Disturbance rejection in general heterodirectional 1-D linear hyperbolic systems using collocated sensing and control

Anfinsen, Henrik; Aamo, Ole Morten

doi:10.1016/j.automatica.2016.10.027

Cited by 48 publications

(11 citation statements)

References 23 publications

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“…By assuming anticollocated measurements a systematic method is proposed for the corresponding PDE-ODE observer design. This extends recent results concerning observers for general heterodirectional PDE-ODE cascades with constant coefficients in Anfinsen and Aamo (2017) and in Deutscher (2017b) for the spatiallyvarying case. For the existence of the corresponding PDE-ODE observers and thus of the resulting observer-based compensator simple conditions are presented in terms of the transfer behaviour w.r.t.…”

Section: Introductionsupporting

confidence: 87%

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Output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients

Deutscher

Gehring

Kern

2018

International Journal of Control

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This paper presents a backstepping solution for the output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients. Thereby, the coupling in the PDE is in-domain and at the uncontrolled boundary, whereby the ODE is coupled with the latter boundary. For the state feedback design a two-step backstepping approach is developed, that yields the conventional kernel equations and additional decoupling equations of simple form. The latter can be traced back to simple Volterra integral equations of the second kind, which are directly solvable with a successive approximation. In order to implement the state feedback controller, the design of observers for the ODE-PDE systems in question is considered, whereby anticollocated measurements are assumed. Simple conditions for the existence of the resulting observer-based compensator are formulated, that can be evaluated in terms of the plant transfer behaviour. The resulting systematic compensator design is illustrated for a 4 × 4 heterodirectional hyperbolic system coupled with a third order ODE modelling a dynamic boundary condition.

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Section: Introductionsupporting

confidence: 87%

“…Hence, they constitute additional design parameters that may be utilized to shape the feedback gains K ξ , K x (z) and thus the transients of the closed-loop dynamics. Further details for solving the kernel BVP (A6) and (A7) with the method of successive approximations can be found in Anfinsen and Aamo (2017); Cor13 (2013).…”

Section: Discussionmentioning

confidence: 99%

Output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients

Deutscher

Gehring

Kern

2018

International Journal of Control

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“…Backstepping design of output‐feedback regulators that achieve finite time regulation for boundary controlled linear 2×2 hyperbolic systems was presented in the work of Deutscher . Moreover, stabilization of n +1 coupled first‐order hyperbolic coupled linear PDEs was considered in the work of Di Meglio et al Control problem of a first‐order hyperbolic linear PDE general system where the number of PDEs in either direction is arbitrary was solved in the work of Hu et al Disturbance rejection and parameter estimation for this general hyperbolic coupled linear PDE systems were also presented in the work of Anfinsen et al A backstepping solution to the output regulation problem for general linear heterodirectional hyperbolic systems with disturbances and spatially varying coefficients was presented in the work of Deutscher …”

Section: Introductionmentioning

confidence: 99%

Control of a 2 × 2 coupled linear hyperbolic system sandwiched between 2 ODEs

Wang

Krstić

2018

Intl J Robust & Nonlinear

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Summary Motivated by an engineering application in cable mining elevators, we address a new problem on stabilization of 2×2 coupled linear first‐order hyperbolic PDEs sandwiched between 2 ODEs. A novel methology combining PDE backstepping and ODE backstepping is proposed to derive a state‐feedback controller without high differential terms. The well‐posedness and invertibility properties of the PDE backstepping transformation are proved. All states, including coupled linear hyperbolic PDEs and 2 ODEs, are included in the closed‐loop exponential stability analysis. Moreover, boundedness and exponential convergence of the designed controller are proved. The performance is investigated via numerical simulation.

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“…Proof. After swapping positions of arguments as B.9-B.10 in [2], i.e., changing the domain D 1 to D, (158)-( 164) has the analogous form with kernels F(x, y), N(x, y), λ (y) (73)-(79). Following the steps in the proof of Lemma 1, including introducing the extended domain D 0 and adding the additional artificial boundary condition, Lemma 3 can be obtained.…”

Section: Observer Backtepping Designmentioning

confidence: 99%

“…For a more general coupled linear transport PDE system where the number of PDEs in either direction is arbitrary, the boundary stabilization problem was first addressed in [17] by backstepping, which leads to a systematic framework for the backstepping-based control of this type of system. Moreover, adaptive control with unknown system parameters or disturbance rejection for external peri-odic disturbances in coupled heterodirectional transport PDEs, have appeared in [3], [4] and [11], [12], [2], [1] respectively. Considering the attached massive payload at the bottom of the cable, boundary control of coupled linear transport PDEs connected with an ODE at the uncontrolled boundary can also be found in [23], [35], [13].…”

Section: Introductionmentioning

confidence: 99%

Vibration Suppression for Coupled Wave PDEs in Deep-Sea Construction

Wang

Krstić

2019

Preprint

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A deep-sea construction vessel is used to instal underwater parts of an off-shore oil drilling platform at the designated locations on the seafloor. By using extended Hamilton's principle, a nonlinear PDE system governing the laterallongitudinal coupled vibration dynamics of the deep-sea construction vessel consisting of a time-varying-length cable with an attached item is derived, and it is linearized at the steady state generating a linear PDE model, which is extended to a more general system including two coupled wave PDEs connected with two interacting ODEs at the uncontrolled boundary. Through a preliminary transformation, an equivalent reformulated plant is generated as a 4 × 4 coupled heterodirectional hyperbolic PDE-ODE system characterized by spatially-varying coefficients on a time-varying domain. To stabilize such a system, an observerbased output-feedback control design is proposed, where the measurements are only placed at the actuated boundary of the PDE, namely, at the platform at the sea surface. The exponential stability of the closed-loop system, boundedness and exponential convergence of the control inputs, are proved via Lyapunov analysis. The obtained theoretical result is tested on a nonlinear model with ocean disturbances, even though the design is developed in the absence of such real-world effects.

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Disturbance rejection in general heterodirectional 1-D linear hyperbolic systems using collocated sensing and control

Cited by 48 publications

References 23 publications

Output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients

Output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients

Control of a 2 × 2 coupled linear hyperbolic system sandwiched between 2 ODEs

Vibration Suppression for Coupled Wave PDEs in Deep-Sea Construction

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