Geodesic
Around certain critical cases in stability studies in hydraulic engineering
Archivum mathematicum, Tome 59 (2023) no. 1, pp. 109-116 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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It is considered the mathematical model of a benchmark hydroelectric power plant containing a water reservoir (lake), two water conduits (the tunnel and the turbine penstock), the surge tank and the hydraulic turbine; all distributed (Darcy-Weisbach) and local hydraulic losses are neglected,the only energy dissipator remains the throttling of the surge tank. Exponential stability would require asymptotic stability of the difference operator associated to the model. However in this case this stability is “fragile” i.e. it holds only for a rational ratio of the two delays, with odd numerator and denominator also. Otherwise this stability is critical (non-asymptotic and displaying an oscillatory mode).
It is considered the mathematical model of a benchmark hydroelectric power plant containing a water reservoir (lake), two water conduits (the tunnel and the turbine penstock), the surge tank and the hydraulic turbine; all distributed (Darcy-Weisbach) and local hydraulic losses are neglected,the only energy dissipator remains the throttling of the surge tank. Exponential stability would require asymptotic stability of the difference operator associated to the model. However in this case this stability is “fragile” i.e. it holds only for a rational ratio of the two delays, with odd numerator and denominator also. Otherwise this stability is critical (non-asymptotic and displaying an oscillatory mode).
DOI : 10.5817/AM2023-1-109
Classification : 34D20, 34K20, 34K40, 35L50
Keywords: neutral functional differential equations; energy Lyapunov functional; asymptotic stability; water hammer 
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Rasvan, Vladimir. Around certain critical cases in stability studies in hydraulic engineering. Archivum mathematicum, Tome 59 (2023) no. 1, pp. 109-116. doi: 10.5817/AM2023-1-109

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