Modeling and adaptive robust wavelet control for a liquid container system under slosh and uncertainty

Abstract

Liquid sloshing in moving or stationary containers and flexible uncertainty caused by the slosh are considered to be the most probable causing unexpected coupling effects on the dynamics of many systems such as aerospace, ground vehicles, and high speed industries arms. The coupling of dynamic liquid slosh in a container system with the uncertainty caused by the sensors or dampers is rare documented and this coupling can be considered as a highly nonlinear system. In this paper, an investigation is presented to demonstrate a new approach for enabling the reduction of the liquid slosh and uncertainty by implementing adaptive robust wavelet control technique. Starting by creating the mathematical dynamic model for the nonlinear slosh coupled by uncertainty, adaptive robust control based wavelet transform is applied for calculating optimal motion that minimize residual slosh and uncertainty. Subsequently the adaptive robust control based wavelet network approximation and the appropriate parameter algorithms for the container system with slosh and uncertainty are derived to achieve the feedback linearization, adaptive control, and H∞ tracking performance. The simulation results show that the effects of slosh errors and external uncertainty can be successfully attenuated within a desired attenuation level.

Attitude-pendulum-sloshing coupled dynamics of quadrotors slung liquid containers

“…The geometric constraint given in (24) shows that determining one of the three angles β 1 , β 2 , and δ is enough to know the other two. While the independent motion variable is defined as u 4 , the dependent motion variables are defined as u 5 and u 6 .…”

“…Therefore, the nonlinear equation ( 23), constraints (24)(25)(26), and fluid forces (53-54) describe compoundpendulum dynamics, while the sloshing frequency (46), mode shape (44-45), and corresponding time function (47), report sloshing dynamics. Additionally, the coupling effects between pendulum and sloshing dynamics are also included in the dynamic model by the quadrotor attitude, cable swing, container slope, and fluid forces on the tank sidewall.…”

“…Feedback control schemes measure motions of the liquid surface in a feedback loop for oscillations suppression. [17][18][19][20][21][22][23][24][25] Nevertheless, accurately sensing the sloshing states is challenging. Open-loop control techniques modify the driving commands to generate a prescribed motion with minimal sloshing.…”

“…All abovementioned works are only focused on sloshing dynamics. Additionally, some of works [17][18][19][20][21][22][23][24][25][26][27][28][29] described sloshing dynamics using the equivalent mechanical model, such as the pendulum model. However, the equivalent pendulum model for fluid-sloshing dynamics is significantly different from attitude-pendulum-sloshing dynamics.…”

Robust Tracking Control for Slosh-Container System Against Viscous Friction Uncertainty

“…Sandhra et al, [7] designed a Sliding Mode Controller using a non-linear sliding surface to provide a better response compared to a Sliding Mode Controller with a linear sliding surface. Also, Mohammad Abdulrahman, [8] developed an adaptive robust control-based wavelet network to approximate the nonlinearity of the system. Furthermore, Rigatos et al, [9], proposed an H-infinity feedback controller to solve the problem of the nonlinearity optimal control for the system which gives fast and accurate tracking for all state variables.…”