Address: Department of Automation and Electronics, Faculty of Automation, Computers and Electronics University of Craiova, A. I. Cuza str. 13, RO-200585 Craiova, Romania and Romanian Academy of Engineering Sciences ASTR
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Abstract: 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).
AMSclassification: primary 34D20; secondary 34K40, 34K20, 35L50.
Keywords: neutral functional differential equations, energy Lyapunov functional, asymptotic stability, water hammer.
DOI: 10.5817/AM2023-1-109