VSS observer for linear time varying system

Hashimoto, Hideki; Utkin, Vadim I.; Xu, Jian‐Xin; Suzuki, Hideyuki; Harashima, Fumio

doi:10.1109/iecon.1990.149106

Cited by 54 publications

(28 citation statements)

References 7 publications

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“…EXACT STATE ESTIMATION FOR LINEAR SYSTEMS where * e þ satisfies (11). In view of (11), one can always satisfy (16) in finite time.…”

Section: Auxiliary Dynamic Systemsmentioning

confidence: 99%

“…To ensure the finite convergence, one idea that has been suggested is to transform the system into a triangular form and use a step-by-step sliding mode observer based on first-order sliding modes, allowing the successive reconstruction of each component of the transformed state vector via the equivalent values (see, e.g. [11][12][13][14]). The methodology previously mentioned ensures finite time convergence theoretically since its realization requires a filtration of the equivalent control at each step.…”

Section: Antecedents and Motivationmentioning

confidence: 99%

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Exact state estimation for linear systems with unknown inputs based on hierarchical super‐twisting algorithm

Bejarano

Fridman

Poznyak

2007

Intl J Robust & Nonlinear

103

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SUMMARYA robust hierarchical observer is designed for linear time invariant systems with unknown bounded inputs under conditions of strong observability, providing exact state estimation. The main condition for designing the state estimator is the, so-called, strong observability condition. The supertwisting (secondorder sliding mode) algorithm is used in each step of the hierarchy; the continuity of the supertwisting output injection allows to reconstruct a vector formed by some full column rank matrix premultiplied by the state vector, and that vector is obtained in a finite time and without any sort of filtration. For the case when the unknown inputs are considered as constant uncertain parameters, the continuous version of the least-square method is developed. Two numerical examples illustrate the efficiency of the suggested technique.

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“…EXACT STATE ESTIMATION FOR LINEAR SYSTEMS where * e þ satisfies (11). In view of (11), one can always satisfy (16) in finite time.…”

Section: Auxiliary Dynamic Systemsmentioning

confidence: 99%

Section: Antecedents and Motivationmentioning

confidence: 99%

Exact state estimation for linear systems with unknown inputs based on hierarchical super‐twisting algorithm

Bejarano

Fridman

Poznyak

2007

Intl J Robust & Nonlinear

103

View full text Add to dashboard Cite

show abstract

“…Even if the real states are measurable, the switching surfaces and the control parameters are obtained from the observer states. For sliding mode control, since the model uncertainty of the observer may be smaller than those in the plant, a sliding mode might occur in the observer controller loop, and then chattering is reduced [8][9][10]. From (21), the state observer is defined as ( )ˆˆ, , X AX Bu L y y y CX…”

Section: Control For Lateral Movement Of Stripmentioning

confidence: 99%

PID sliding mode control for steering of lateral moving strip in hot strip rolling

Choi

Lee

2009

Int. J. Control Autom. Syst.

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Lateral movement of a strip in the hot rolling process is an important unsolved technical problem. It results in reduced productivity and, in the extreme case, in strip tearing during tailing out at the finishing mill. Lateral movement of a strip is caused by various asymmetric factors such as mechanical asymmetry of the mill, and different temperatures along the strip width direction. This study aims to understand the influences of these various factors on lateral movement, and to develop a controller that is useful for reducing lateral movement. Mathematical models which consider initial off-center value, leveling error of the mill, and strip tension for lateral movement of the strip are proposed. A Proportional-Integral-Derivative(PID) based sliding mode controller using an observer is also proposed to prevent lateral movement of strips. In addition, a control algorithm is designed to solve the chattering problem of a sliding mode control. The effectiveness of the proposed method is evaluated by numerical simulation of hot rolling by a pinch roll. NOMENCLATURE b = strip width h = strip thickness df h = strip thickness difference (work side thicknessdrive side thickness) M = strip bending moment between mill and pinch roll 1 R = the radius of curvature 2 R = the radius of momentum curvature 4 d = time delay T = strip tension v = strip speed at the back of pinch roll df v = strip speed difference (work side speed -drive side speed) θ = inclination angle of the centerline of the strip at the back of pinch roll ω = angular velocity of strip at the back of pinch roll c y = off-center value ϕ ∆ = strip wedge ratio while pinching P = total pinching force at the cylinder load point A P = pinching force at the cylinder load point of drive side B P = pinching force at the cylinder load point of work side P ∆ = difference value between cylinder force (P B -P A ) a p = pressure at drive side b p = pressure at work side A S = cylinder gap at the cylinder load point of drive side B S = cylinder gap at the cylinder load point of work side S ∆ = difference value between cylinder gap (S B -S A ) 1 A X = roll gap at drive side 1 B X = roll gap at work side H K = bending spring constant of pinch roll necks and bearings f k = spring constant of pinch roll in roll bite P h ∂ ∂ = influence coefficient of strip thickness on the pinching force S l = distance between pinching points of load R l = barrel length of roll P K = proportional gain I K = integral gain D

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“…In Hashimoto et al (1990), Barbot et al (1996), Utkin et al (1999) and Barbot and Floquet (2004) a step by step form of sliding mode observers were proposed. Such observers were based on the transformation of a given system to a block triangular observable form and the step by step estimation of each state by using of the value of the equivalent output injection.…”

Section: Antecedents and Motivationsmentioning

confidence: 99%

Observation and identification of mechanical systems via second order sliding modes

Dávila

Fridman

Poznyak

2006

International Journal of Control

188

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VSS observer for linear time varying system

Cited by 54 publications

References 7 publications

Exact state estimation for linear systems with unknown inputs based on hierarchical super‐twisting algorithm

Exact state estimation for linear systems with unknown inputs based on hierarchical super‐twisting algorithm

PID sliding mode control for steering of lateral moving strip in hot strip rolling

Observation and identification of mechanical systems via second order sliding modes

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