Stabilization of food-chain systems using a port-controlled Hamiltonian description

Astolfi, Alessandro; Bastin, G.; Rodríguez, H.

doi:10.1109/acc.2000.878579

Cited by 24 publications

(19 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This set of partial differential equations can be related to the ones used in the context of port-controlled Hamiltonian passivity-based control given for Lotka-Volterra systems in [30,29]. A particular solution of the system of nonlinear PDEs is…”

Section: Periodic Orbit Stabilization Of the Lotka-volterra Systemmentioning

confidence: 99%

Construction of control Lyapunov functions for damping stabilization of control affine systems

Hudon

Guay

2013

Systems & Control Letters

View full text Add to dashboard Cite

Section: Periodic Orbit Stabilization Of the Lotka-volterra Systemmentioning

confidence: 99%

Construction of control Lyapunov functions for damping stabilization of control affine systems

Hudon

Guay

2013

Systems & Control Letters

View full text Add to dashboard Cite

“…Spong, Gomez-Estern, et Blankenstein (2002)), magnetic levitation systems (Rodrıguez, Ortega, et Mareels (2000); Rodrıguez, Siguerdidjane, et Ortega (2000a)), mass balance systems (Ortega, Astolfi, Bastin, et Rodrıguez (2000)), electrical machines (Batlle, Doria-Cerezo, et Ortega (2005); Petrovic, Ortega, et Stankovic (2001)), power converters (Rodrıguez, Ortega, Escobar, et Barabanov (2000)). For an in-depth review of IDA-PBC the reader is referred to (Ortega et Garcıa-Canseco (2004)).…”

Section: International Journal Of Control Paper1˙aoutcormentioning

confidence: 99%

Robustness enhancement of IDA-PBC controller in stabilising the inertia wheel inverted pendulum: theory and real-time experiments

Haddad

Chemori

Belghith

2017

International Journal of Control

View full text Add to dashboard Cite

Improving the robustness, vis-à-vis matched input disturbances of IDA-PBC (Interconnection Damping Assignment, Passivity Based Control) for a class of underactuated mechanical systems is addressed in this paper. The characterized class of systems is the one for which IDA-PBC yields a smooth stabilizing controller. Our main contribution consists in combining the so-called IDA-PBC controller with an adaptive control technique. Some sufficient stability conditions on matched input disturbances are given. The comparison of the stability robustness between the classical controller IDA-PBC and the proposed one is then provided. As illustration we propose to revisit the application of IDA-PBC controller to the Inertia Wheel Inverted Pendulum (IWIP) in the presence of matched disturbances. Simulation and real-time experimental results are presented as validations of the theoretical results.

show abstract

“…Therefore, by (20) and recalling the arguments in the proof of Proposition 2, the closed-loop system (1)- (19) can be written asẋ …”

Section: Extended Port-controlled Hamiltonian Systemsmentioning

confidence: 99%

“…Consider the normalized third order food-chain system from [13] for which an IDA-PBC controller has been designed in [20]. In this food-chain system the variable x i for i = 1, 2, 3 represents the population of the i-th species involved in the system.…”

Section: B Third Order Food-chain System 1) Modelmentioning

confidence: 99%

“…It has been shown in [20] that the matching equation PDE cannot be solved when J d = J and with a D d > 0 because the distribution spanned by the vector fields defined by the column vectors obtained from the first 2 rows of J(x) − D(x) is not involutive. To overcome this limitation the damping of the closed-loop system is modified to be D d = diag(0, 0, x 3 ) which is clearly positive semidefinite.…”

Section: ) Controller Designmentioning

confidence: 99%

See 1 more Smart Citation

Constructive Interconnection and Damping Assignment for Port-Controlled Hamiltonian Systems

Nunna

Sassano

Astolfi

2015

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

Abstract-The Interconnection and Damping AssignmentPassivity-Based Control (IDA-PBC) problem for port-controlled Hamiltonian systems is revisited. We propose a methodology that exploits the novel notion of algebraic solution of the socalled matching equation. This notion is instrumental for the construction of an energy function, defined on an extended statespace, which does not rely upon the solution of any partial differential equation. This yields, differently from the classical solution, a dynamic state feedback that stabilizes a desired equilibrium point. In addition, conditions that allow to preserve the port-controlled Hamiltonian structure in the extended closedloop system are provided. The theory is validated on two physical systems: the magnetic levitated ball and a third order food-chain system. A dynamic control law is constructed for both these systems by assigning a damping factor that cannot be assigned by the classical IDA-PBC.

show abstract

Stabilization of food-chain systems using a port-controlled Hamiltonian description

Cited by 24 publications

References 3 publications

Construction of control Lyapunov functions for damping stabilization of control affine systems

Construction of control Lyapunov functions for damping stabilization of control affine systems

Robustness enhancement of IDA-PBC controller in stabilising the inertia wheel inverted pendulum: theory and real-time experiments

Constructive Interconnection and Damping Assignment for Port-Controlled Hamiltonian Systems

Contact Info

Product

Resources

About