### Abstract

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 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 multiport-coupled 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 parameterisation 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.

Language | English |
---|---|

Pages | 420-436 |

Number of pages | 17 |

Journal | International Journal of Control |

Volume | 91 |

Issue number | 2 |

Early online date | 23 Feb 2017 |

DOIs | |

Status | Published - 2018 |

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### Cite this

**Passivity-based control of linear time-invariant systems modelled by bond graph.** / Galindo, R.; Ngwompo, R. F.

Research output: Contribution to journal › Article

*International Journal of Control*, vol. 91, no. 2, pp. 420-436. https://doi.org/10.1080/00207179.2017.1283062

}

TY - JOUR

T1 - Passivity-based control of linear time-invariant systems modelled by bond graph

AU - Galindo, R.

AU - Ngwompo, R. F.

PY - 2018

Y1 - 2018

N2 - 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 activebonds 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 bond graph models which assure that each storage element is connected to a dissipative element and the overall systemmay 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 structures are called pseudo due to the structural properties of powerconservation 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 parameterisation 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.

AB - 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 activebonds 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 bond graph models which assure that each storage element is connected to a dissipative element and the overall systemmay 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 structures are called pseudo due to the structural properties of powerconservation 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 parameterisation 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.

UR - http://dx.doi.org/10.1080/00207179.2017.1283062

U2 - 10.1080/00207179.2017.1283062

DO - 10.1080/00207179.2017.1283062

M3 - Article

VL - 91

SP - 420

EP - 436

JO - International Journal of Control

T2 - International Journal of Control

JF - International Journal of Control

SN - 0020-7179

IS - 2

ER -