Input shaping for vibration-free positioning of flexible systems

Abstract

Input shaping is a simple and effective method for reducing the residual vibration when positioning lightly damped systems, and it remains an active research area. In this paper, a continuous and differentiable function is introduced to define the desired motion, and then the input is shaped by inverse dynamic analysis. In the proposed method the only parameter that needs to be defined is the output speed, which is limited only by the physical constraints of the drive system. The calculation of an optimum speed is demonstrated by simulation examples. It is also shown that, under certain circumstances, the process can be further simplified and the need for inverse dynamics is eliminated.

Inverse dynamic analysis of multiphysics systems

“…As an example, it is assumed that the load is required to move from an initial steady position of (0.5, 0.5, 0.46) m to a new steady position of (0.8, 0.0, 0.14) m within a settling time of 2 s. It follows from previous work [13] that the required motion satisfying the initial and the nal conditions can be formulated as follows:…”

“…The desired motion is to move the third bar from its initial horizontal position to a vertical position smoothly within 0.9 s while keeping its centre of gravity stationary. This motion can be de ned by setting the second derivatives of x 3 and y 3 to zero, and the second derivatives of h 3 as per equation (13) as described in the mechatronic example. The required control inputs, calculated by the inverse dynamic analysis, are shown in Fig.…”

Inverse dynamic analysis with feedback control for vibration-free positioning of a gantry crane system

“…The most popular technique for input shaping is to convolve a sequence of impulses and various methods for shaping impulse sequence of impulses have been testified and applied to crane system as in [4]. M N Sahinkaya in his paper [5] also has reported the same inverse dynamic technique in spring-mass-damper system. However all the above method is still an openloop approach that avoid the system from become less sensitive to disturbances.…”

Vibration Reduction of a Lightly Damped System Using a Hybrid Input Shaping Method

“…Mimmi and Pennacchi [6] have proincluded shaping a rectangular or 'bang-bang' forcing posed an input shaping strategy based on two types function by a short, finite Fourier series to reduce of acceleration input: a constant acceleration with a variable time interval, and a trapezoidal acceleration input. Sahinkaya [7] has described a method for function. The robustness of the proposed method important.…”

“…To achieve this, in section 3.1 of this paper, a new and novel assumed to have this format. The equation of motion of such a system with damping ratio f and natural preshaped input is proposed, formed by superimposing three functions, a cycloid, a ramped versine, frequency v n can be written as [7] and a ramp. A cycloidal motion profile is commonly…”