A Bond Graph Pseudo-Junction Structure for Non-Linear Non-conservative Systems

Bond graph (BG) models are widely used to display various fields of a physical system and their interconnection. In this paper, a BG pseudo-junction structure for non-linear and non-conservative systems is proposed. This BG pseudojunctionstructure has an inner structure that satisfies energy conservation properties and a multiport-coupled dissipative field that determines the physical realisability of the system. Properties of the dissipative field like passivity are highlighted by the proposed BG pseudo-junction structure. The results are illustrated through examples

Passivity analysis and control of nonlinear systems modelled by bond graphs

Recent results on the passivity analysis and control of physical systems, based on the balance of dissipated and internally generated energy, are generalised to nonlinear systems represented by bond graphs. For linear systems, the internally generated energy associated with modulated sources can be coupled with the dissipative field, so that if external energy sources are excluded, then the system is passive (or dissipative) if the resulting composite multiport field is passive. Such a result for linear systems was previously conveniently expressed in terms of a characteristic matrix being positive semi-definite. Parasitic elements of previous works are no longer required, which allows working on the original bond graph of lower dimension than the augmented bond graph and for no-linear systems avoid inverting the dissipative nonlinear constitutive relations. For nonlinear systems, passivity is now considered through the explicit difference between the dissipated and the internally generated energy. If this energy difference is positive, the system is passive. For control systems, the current work proposes that the controller is designed to have a structure similar to the plant (linear or nonlinear), and its parameters are chosen to assure that in closed-loop the difference between the dissipated and the internally generated energy is positive. In particular, the control parameters can be chosen to assign a desired dissipated energy or to cancel by feedback the internally generated energy and to add damping, therefore achieving sufficient conditions for the passivity of the closed-loop system

Passivity analysis of linear physical systems with internal energy sources modelled by bond graphs

Integrated dynamic systems such as mechatronic or control systems generally contain passive elements and internal energy sources that are appropriately modulated to perform the desired dynamic actions. The overall passivity of suchsystems is a useful property that relates to the stability and the safety of the system, in the sense that the maximum net amount of energy that the system can impart to the environment is limited by its initial state. In this paper, conditions under which a physical system containing internal modulated sources is globally passive are investigated using bond graph modelling techniques. For the class of systems under consideration, bond graph models include power bonds and active (signals) bonds modulating embedded energy sources, so that the continuity of power (or energy conservation) in the junction structure is not satisfied. For the purpose of the analysis, a so-called bond graph pseudo junction structure is proposed as an alternative representation for Linear Time-Invariant (LTI) bond graph models with internal modulated sources. The pseudo junction structure highlights the existence of a multiport coupled resistive field involving the modulation gains of the internal sources and the parameters of dissipative elements, therefore implicitly realising the balance of internal energy generation and dissipation. Moreover, it can be regarded as consisting of an inner structure which satisfies the continuity of power, and an outer structure in which a power scaling is performed in relation with the dissipative field. The associated multiport coupled resistive field constitutive equations can then be used to determine the passivity property of the overall system. The paper focuses on systems interconnected in cascade (with no loading effect) or in closed-loop configurations which are common in control systems

Passivity-based control of linear time-invariant systems modelled by bond graph

Closed-loop control systems are designed for linear time-invariant (LTI) controllable and observable systems modelled by bond graph (BG). Cascade and feedback interconnections of BG models are realised through active bonds with no loading effect. The use of active bonds may lead to non-conservation of energy and the overall system is modelled by proposed pseudo-junction structures. These structures are build by adding parasitic elements to the BG models and the overall system may become singularly perturbed. The structures for these interconnections can be seen as consisting of inner structures that satisfy energy conservation properties and outer structures including multiport-coupled dissipative fields. These fields highlight energy properties like passivity that are useful for control design. In both interconnections, junction structures and dissipative fields for the controllers are proposed, and passivity is guaranteed for the closed-loop systems assuring robust stability. The cascade interconnection is applied to the structural representation of closed-loop transfer functions, when a stabilising controller is applied to a given nominal plant. Applications are given when the plant and the controller are described by state-space realisations. The feedback interconnection is used getting necessary and sufficient stability conditions based on the closed-loop characteristic polynomial, solving a pole-placement problem and achieving zero-stationary state error.</p

Development of a cardiopulmonary mathematical model incorporating a baro-chemoreceptor reflex control system

