This paper investigates the use of the method of inequalities （MoI） to design output-feedback compensators for the problem of the control of instabilities in a laminar plane Poiseuille flow. In common with many flow...This paper investigates the use of the method of inequalities （MoI） to design output-feedback compensators for the problem of the control of instabilities in a laminar plane Poiseuille flow. In common with many flows, the dynamics of streamwise vortices in plane Poiseuille flow are very non-normal. Consequently, small perturbations grow rapidly with a large transient that may trigger nonlinearities and lead to turbulence even though such perturbations would, in a linear flow model, eventually decay. Such a system can be described as a conditionally linear system. The sensitivity is measured using the maximum transient energy growth, which is widely used in the fluid dynamics community. The paper considers two approaches. In the first approach, the MoI is used to design low-order proportional and proportional-integral （PI） controllers. In the second one, the MoI is combined with McFarlane and Glover＇s H∞ loop-shaping design procedure in a mixed-optimization approach.展开更多
The positive thermal gradient is one of the most important parameters during directional solidification. The increase of the thermal gradient usually stabilizes the planar interface in the steady state analysis. Howev...The positive thermal gradient is one of the most important parameters during directional solidification. The increase of the thermal gradient usually stabilizes the planar interface in the steady state analysis. However, in the initial transient range of planar instability, the thermal gradient presents complicated effects. Time-dependent analysis shows that the increase of the thermal gradient can enhance both the stabilizing effects and the destabilizing effects on a planar interface. The incubation time first decreases and then increases with the increase of the thermal gradient. Moreover, the initial average wavelength always increases with the thermal gradient increasing, contrary to the effect of the thermal gradient on the steady cellular/dendritic spacing. This reveals the types of spacing adjustment after planar instability.展开更多
文摘This paper investigates the use of the method of inequalities （MoI） to design output-feedback compensators for the problem of the control of instabilities in a laminar plane Poiseuille flow. In common with many flows, the dynamics of streamwise vortices in plane Poiseuille flow are very non-normal. Consequently, small perturbations grow rapidly with a large transient that may trigger nonlinearities and lead to turbulence even though such perturbations would, in a linear flow model, eventually decay. Such a system can be described as a conditionally linear system. The sensitivity is measured using the maximum transient energy growth, which is widely used in the fluid dynamics community. The paper considers two approaches. In the first approach, the MoI is used to design low-order proportional and proportional-integral （PI） controllers. In the second one, the MoI is combined with McFarlane and Glover＇s H∞ loop-shaping design procedure in a mixed-optimization approach.
基金supported by the National Natural Science Foundation of China (Grant No. 51071128)the Program for New Century Excellent Talents in University (Grant No. NCET-09-0683)+2 种基金the Fund of State Key Laboratory of Solidification Processing in Northwestern Polytechnical University, China (Grant Nos. 17-TZ-2007, 03-TP-2008, and 24-TZ-2009)the National Basic Research Program of China (Grant No. 2011CB610401)the China Postdoctoral Science Foundation (Grant No. 20110491689)
文摘The positive thermal gradient is one of the most important parameters during directional solidification. The increase of the thermal gradient usually stabilizes the planar interface in the steady state analysis. However, in the initial transient range of planar instability, the thermal gradient presents complicated effects. Time-dependent analysis shows that the increase of the thermal gradient can enhance both the stabilizing effects and the destabilizing effects on a planar interface. The incubation time first decreases and then increases with the increase of the thermal gradient. Moreover, the initial average wavelength always increases with the thermal gradient increasing, contrary to the effect of the thermal gradient on the steady cellular/dendritic spacing. This reveals the types of spacing adjustment after planar instability.
