Adjustable-Smooth Polynomial Command-Shaping Control With Linear Hoisting

Abstract

Great amount of work has been dedicated to eliminate residual vibrations in rest-to-rest motion. Considerable amount of these methods is based on convolving a general input signal with a sequence of timed impulses. These impulses usually have large jumps in their profiles and are chosen depending on the system modal parameters. Furthermore, classical input shaping methods are usually used for constant cable length and are sensitive to any change in the system parameters. To overcome these limitations, polynomial command shapers with adjustable maneuvering time are proposed. The equation of motion of a simple pendulum with the effect of hoisting is derived, linearized, and solved in order to eliminate residual vibrations in rest-to-rest maneuvers. Several cases including smooth, semi-smooth and unsmooth continuous shapers are simulated numerically and validated experimentally on an experimental overhead crane. Numerical and experimental results show that the proposed polynomial command shaper eliminates residual vibrations effectively. The effect of linear hoisting is also included and discussed. To enhance the shaper performance, extra parameters are added to the polynomial function to reduce shaper sensitivity. Results show that the effect of adding these parameters greatly enhances the shaper performance.

A smooth optimized input shaping method for two-dimensional crane systems using Bezier curves

“…One of the main features of the proposed Bezier-curve technique is its capability to handle complex hoisting mechanism. It is assumed that the hoisting-cable length L ( t ) to be linearly varying with time (Alghanim et al, 2018; Alhazza, 2017), namely…”

“…The trolley is represented as a point mass of m t while the payload is modeled as a rigid mass with a mass of m p . Neglecting both the friction force and the disturbances, the governing nonlinear equation of motion in θ -coordinate is derived using the Lagrange formulation (Alghanim et al, 2018) as…”

Anti-sway control of variable rope length container crane based on phase plane trajectory planning

“…The dynamics equations of the system are obtained using the Lagrangian equation (Alghanim et al, 2018; Alhazza, 2017; Matsui and Kajiwara, 2022). The kinetic energy of the load for the system shown in Figure 1 is shown in equation (1)where x˙ is the trolley velocity, li is the rope length at time t, and li˙ is velocity of the hoisting.…”

“…When crane systems include simultaneous hoisting and trolley moving, which are more complex than fixed rope length systems, several input shaping methods are reported, such as the smooth waveform command shaping technique (Alhazza, 2016), an anti-vibration control using trapezoidal velocity patterns (Gao et al, 2007), negative zero vibration (NZV) shaper (Cao et al, 2021), and unit magnitude zero vibration (UMZV) shaper (Maghsoudi et al, 2019). To address issues of residual oscillations, discrete-time command-profile (Alghanim et al, 2015), polynomial command shapers with adjustable maneuver times (Alghanim et al, 2018), and input shaping with frequency modulation (Arabasi and Masoud, 2017) have been proposed. These methods can achieve good anti-sway effect or eliminate residual oscillation, but cannot control the magnitude of the swing angle.…”

A smooth polynomial shaped command for sloshing suppression of a suspended liquid container

“…Alhazza and Masoud (2016), Masoud and Alhazza (2017), and Alshaya and Alghanim (2020) proposed a multi-steps input command and a waveform command to eliminate the residual vibrations of multi-mode systems. Alghanim et al (2018) proposed a polynomial-based command for a single degree-of-freedom system. Unlike multi-steps input commands which usually degrade the performance due to actuation delay and mismatch timing, reduce the life expectancy of the actuator, and increase maintenance due to jerks, the continuous form of the polynomial-based command can be easily adjusted to have any level of smoothness.…”