Parameter Selection Procedure for an Amplitude- and Rate-saturated Controller

Baiomy, Nehal; Kikuuwe, Ryo

doi:10.1007/s12555-018-0450-x

Cited by 2 publications

(4 citation statements)

References 19 publications

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“…The conclusions drawn for first-order SMC are still valid: drastic decrease of input and output chattering, and insensitivity of the input with respect to the gain β increase. It is noteworthy that in general, the second order dynamics for σ(•) stems from a higher dimensional system that has relative degree two with respect to σ(•) seen as an output, so that σ(•) andσ(•) are designed as functions of some measured output y(•) and of its derivatives, usually obtained as the output of linear filters that approximate differentiation (so-called "dirty filters" τ s s+τ , τ > 0, which introduce phase lags 11 ). This is a feature shared by the first order SMC.…”

Section: Resultsmentioning

confidence: 99%

“…These are introduced in [11,10], to control linear invariant systems with matched perturbations, as in (21). The input is defined through a differential inclusion as:…”

Section: Amplitude-and Rate-saturated Controllermentioning

confidence: 99%

“…These are introduced in References 39,48, to control linear invariant systems with matched perturbations, as in (18). The input is defined through a differential inclusion as:

\{\begin{matrix} \overset{u}{true} false(t false) \in prefix- g sgn ((), u false(t false) + sat ((), \frac{C x}{γ false(x false(t false), u false(t false) false)})) \\ γ false(x, u false) = \min ((), γ_{c}, \frac{false| C A x false| + C B false| u false| + C B M}{g}), \end{matrix}

with

C \in ℝ^{1 \times n}

, CB > 0, | d ( t )| ≤ M ,

γ (x, u) \leq γ_{c}

, sat(·) is the usual saturation function, with saturation width

α > M

.…”

Section: First‐order Sliding‐mode Controlmentioning

confidence: 99%

“…We should also mention the analysis of the implicit Euler method for linear complementarity systems and relay systems, with main applications in circuits with nonsmooth components [21,70,22]. In slidingmode control and observation, the implicit approach has been initiated and deeply analysed by two main research groups, in France [2,3,4,7,19,48,50,51,47,83,85,87,101,36,119,49,20], and in Japan [9,64,11,79,56,65,55,125,126,59,62,10,60,123,124]. We may also mention [66,67,121] (who apply a kind of semi-implicit discretization method based on pseudo linear representations), as well as the pioneering work in [30] where the implicit Euler discretization was advocated for the first time in Automatic Control for a scalar system with known perturbation (see Remark 1 below), and with a short analysis of its finite-time convergence properties.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Digital implementation of sliding‐mode control via the implicit method: A tutorial

Brogliato

Polyakov

2020

Intl J Robust & Nonlinear

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The objective of this article, is to provide a clear presentation of the discretization of continuoustime sliding-mode controllers, also known in the Automatic Control literature as the emulation method, when the implicit (backward) Euler scheme is used. First-order, second-order and homogeneous controllers are considered. The main theoretical results are recalled in each case, and the focus is put on the discrete-time implementation structure and on the algorithms which allow the designer to solve, at each time-step, the one-step generalized equations which are needed to compute the controllers. The article ends with some open issues.

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Section: Resultsmentioning

confidence: 99%

“…These are introduced in [11,10], to control linear invariant systems with matched perturbations, as in (21). The input is defined through a differential inclusion as:…”

Section: Amplitude-and Rate-saturated Controllermentioning

confidence: 99%

“…These are introduced in References 39,48, to control linear invariant systems with matched perturbations, as in (18). The input is defined through a differential inclusion as: