Design, Analysis and Implementation of Smoothed Input Shapers with Distributed Delays

Vyhlídal, Tomáš; Kučera, V.; Hromčík, Martin

doi:10.1007/978-3-319-26369-4_12

Cited by 2 publications

(2 citation statements)

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“…If the delay is lumped, then

h false(η false) = H false(η - T false)

, where

H false(\cdot false)

denotes the Heaviside step function and

G false(s false) = e^{- s T}

. Then for example, the equally distributed delays with ramp‐wise step response, which is often use for smoothing the commands is derived as follows:

h false(η false) = ({, \begin{array}{cc} 0, & η < 0, \\ \frac{1}{T} η, & η \in false[0, T false], \\ 1, & η > 0. \end{array})

See [14, 22], for more complex delays that can perform or be utilised in the input smoothing and shaping tasks. Notice that if reasonably distributed, in fact, the delay (1) may perform a task of a finite impulse response filter [14], e.g.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…Consequently, the step response of the smoother (5) is

S

‐curve function until the determined delay. Let us remark that all the above smoothers can be considered directly as distributed delays with equal, triangular and trigonometric distribution [22]. Let us also point out that the closed‐form parametrisation of the above shapers is not possible to cancel fully the damped mode, unless their structure is modified, which will be presented in the following section.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

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