Safe PDE Backstepping QP Control with High Relative Degree CBFs: Stefan Model with Actuator Dynamics

Koga, Shumon; Krstić, Miroslav

doi:10.23919/acc53348.2022.9867781

Cited by 6 publications

(6 citation statements)

References 26 publications

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“…Indeed, considering the switching-mode strategy aforementioned (sending a sufficient amount of energy to break the static friction before stabilizing the system aroung the reference trajectory), we can guarantee that |ω(t)| > ω c (see [5] for more details) such that the d terms are constant. However, to guarantee that the transient satisfies the condition |ω(t)| > ω c , control Barrier Functions [18] may be of interest. Unlike simple control algorithms (as PID controllers), the recursive control law we design requires a real-time estimation of the distributed states all over the drill string, as well as a prediction of their future values.…”

Section: State Estimation and Predictionmentioning

confidence: 99%

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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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Section: State Estimation and Predictionmentioning

confidence: 99%

“…2) Estimation of the distributed states: Injecting ( 8)-( 9) into the time-delay equations ( 17)- (18), we obtain…”

Section: A Boundary State Estimationmentioning

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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“…Control Barrier Functions (CBFs) are introduced to render the equivalency between the forward invariance of a safe set satisfying the imposed constraints with the positivity of the CBFs. Followng [11], let h 1 (t), h 2 (t), h 3 (t), and h(x, t) be CBFs defined by…”

Section: Stefan Model and Constraintsmentioning

confidence: 99%

“…While most of the research in safe/constrained control has focused on the systems described by Ordinary Differential Equations (ODEs), a few recent works have been developing and analyzing the safety or state constraints in the systems described by Partial Differential Equations (PDEs), where the safety in the infinite-dimensional state needs to be satisfied, such as for distributed concentration [8], gas density [9], or the liquid level [10]. Our recent work [11] has incorporated the concept of CBF into the boundary control of a PDE system, the so-called "Stefan system" [12], [13], which is a representative model for the thermal melting process [14] and biological growth process [15]. We have designed the nonovershooting control [16] to achieve both safety and stabilization of the system around the setpoint, and also developed a CBF-QP safety filter for a given nominal control input.…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, the condition of the sampling schedule in [32] serves as the necessary condition for ensuring the required constraint in the Stefan system. While, such a necessary condition has not been clarified in the Stefan system with actuator dynamics considered in [11], which requires the methodology from high-relative-degree CBF for satisfying the state constraint.…”

Section: Introductionmentioning

confidence: 99%

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Event-Triggered Safe Stabilizing Boundary Control for the Stefan PDE System with Actuator Dynamics

Koga¹,

Demir²,

Krstić³

2022

Preprint

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This paper proposes an event-triggered boundary control for the safe stabilization of the Stefan PDE system with actuator dynamics. The control law is designed by applying Zero-Order Hold (ZOH) to the continuous-time safe stabilizing controller developed in our previous work. The event-triggering mechanism is then derived so that the imposed safety conditions associated with high order Control Barrier Function (CBF) are maintained and the stability of the closed-loop system is ensured. We prove that under the proposed event-triggering mechanism, the so-called "Zeno" behavior is always avoided, by showing the existence of the minimum dwell-time between two triggering times. The stability of the closed-loop system is proven by employing PDE backstepping method and Lyapunov analysis. The efficacy of the proposed method is demonstrated in numerical simulation.

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Safe Backstepping with Control Barrier Functions

Taylor

Ong

Molnár

et al. 2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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Complex control systems are often described in a layered fashion, represented as higher-order systems where the inputs appear after a chain of integrators. While Control Barrier Functions (CBFs) have proven to be powerful tools for safetycritical controller design of nonlinear systems, their application to higher-order systems adds complexity to the controller synthesis process-it necessitates dynamically extending the CBF to include higher order terms, which consequently modifies the safe set in complex ways. We propose an alternative approach for addressing safety of higher-order systems through Control Barrier Function Backstepping. Drawing inspiration from the method of Lyapunov backstepping, we provide a constructive framework for synthesizing safety-critical controllers and CBFs for higherorder systems from a top-level dynamics safety specification and controller design. Furthermore, we integrate the proposed method with Lyapunov backstepping, allowing the tasks of stability and safety to be expressed individually but achieved jointly. We demonstrate the efficacy of this approach in simulation.

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Safe PDE Backstepping QP Control with High Relative Degree CBFs: Stefan Model with Actuator Dynamics

Cited by 6 publications

References 26 publications

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

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

Event-Triggered Safe Stabilizing Boundary Control for the Stefan PDE System with Actuator Dynamics

Safe Backstepping with Control Barrier Functions

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