Input Shaping for Flexible Systems with Non-Zero Initial Conditions

Abstract

Input shaping is a finite-impulse response (FIR) filter whose coefficients are designed to produce a shaped input that avoids exciting lightly-damped modes. As a result, flexible systems can be commanded to move quickly from point to point with minimum residual vibration. However, traditional input shaping techniques assume zero initial conditions, limiting their usability for systems with non-zero initial conditions, such as, emergency stops of cranes. Besides, in practice, movement of flexible systems is often initiated when the systems are not completely stationary. In these situations, the performance of the input shaping technique deteriorates. In this paper, a modification of shaper’s impulse sequence at the beginning of the move is proposed to bring the moving flexible system to a stop before commencing movement. The modification utilizes the work and energy method to determine the distance and time as functions of the initial states for base excitation of flexible systems, rendering its application to nonlinear systems. By concatenating this modification with the existing input shapers, a novel shaper called the non-zero initial conditions zero-vibration-derivative (NI-ZVDk) input shaper is introduced. The NI-ZVDk input shaper effectively prevents the movement of flexible systems from their initial states. To demonstrate the effectiveness of the approach, a 2-mass system is utilized as a benchmark for general flexible systems with 2 degrees of freedom. Various types of motion, including pure translation, pure rotation, and combined translation-rotation, are considered. Extensive simulation results showed that, using the proposed NI-ZVDk input shaper, the flexible systems can move from non-zero initial conditions to their desired destinations with less time and less residual vibration. HIGHLIGHTS The Input Shaping (IS) technique is used to suppress residual vibrations by creating destructive interference in impulse responses This method presents a novel design modification for IS when initial conditions are non-zero This technique can be extended for use in various nonlinear vibratory systems For example, it can be used when a crane needs to stop abruptly from non-zero initial conditions without residual vibrations GRAPHICAL ABSTRACT