Removing the algebraic loops of a bond graph model

International Journal of Control

2017

Closed loop control systems are designed for Linear Time-Invariant (LTI) controllable and observable systems modelled by bond graph. Cascade and feedback interconnections of bond graph models are considered and are realized through active (signal) 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 pseudojunction structures. These structures are build by adding parasitic elements to the bond graph models which assure that each storage element is connected to a dissipative element 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 multiportcoupled dissipative fields. These structures are called pseudo due to the structural properties of power conservation not being satisfied in the outer structures. The multiport-coupled dissipative fields highlight energy properties like passivity. These properties are useful for control design. In both interconnections, junction structures and multiport-coupled dissipative fields for the controllers are proposed and passivity is guaranteed for the closed loop systems assuring robust stability. The pseudo-junction structure for the cascade interconnection is applied to the structural representation of the closed loop transfer functions, in a one-degree of freedom feedback configuration, when a controller from the parametrisation of all stabilizing controllers is applied to a given nominal plant. Applications are given when the plant and the controller are described by state-space realizations, in this case parasitic elements are not added. Moreover, the feedback interconnection is used and the controller is tuned getting necessary and sufficient stability conditions based on the characteristic polynomial of the closed loop transfer function, solving a pole-placement problem and achieving zero-stationary state error.

Section: Background and Problem Statementsupporting

confidence: 87%

Section: Background and Problem Statementmentioning

confidence: 99%

Section: Ideal Plant and Controller Described By State-space Realizatmentioning

confidence: 99%

Section: Ideal Plant and Controller Described By State-space Realizatmentioning

confidence: 99%

Section: Ideal Plant and Controller Described By State-space Realizatmentioning

confidence: 99%

See 3 more Smart Citations

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

International Journal of Control

2017

Passivity analysis and control of nonlinear systems modelled by bond graphs

International Journal of Control

2022

Recent results on the passivity analysis and control of physical systems, based on the balance of dissipated and internally generated energy, are generalized 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 non-linear 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 condition for the passivity of the closed-loop system.

A bond graph pseudo-junction structure for non-linear non-conservative systems

2016 UKACC 11th International Conference on Control (CONTROL)

2016

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 pseudojunction structure 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.