-osmosis, which is a water transport by an electric field, and a streaming potential, which is an electric field created by a water transport. We discuss the relationship of stress and bending moment induced by swelling. The third part is a mechanical system modeled as a flexible beam with large deformations. The representation has the capability extracting the control structure based on passivity from distributed parameter systems possessing a complex behavior.

Virtual Lagrangian Construction Method for Infinite-Dimensional Systems with Homotopy Operators

This paper presents a general modeling method to construct a virtual Lagrangian for infinite-dimensional systems. If the system is self-adjoint in the sense of the Fretchet derivative, there exists some Lagrangian for a stationary condition of variational problems. A system having such a Lagrangian can be formulated as a field port-Lagrangian system by using a Stokes-Dirac structure on a variational complex. However, it is unknown whether any infinite-dimensional system can be expressed as an Euler-Lagrange equation. Then, we introduce a virtual Lagrangian with a homotopy operator. The virtual Lagrangian defines a self-adjoint subsystem, which is realized by a cancellation of non-self-adjoint error subsystems.

Disturbance structure decomposition for distributed-parameter port-Hamiltonian systems

In this paper, a decomposition of a disturbance structure for distributed-parameter port-Hamiltonian systems is presented. A Stokes-Dirac structure can be extended to an externally supplied distributed energy besides an energy exchange through the boundary. First, we show that any disturbance can be decomposed into a boundary energy structure and a distributed energy structure. Next, the system representation is given by the decomposed structures. Finally, two examples are presented.

Multi-Input Multi-Output Integrated Ionic Polymer-Metal Composite for Energy Controls

This paper presents an integrated sensor/actuator device with multi-input and multi-output designed on the basis of a standard control representation called a distributed port-Hamiltonian system. The device is made from soft material called an ionic polymer-metal composite (IPMC). The IPMC consists of a base film of a polyelectrolyte gel and a double layer of plated metal electrodes. The electrodes of the experimental IPMC are sectioned, and it is implemented as a control system with four pairs of inputs/outputs. We stabilize the system, and detect changes in dynamics by using the control representation.

Distributed port hamiltonian formulation of flexible beams under large deformations

In this paper, a formulation of flexible beams under large deformations for distributed parameter port Hamiltonian systems is presented. This model is one example of systems that have complex energy variables. For such a model, a unified modeling method is introduced with multivariable representation. First, a Stokes-Dirac structure is related to the calculus of variations by using a jet bundle formalism. Next, the flexible beams model is represented as the port Hamiltonian system. Finally, the model is compared to a conventional model and two reduced models

Implicit Representation for Passivity-Based Boundary Controls

Abstract This paper derives a standard system representation for passivity-based boundary controls of Euler-Lagrange equations, called a distributed port-Lagrangian (DPL) system from implicit Lagrangian representations and the multi-symplectic instantaneous formalism. The DPL system is a local representation of implicit Lagrangian systems extended for field equations. First, we extend an induced Dirac structure to multi-symplectic instantaneous systems by defining a Stokes-Dirac differential and a field implicit Lagrangian system. Second, the DPL system is derived from the extended field implicit Lagrangian systems. Finally, we define passivity-based boundary controls based on a power balance equation of DPL systems.

Discretized Hamiltonian Systems with Distributed Energy Flows on Divisible Meshes

Abstract This paper discusses two extensions of the discretization of distributed port-Hamiltonian systems. One of them is the incorporating non-boundary integrable energy flows, called distributed energy structures. The other is the derivation of transformations of basis forms used for dividing and assembling of meshes.

Topological geometry and control for distributed port-Hamiltonian systems with non-integrable structures

This paper discusses topological geometrical aspects and a control strategy for a distributed port-Hamiltonian system with a non-integrable structure called a distributed energy structure. First, we show a geometrical structure of port variables determined by differential forms. Next, we state the necessary condition for regarding the distributed energy structure as a boundary energy structure which is boundary integrable. From these results, we define the fundamental form that generates the distributed port-Hamiltonian system with distributed energy structures in a variational problem. Finally, we present a new concept of boundary controls for the distributed port-Hamiltonian system with distributed energy structures in space-time coordinates.

Field port-Lagrangian systems with degenerate Lagrangian and external forces

The relation between a port-representation and an infinite-dimensional Euler-Lagrange equation has previously been studied before by the authors. The formal form is called a field port-Lagrangian system. However, this system was considered under the condition that the Lagrangian was regular and the case of a degenerate Lagrangian was not explicitly shown. This paper presents a more general framework for the field port-Lagrangian system from the viewpoint of the treatment of degenerate Lagrangian and external forces.