Bond Graph Domain Research Articles

Reactive Power Compensation in Distribution Systems Through the DSTATCOM Integration Based on the Bond Graph Domain

In this paper, the distribution static compensator model based on the bond graph (BG) domain is presented. The methodology is applied to reactive power compensation in distribution systems where a traditional phase lock loop for sensing the AC grid frequency is not needed. The control law is developed using the inverse BG model, which is extracted using the bi-causality concept. In this way, it is possible to perform the distribution system analysis completely in the BG domain. This means that the graphical model is inverted by obtaining the open-loop control law structure, and then the close loop is formulated. The balanced and unbalance conditions are analyzed, generating a control structure that is robust and efficient. The efficacy of the proposed methodology is shown through: partial and complete system simulations in MATLAB/Simulink® (MATLAB r2015b, Natick, Massachusetts, 01760, USA), as well as experimental laboratory tests. Such tests use: the rapid control prototyping concept and the real-time simulator Opal-RT Technologies® (Montreal, QC, Canada).

Bond graph approach for port-controlled Hamiltonian modeling for SST

Energy-based modeling is often very appropriate for physical system modeling for development and analysis of multi domain dynamic system models. One such tool for modelling of system is bond graph (BG), which allows to model complex system, with clear interconnection rules and preserving the physical structure of the system. In various engineering system, operation is carried out on various time scale. One such area of generic system is microgrid, where multidisciplinary microgrid components operating on various time scales. In such hybrid system, flows and efforts comprise a very good choice of variables to link components for system stability and performance analysis. Since components are typically connected through various power electronics devices, mathematical modeling capable of capturing high frequency behavior is of utmost concern in stability analysis. Solid state transformer (SST) is one such device playing a key role in bi-directional power flow between the grid and various renewable sources. This paper proposes the use of the BG approach to recognize the energy representation of the microgrid in port-Hamiltonian form by looking at the energy transformation aspects of microgrid components. The port-controlled Hamiltonian systems (PCHS) are the mathematical description of bond graphs which allows integration of subsystems of hybrid microgrid using energy as the linking concept. To illustrate the utility of BG in hybrid systems, basic PI controller is implemented. The aim of the paper is to show how to model complex systems in bond graph domain.

Generalized controlled switched bond graph junctions

This article presents two dual-controlled switched bond graph structures called generalized switched junction structures. These structures can represent all the interconnections enforced by commutations involving bond graph elements around standard 0- and 1-junctions. Moreover, pre-existing multiport switched bond graph formalisms like controlled junctions and switched power junctions can be represented as particular configurations of generalized switched junction structures. The generalized switched junction structures incorporate some algebraic constraints into their equation sets, which in the bond graph domain can be represented with residual sinks, in order to make them able to keep fixed the causality assignment even under ideal switching (zero transition time switching), as a convenient tool for simulation purposes. However, just performing some minor modifications on their internal implementation using basic bond graph components, the generalized switched junction structure can also be used to model commutations relaxing the ideal switching hypothesis in favor of the approximate one which introduces some parasitic components, which is frequently used as a means to avoid possibly appearing causality changes. The generalized switched junction structure can be implemented in a compact way at high level using the equation sets defining their behavior, or in detailed way using elements out of the standard set of bond graph components.

Bond-graph-based controller design for the quadruple-tank process

The quadruple-tank process has been proposed as a benchmark for multivariable control system design. This paper addresses the design in the bond-graph domain of a robust controller having the volumetric flows of two pumps as manipulated variables and the level of the two lower tanks as the regulated outputs. The basic control objectives are expressed in terms of desired closed-loop energy and power-dissipation functions and captured in the bond-graph domain by means of a so-called target bond-graph. A basic controller design performed via bond-graph prototyping yields a primary control law which is further robustified against parameter uncertainties, measurement deviations and faults using the diagnostic bond-graph concept. This results in an additional closed-loop consisting of a PI-law which is represented by a physically meaningful bond-graph subsystem. The design methodology is first developed on a simpler two-tank SISO-control problem and then straightforwardly extended to the multivariable problem with the help of some causal manipulations on the four-tank bond-graph model.

Switchable structured bond: A bond graph device for modeling power coupling/decoupling of physical systems

This paper presents a controlled Bond Graph interconnection structure named Switchable Structured Bond, or SS-Bond for short, basically intended for modeling and simulation of ideal switching phenomena (zero transition time) with fixed causality. Serving to model the presence or absence of a power preserving connection between two power ports, these new structures are inspired in the idea yielding the switchable bond (or SB) formalism, but embody some features correcting the shortcomings of the latter. Indeed, when both power ports are connected, both the SB and the SS-Bond behave like a standard power bond, but when the power connection is absent, the SS-Bond fully captures the possible states of the adjacent power ports, unlike the SB, which in many cases leaves undefined the situation of these ports. As SS-Bonds are originally defined to model ideal switching, these possible states are zero-flow or zero-effort for each of the disconnected power ports. These four situations, together with the normally connected state, define the five possible switching modes of an SS-Bond.The SS-Bonds can be internally represented with standard bond graph elements. To keep fixed the causality assignment even under switching, some algebraic constraints are added to the equation set of the switched structure, which in the Bond Graph domain can be represented with residual sinks. A minor modification on the internal implementation of the SS-Bonds allows the formalism for commutation modeling with the non-ideal approach consisting in adding parasitic components to avoid causality changes. Besides some models of electric–electronic circuits, slip-stick friction in a simple mechanical system and abrupt faults in a hydraulic two tank system are used to illustrate the new formalism and its performance in modeling and simulation.

Energy shaping, interconnection and damping assignment, and integral control in the bond graph domain

This paper presents a methodology to perform energy shaping and interconnection and damping assignment in the bond graph domain, and addresses a new result on integral action control which improves the robustness of these passivity based control methods, which were first introduced on the port-controlled Hamiltonian systems with dissipation formalism. The methods perform expressing the desired closed-loop energy, interconnection and damping properties on a so-called target bond graph, which is built as follows on the plant bond graph: (i) adding virtual storage elements enforces a minimum on the target bond graph energy at a prespecified stable closed-loop equilibrium state, (ii) changing the R -field and its interconnection with the rest of the graph assigns a new dissipation function, and (iii) suitably inserting of power conserving elements (bonds and other structural BG-elements) among junctions yields the desired power conserving interconnection structure. The control law is then determined developing physically based heuristics and formal techniques on the target and plant bond graphs, which deliver a set of partial differential equations to be solved. The method to achieve integral control consists in adding to the target bond graph virtual elements representing the integral action and a change of variables, and then computing the integral control law with standard BG equation-reading procedures. These BG heuristics and prototyping allow to provide integral action on outputs of relative degree greater than one, a contribution of this work not previously available in the literature. This shows that the physical properties of bond graphs are beneficial not only to expediently perform methods contributed by control theory, but also to derive new theoretical results.

Non-linear control of a series direct current motor via flatness and decomposition in the bond graph domain

A bond graph (BG) based methodology for non-linear control system synthesis is presented through its application to a speed-tracking problem stated on a series direct current motor. After a global flatness analysis of the motor BG model, a two-loop cascade control structure is decided and developed on the basis of a physical system decomposition in electrical, mechanical, and coupling submodels. Each loop of the cascade tracks a reference for a flat output that is local to a subsystem of the decomposition. Bond graph techniques are given for the three main components of the design methodology: system decomposition, flatness analysis, and tracking controller design. Theoretical and practical properties of the resulting control system are discussed, and its performance is demonstrated through simulation experiments. The methodology is applicable to the broader class of non-linear BG models where input-output system inversion is well defined.