Output-feedback control of an underactuated network of interconnected hyperbolic PDE–ODE systems

Redaud, Jeanne; Auriol, Jean; Niculescu, Silviu–Iulian

doi:10.1016/j.sysconle.2021.104984

Cited by 18 publications

(16 citation statements)

References 39 publications

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“…The proposed approach paves the way for future contributions on networks with actuation inside the graph structure. We believe that this approach could be combined with [14] to tackle a wider diversity of physical systems with an arbitrary number of PDEs or ODEs. It is also a milestone towards the stabilization of under-actuated systems.…”

Section: Discussionmentioning

confidence: 99%

“…This will simplify the analysis. Although there is now a cascade structure from the first subsystem to the second one, the stabilization problem is fundamentally different from the one studied in [14]. This structure difference would clearly appear when considering the natural extension of three interconnected subsystems for which the actuator would be located on the second subsystem.…”

Section: Structure Simplificationmentioning

confidence: 97%

“…For an interconnection of two scalar hyperbolic systems with boundary input (or output), there are only two possible locations for the actuator: at the end of the chain (a case that has already been solved in the literature) or between the two subsystems. The fact that the actuator is here located at the junction makes difficult the application of classical methods as the recursive methodology developed in [14]. More precisely, the re-circulation induced by the couplings between the two subsystems may create some unstable loops that prevent the stabilization.…”

Section: A System Under Considerationmentioning

confidence: 99%

“…This approach has been extended to a chain with an arbitrary number of subsystems in [10]. Other types of interconnected systems have also been considered [11]- [13], including, more recently, a chain of many interconnected PDE systems coupled at one end with an ODE [14].…”

Section: Introductionmentioning

confidence: 99%

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Stabilizing Output-Feedback Control Law for Hyperbolic Systems Using a Fredholm Transformation

Redaud

Auriol

Niculescu

2022

IEEE Trans. Automat. Contr.

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For most networked systems found in the literature, the actuated boundary is usually located at one end. In this paper, we first consider the stabilization of a chain of two interconnected subsystems, actuated at the in-between boundary. Each subsystem corresponds to coupled hyperbolic partial differential equations. Such in-domain actuation leads to higher complexity, and represents a significant difference with existing results.Then, starting from a classical controllability condition, we design a state feedback control law for the considered class of systems. The proposed approach is based on the backstepping methodology. However, to deal with the complex structure of the system, we use Fredholm integral transforms instead of classical Volterra transforms. We prove the invertibility of such transforms using an original operator framework. The well-posedness of the backstepping kernel equations defining the transformations is also shown with the same arguments. By using a similar procedure, we are then able to design a Luenberger-type observer. Finally, we use the state estimation in the stabilizing controller to obtain an output-feedback law, and some test cases complete the paper.

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Section: Discussionmentioning

confidence: 99%

Section: Structure Simplificationmentioning

confidence: 97%

Section: A System Under Considerationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stabilizing Output-Feedback Control Law for Hyperbolic Systems Using a Fredholm Transformation

Redaud

Auriol

Niculescu

2022

IEEE Trans. Automat. Contr.

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“…To reach our control objective, we use the recursive dynamics interconnection framework introduced in [6] and completed in [21] to design output-feedback controllers. In this approach, we consider each section of the drill pipe as an independent subsystem, for which we solve a stabilization and output tracking problem.…”

Section: Frameworkmentioning

confidence: 99%

Recursive dynamics interconnection framework applied to angular velocity control of drilling systems

Redaud

Auriol

Niculescu

2022

2022 American Control Conference (ACC)

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In this paper, we apply a recursive dynamics interconnection framework to achieve reliable angular velocity control of a multi-sectional drilling device with the bit offbottom. The proposed model describing the torsional motion of the drill string takes into account the Coulomb friction between the drill string and the borehole. It has been field validated. Compensating the effects of these Coulomb side forces is necessary to avoid stick-slip oscillations. More precisely, the torsional motion of each section of the drilling pipe is modeled by a wave equation (with some non-linear terms corresponding to the Coulomb friction), while the dynamics of the top-drive and Bottom Hole Assembly are modeled by ordinary differential equations. The reference trajectory tracking problem for the drill string is solved by considering each section independently. The Coulomb side forces are seen as disturbances acting on each section of the drill string. These disturbances do not depend on time, providing there is enough energy in the system (i.e., that we have overcome the static friction). We propose here a switching-mode controller: using first a classical PI controller (with poor performance), we break the static friction. Then, the disturbance terms that correspond to the Coulomb friction terms can be estimated and compensated. The trajectory tracking is guaranteed using a recursive control procedure. The performances of the controller are illustrated through simulations using various field scenarios.

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Predictive feedback boundary control of semilinear and quasilinear 2 × 2 hyperbolic PDE–ODE systems

2022

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Output-feedback control of an underactuated network of interconnected hyperbolic PDE–ODE systems

Cited by 18 publications

References 39 publications

Stabilizing Output-Feedback Control Law for Hyperbolic Systems Using a Fredholm Transformation

Stabilizing Output-Feedback Control Law for Hyperbolic Systems Using a Fredholm Transformation

Recursive dynamics interconnection framework applied to angular velocity control of drilling systems

Predictive feedback boundary control of semilinear and quasilinear 2 × 2 hyperbolic PDE–ODE systems

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