The spectral element method as an efficient tool for transient simulations of hydraulic systems

Mennemann, Jan-Frederik; Marko, Lukas; Schmidt, Jakob; Kemmetmüller, Wolfgang; Kugi, Andreas

doi:10.1016/j.apm.2017.10.010

Cited by 14 publications

(30 citation statements)

References 35 publications

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“…The discussions in the previous section together with the results of Mennemann et al 15,16 lead to the conclusion that utilizing the SEM to derive a spatially discretized model similar to (55) is meaningful. Thus, the discretized version of (10) results in…”

Section: Early-lumping Observer Designmentioning

confidence: 89%

“…By doing so, one combines the flexibility of a finite-element method with the high accuracy of SMs. [15][16][17] As stated by Mennemann et al, 16 the SEM works well as long as the solutions of the approximated hyperbolic systems remain sufficiently smooth. Since pumped-storage power plants are operated within quite conservative margins regarding the gradients of pressure and volumetric flow, it can be assumed that this smoothness condition is fulfilled.…”

Section: Backstepping-based Observer Designmentioning

confidence: 92%

“…This gives a total of J global continuous basis functions j , with j = 1, … , J. 15,16 Combining the basis functions in the vector…”

Section: Backstepping-based Observer Designmentioning

confidence: 99%

“…with the vectorsĥ andq containing the nodal weights of the corresponding approximations of the estimated states. Based on the Galerkin discretization method and the Legendre-Gauß-Lobatto quadrature, 17,32 these approximations can be utilized to formulate (13) in a spatially discretized form as a set of 2J ordinary differential equations, 15,16 ie,…”

Section: Backstepping-based Observer Designmentioning

confidence: 99%

“…In contrast, the global approximations used in SMs, which lead to computationally efficient discretizations, may be too inflexible to accurately describe pipe sections with spatially varying parameter values. In this work, the spectral element method (SEM [15][16][17] ) is used for spatial approximation to overcome these issues by combining the flexibility of finite-element methods with the efficiency of SMs.…”

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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: Early-lumping Observer Designmentioning

confidence: 89%

Section: Backstepping-based Observer Designmentioning

confidence: 92%

“…This gives a total of J global continuous basis functions j , with j = 1, … , J. 15,16 Combining the basis functions in the vector…”

Section: Backstepping-based Observer Designmentioning

confidence: 99%

Section: Backstepping-based Observer Designmentioning

confidence: 99%

mentioning

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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Optimal feedforward control of hydraulic drive systems with long pipelines

Pietschnig

Marko

Kemmetmüller

et al. 2019

Proc Appl Math and Mech

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Hydraulic drives are used in many technical systems, ranging from automotive and aerospace applications to industrial production systems. They provide high forces and torques at a compact design. The typical setup of hydraulic drive systems comprises a valve which controls a hydraulic cylinder or motor. In many practical applications, the valve is connected to the hydraulic cylinder via hydraulic pipelines, whose length can amount to several meters. Typically, the distributed-parameter characteristics of these pipelines is not considered in the controller design. For very fast operation scenarios, wave effects can be excited which may cause a significant reduction of the control accuracy or even lead to instability of the closed-loop system. In this paper, a model-based control strategy is proposed which allows to systematically account for long pipelines. One main element is the spatial discretization of the partial differential equations of the pipelines by means of the spectral elemental method (SEM), which yields a low-dimensional, but yet accurate model. Based on this model, an optimal feedforward control strategy is developed, which also enables to take into account actuator constraints. The resulting optimal control problem is efficiently solved on a moving horizon, resulting in a real-time capable moving horizon trajectory planning strategy. An observer is added to account for uncertain model parameters. The high potential of the proposed approach is demonstrated in simulation by applying the method to the actuation system of a looper in a hot strip rolling mill.

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Dynamic analysis of liquid-filled clamp-pipe systems based on the spectral element method

Sun,

Yu,

Wang

et al. 2024

Arch Appl Mech

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The spectral element method as an efficient tool for transient simulations of hydraulic systems

Cited by 14 publications

References 35 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

Optimal feedforward control of hydraulic drive systems with long pipelines

Dynamic analysis of liquid-filled clamp-pipe systems based on the spectral element method

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