Boundary observer design for hyperbolic PDE–ODE cascade systems

Hasan, Agus; Aamo, Ole Morten; Krstić, Miroslav

doi:10.1016/j.automatica.2016.01.058

Cited by 137 publications

(66 citation statements)

References 37 publications

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“…Furthermore, the feedback gain k l and k derived based on (24) can be used in (23) as well to obtain locally exponentially stable error dynamics. 19,22 The backstepping-based observer design for linear hyperbolic systems like (24) is well described in literature. [18][19][20] However, the calculation of the backstepping kernels, which is unavoidable for an actual implementation, is mainly shown for systems with constant parameters.…”

Section: Backstepping-based Observer Designmentioning

confidence: 99%

“…which combines the transformation to characteristic form 20,22 with an additional transformation 19,28 to get rid of source terms linear in w + and w − . † This gives (24) in characteristic form as…”

Section: Backstepping-based Observer Designmentioning

confidence: 99%

“…Contrary to the early-lumping designs, the late-lumping approaches [18][19][20][21][22] also systematically cover spatially varying parameters. Unfortunately, all examined test cases in the cited references only consider constant parameter systems.…”

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confidence: 99%

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Early‐ and late‐lumping observer designs for long hydraulic pipelines: Application to pumped‐storage power plants

Marko

Mennemann

Jadachowski

et al. 2018

Intl J Robust & Nonlinear

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Pumped-storage power plants typically feature very long hydraulic pipelines, which can be modeled by a set of partial differential equations. The estimation of the pressure and volumetric flow along the pipes is an important task for the operation of such a plant. Therefore, this work compares different earlyand late-lumping-based observer designs for this system. Two late-lumping observers, ie, a Lyapunov-based design and an observer using the backstepping design method, are examined. The Lyapunov-based approach uses a simple boundary correction to stabilize the estimation error dynamics. In contrast, the backstepping-based approach allows utilizing additional in-domain correction to obtain a faster rate of convergence. For the implementation of these distributed-parameter observers, the spectral element method as a flexible and computationally efficient discretization method is introduced. It is shown that, compared with that of the Lyapunov-based design, the discretization of the backstepping-based design requires additional spatial grid points for the accurate approximation of its feedback gains. For the early-lumping approach, the spectral element method is used to approximate the model equations by a system of differential equations. Based on this approximation, an extended Kalman filter is designed. All observer designs are validated and compared for a representative test case. KEYWORDS distributed-parameter system, hydraulic pipeline, late lumping, spectral element method, state estimation INTRODUCTIONNowadays, the amount of electrical energy produced by renewable sources like wind turbines or solar panels is steadily increasing. Despite all their positive properties, most of these energy sources have the major drawback of being highly volatile in comparison to conventional sources like coal or gas. In order to compensate for the differences between generation and load and, thus, to ensure grid stability, large-scale energy storage capabilities like pumped-storage power plants are necessary. 1,2 A typical pumped-storage power plant comprises several turbines (Francis or Pelton type), which are connected to an upper and a lower reservoir by long hydraulic pipelines. The control of pumped-storage power plants, with the aim to react as fast as possible to load fluctuations in the electric grid while respecting the physical limits of the system at Int J Robust Nonlinear Control. 2018;28:2759-2779.wileyonlinelibrary.com/journal/rnc

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Section: Backstepping-based Observer Designmentioning

confidence: 99%

Section: Backstepping-based Observer Designmentioning

confidence: 99%

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Early‐ and late‐lumping observer designs for long hydraulic pipelines: Application to pumped‐storage power plants

Marko

Mennemann

Jadachowski

et al. 2018

Intl J Robust & Nonlinear

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“…For dynamic analysis, the flexible manipulator system is regarded as a distributed parameter system (DPS), which is mathematically represented by partial differential equations (PDEs) and ordinary differential equations (ODEs). Many remarkable achievements have been presented for the DPS in many areas, such as flexible marine risers, flexible manipulators, flexible strings, crane cables, flexible wings, moving strings, and moving belts …”

Section: Introductionmentioning

confidence: 99%

Dynamic modeling and vibration control for a nonlinear 3‐dimensional flexible manipulator

Liu

2018

Intl J Robust & Nonlinear

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Summary In this paper, the control design and stability analysis are presented for a 3‐dimensional flexible manipulator system with input disturbances. To provide an accurate and concise representation of the manipulator's dynamic behavior, the flexible manipulator is described by a distributed parameter system with a set of partial differential equations and ordinary differential equations. Boundary control laws with disturbance observers are proposed to regulate orientation and suppress elastic vibrations simultaneously. The closed‐loop stability is achieved through rigorous analysis without any simplification of the dynamics based on the Lyapunov direct method. Numerical simulations demonstrate the effectiveness of the proposed scheme.

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“…The estimated states and parameters are in turn used in a feedback control algorithm that automates the control input to maintain a desired state trajectory. Observer design for PDE-ODE cascade systems has been studied for many types of coupling such as an ODE and a diffusion PDE ( [7], [8], [9]), an ODE and a hyperbolic PDE ( [10], [11], [12]), and an ODE and a wave PDE ( [13], [14]). …”

Section: Introductionmentioning

confidence: 99%

State estimation for nonlinear hyperbolic PDE-ODE cascade systems

Hasan

Aamo

Krstić

2015

2015 10th Asian Control Conference (ASCC)

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This paper presents state estimation for a class of nonlinear hyperbolic PDE-ODE cascade systems. The observer is based on the backstepping method and relies only on a single boundary measurement. The observer consists of a copy of the plant plus output injection terms both in the PDEs and the ODEs. Furthermore, both sensing and actuation are located at the same boundary (collocated setup). The observer gains are computed analytically by solving Goursat-type PDEs in terms of modified Bessel functions of the first kind. A field-scale test experiment in a flow-loop test facilities is conducted by Statoil oil company to show the applicability of the observer.

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Boundary observer design for hyperbolic PDE–ODE cascade systems

Cited by 137 publications

References 37 publications

Early‐ and late‐lumping observer designs for long hydraulic pipelines: Application to pumped‐storage power plants

Early‐ and late‐lumping observer designs for long hydraulic pipelines: Application to pumped‐storage power plants

Dynamic modeling and vibration control for a nonlinear 3‐dimensional flexible manipulator

State estimation for nonlinear hyperbolic PDE-ODE cascade systems

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