Sloshing is a complex nonlinear dynamic phenomenon which has a significant influence on the stability of structure–fluid systems. In this study, the dynamic equation of sloshing based on Hamilton principle is established and linearized into a state space equation. Considering the uncertainty of the system, a robust H infinite guaranteed cost control method is proposed to mitigate the response of fluid wave height to horizontal acceleration of the tank body. Simulation results are given to demonstrate the closed-loop performance of the nonlinear dynamic modeling and linear optimal control method.
Abramson HN (1966) The dynamics of liquids in moving containers. Report SP 106. Washington, DC: NASA.
2.
BandyopadhyayBGandhiPSKurodeS (2009) Sliding mode observer based sliding mode controller for slosh-free motion through PID scheme. IEEE Transactions on Industrial Electronics56(9): 3432–3442.
3.
ChenKLiJWangT (2005) Nonlinear dynamics modeling and analysis of liquid sloshing in rectangular tank. Acta Mechanica Sinica37(3): 339–345.
4.
De SouzaAGde SouzaLCG (2014) Satellite attitude control system design taking into account the fuel slosh and flexible dynamics. Mathematical Problems in Engineering2014(1): 1–8.
5.
Ferrant P and Le Touze D (2001) Simulation of sloshing waves in a 3D tank based on a pseudo-spectral method. In: Proceedings of the 16th international workshop on water waves and floating bodies, Hiroshima, Japan, 22–25 April 2001.
6.
LiY (2000) Optimal guaranteed cost control of linear uncertain systems: an LMI approach. Control Theory and Applications17(3): 423–428.
7.
LiuY (2015) A survey of approaches in dynamics of rigid body containing liquid. Mechanics in Engineering37(3): 397–400.
8.
LoveJSTaitMJ (2014) Equivalent mechanical model for tuned liquid damper of complex tank geometry coupled to a 2D structure. Structural Control & Health Monitoring21(1): 43–60.
9.
TakashiIRaoufAIYujiHet al.(2012) Nonlinear liquid sloshing in a square tank subjected to obliquely horizontal excitation. Journal of Fluid Mechanics700: 304–328.
10.
Telste JG (1985) Calculation of fluid motion resulting from large amplitude forced heave motion of a two-dimensional cylinder in a free surface. In: Proceedings of the fourth international conference on numerical ship hydrodynamics, Washington, DC, 24–27 September 1985, paper no. 81C93.
11.
Venugopal R and Bernstein DS (1996) State space modeling and active control of slosh. IEEE international conference on control applications, Dearborn, MI, 15–18 September 1996, pp.1072-1077. New York: IEEE.
12.
YueB (2005) Three-dimensional large amplitude liquid sloshing under pitching excitations. Acta Mechanica Sinica37(2): 199–203.
13.
ZanQHuangJ (2015) Dynamics and control of three-dimensional slosh in a moving rectangular liquid container undergoing planar excitations. IEEE Transactions on Industrial Electronics62(4): 2309–2318.
