Robust multi-steps input command for liquid sloshing control

Abstract

A robust input command based on multiple steps for eliminating the residual vibrations of a multimode linear system is proposed. Only the system resonant frequencies are needed to determine the step magnitudes in the shaped command. The command duration is selectable to help in designing an optimum command that compensates between the reduction in the transient vibration, the enhancement in the command robustness, and the increase in the total maneuver time. The induced transient and residual sloshing oscillations of a suspended water-filled container are suppressed using the proposed command. The dynamics of the sloshing is numerically simulated using finite element method that accommodates the interactions between the fluid, structural, and multi-body dynamics. A short move time penalty is incurred with the price of significant reduction in the liquid sloshing. The performance of the shaped command to the system parameters and the robustness to their uncertainty are investigated. An improved robust input command in the presence of uncertainties in the cable length and water depth is also introduced. The effectiveness and excellence of the proposed command is demonstrated through a comparison with multimode zero-vibration input shaper and time-optimal flexible-body control.

Data-Driven Fractional-Order PID Controller Tuning for Liquid Slosh Suppression Using Marine Predators Algorithm

“…In (10), 𝑤 1 , 𝑤 2 and 𝑤 3 are the weighting coefficients as per determined by the system's designer. The FOPID controller parameters i.e.…”

“…This includes the command shaping techniques which generates a command from the convolution between the reference and a multi-sine wave function [9]. Another feed-forward control was introduced by Alshaya and Alshayji [10] which proposed an equidistant multistep input command for eliminating the liquid slosh. They have modeled the liquid sloshing based on finite element method (FEM) to numerically predict the elevation of the free-surface liquid level.…”

Specified-duration shapers for suppressing residual vibrations

“…For a given θ 3 , we assume a specific value of the final impulse magnitude A 3 (0 < A 3 < 1), and find A 1 , A 2 , t 2 that satisfy Eqs ( 8)- (10). Then, we vary the value of A 3 , and find A 1 , A 2 , t 2 that satisfy Eqs ( 8)-( 10), repeatedly.…”

“…Next, we obtain an SD shaper for the case when T s is between 1 and 1.5. Even when T s is between 1 and 1.5, an input shaper with three impulses can be obtained from constraints Eqs ( 8)- (10). However, to maximize 5% insensitivity, we obtain an SD shaper with four impulses as displayed in Fig 3 by adding derivative constraints.…”

“…For example, the forced lateral vibration of a building during earthquakes should be minimized to avoid structural damage [1]. Another example is that when cranes [2][3][4], disk drives [5,6], sloshing liquid containers [7][8][9][10], industrial robots [11], and soft robots [12,13] are operated, residual vibrations should be mitigated swiftly to reduce working hours and increase working efficiency.…”