Adaptive bounded bilinear control of coupled first-order 1-D hyperbolic PDEs and infinite ODEs with unknown time-varying source term

Author(s):  
Sarah Mechhoud
2016 ◽  
Vol 23 (4) ◽  
pp. 319-330
Author(s):  
Jean-Louis Le Mouël ◽  
Vladimir G. Kossobokov ◽  
Frederic Perrier ◽  
Pierre Morat

Abstract. We report the results of heating experiments carried out in an abandoned limestone quarry close to Paris, in an isolated room of a volume of about 400 m3. A heat source made of a metallic resistor of power 100 W was installed on the floor of the room, at distance from the walls. High-quality temperature sensors, with a response time of 20 s, were fixed on a 2 m long bar. In a series of 24 h heating experiments the bar had been set up horizontally at different heights or vertically along the axis of the plume to record changes in temperature distribution with a sampling time varying from 20 to 120 s. When taken in averages over 24 h, the temperatures present the classical shape of steady-state plumes, as described by classical models. On the contrary, the temperature time series show a rich dynamic plume flow with intermittent trains of oscillations, spatially coherent, of large amplitude and a period around 400 s, separated by intervals of relative quiescence whose duration can reach several hours. To our knowledge, no specific theory is available to explain this behavior, which appears to be a chaotic interaction between a turbulent plume and a stratified environment. The observed behavior, with first-order factorization of a smooth spatial function with a global temporal intermittent function, could be a universal feature of some turbulent plumes in geophysical environments.


Author(s):  
Xiong Zhao ◽  
Lianyu Zheng ◽  
Yuehong Zhang

Abstract Mirror error compensation is usually employed to improve the machining precision of thin-walled parts. However, this zero-order method may result in inadequate error compensation, due to the time-varying cutting condition of thin-walled parts. To cope with this problem, an on-line first-order error compensation method is proposed for thin-walled parts. With this context, firstly, the time-varying cutting condition of thin-walled parts is defined with its in-process geometric and physical characteristics. Based on it, a first-order machining error compensation model is constructed. Then, during the process planning, the theory geometric and physical characteristic of thin-walled parts are respectively obtained with CAM software and structure dynamic modification method. After process performing, the real geometric characteristic of thin-walled parts is measured, and it is used to calculate the dimension error of thin-walled parts. Next, the error compensated value is evaluated based on the compensation model, from which, an error compensation plane is constructed to modify the tool center points for next process step. Finally, the machining error is compensated by performing the next process step. A milling test of thin-walled part is employed to verify the proposed method, and the experiment results shown that the proposed method can significantly improve the error compensation effect for low-stiffness structure, and thickness precision of thin-walled parts is improved by 71.4 % compared with the mirror error compensation method after machining.


2021 ◽  
Author(s):  
Arnab Pal ◽  
Ramashis Banerjee ◽  
Debottam Mukherjee ◽  
Samrat Chakraborty ◽  
Pabitra Kumar Guchhait ◽  
...  

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