This article describes the development of a comprehensive mathematical model of the human cardiopulmonary system that combines the respiratory and cardiovascular systems and their associated autonomous nervous control actions. The model is structured to allow the complex interactions between the two systems and the responses of the combined system to be predicted under different physiological conditions. The cardiovascular system model contains 13 compartments, including the heart chambers operating as a pump and the blood vessels represented as distensible tubes configured in a serial and parallel arrangement. The accurate representation of the hemodynamics in the system and the good fit to published pressure and flow waveforms gave confidence in the modelling approach adopted for the cardiovascular system prior to the incorporation of the baroreflex control and the respiratory models. An improved baroreceptor reflex model is developed in this research, incorporating afferent, central and efferent compartments. A sigmoid function is included in the efferent compartment to produce sympathetic and parasympathetic nerve outflow to the effector sites. The baroreflex action is modelled using physiological data, its interaction with the chemoreflex control is explained and the simulation results presented show the ability of the model to predict the static and dynamic hemodynamic responses to environmental disturbances. A previously published respiratory model that includes the mechanics of breathing, gas exchange process and the regulation of the system is then combined with the cardiovascular model to form the cardiopulmonary model. Through comparison with published data, the cardiopulmonary model with the baro–chemoreflex control is validated during hypoxia and hypercapnia. The percentage difference between the predicted and measured changes in the heart rates and the mean arterial pressures are within 3% in both cases. The total peripheral resistance correlates well for hypoxia but is less good for hypercapnia, where the predicted change from normal condition is around 7% compared with a measured change of 23%. An example showing the application of the proposed model in sport science is also included. </jats:p

Bond graph-based filtered inversion of multivariable physical systems

In a variety of fields, system inversion is often required in order to determine inputs from measured or for desired outputs. However, inverse systems are often non-proper in the sense that they require differentiators in their realization. This leads to numerical difficulties associated with the computer implementation of their mathematical models. To overcome these problems, approximate inversion (also referred to as filtered inversion) is proposed for systems modelled by bond graphs. Generic configurations of right and left filtered inverse bond graph models are proposed with dynamic structural conditions on the filters so that the resulting composite bond graph represents a proper system suitable for effective numerical implementation. </jats:p

A Bond Graph Pseudo-Junction Structure for Non-Linear Non-conservative Systems

Bond graph (BG) models are widely used to display various fields of a physical system and their interconnection. In this paper, a BG pseudo-junction structure for non-linear and non-conservative systems is proposed. This BG pseudojunctionstructure has an inner structure that satisfies energy conservation properties and a multiport-coupled dissipative field that determines the physical realisability of the system. Properties of the dissipative field like passivity are highlighted by the proposed BG pseudo-junction structure. The results are illustrated through examples

Passivity analysis of linear physical systems with internal energy sources modelled by bond graphs

Integrated dynamic systems such as mechatronic or control systems generally contain passive elements and internal energy sources that are appropriately modulated to perform the desired dynamic actions. The overall passivity of such systems is a useful property that relates to the stability and the safety of the system, in the sense that the maximum net amount of energy that the system can impart to the environment is limited by its initial state. In this paper, conditions under which a physical system containing internal modulated sources is globally passive are investigated using bond graph modelling techniques. For the class of systems under consideration, bond graph models include power bonds and active (signals) bonds modulating embedded energy sources, so that the continuity of power (or energy conservation) in the junction structure is not satisfied. For the purpose of the analysis, a so-called bond graph pseudo-junction structure is proposed as an alternative representation for linear time-invariant (LTI) bond graph models with internal modulated sources. The pseudo-junction structure highlights the existence of a multiport coupled resistive field involving the modulation gains of the internal sources and the parameters of dissipative elements, therefore implicitly realizing the balance of internal energy generation and dissipation. Moreover, it can be regarded as consisting of an inner structure which satisfies the continuity of power, and an outer structure in which a power scaling is performed in relation with the dissipative field. The associated multiport coupled resistive field constitutive equations can then be used to determine the passivity property of the overall system. The paper focuses on systems interconnected in cascade (with no loading effect) or in closed-loop configurations which are common in control systems. </jats:p

Passivity-based control of linear time-invariant systems modelled by bond graph

Closed-loop control systems are designed for linear time-invariant (LTI) controllable and observable systems modelled by bond graph (BG). Cascade and feedback interconnections of BG models are realised through active bonds with no loading effect. The use of active bonds may lead to non-conservation of energy and the overall system is modelled by proposed pseudo-junction structures. These structures are build by adding parasitic elements to the BG models and the overall system may become singularly perturbed. The structures for these interconnections can be seen as consisting of inner structures that satisfy energy conservation properties and outer structures including multiport-coupled dissipative fields. These fields highlight energy properties like passivity that are useful for control design. In both interconnections, junction structures and dissipative fields for the controllers are proposed, and passivity is guaranteed for the closed-loop systems assuring robust stability. The cascade interconnection is applied to the structural representation of closed-loop transfer functions, when a stabilising controller is applied to a given nominal plant. Applications are given when the plant and the controller are described by state-space realisations. The feedback interconnection is used getting necessary and sufficient stability conditions based on the closed-loop characteristic polynomial, solving a pole-placement problem and achieving zero-stationary state error.</p

Physical interpretation of inverse dynamics using bicausal bond graphs

A physical interpretation of the inverse dynamics of linear and nonlinear systems is given in terms of the bond graph of the inverse system. It is argued that this interpretation yields physical insight to guide the control engineer. Examples are drawn from both robotic and process systems