High-gain nonlinear observer design using the observer canonical form

Röbenack, Klaus; Lynch, Alan F.

doi:10.1049/iet-cta:20060418

Cited by 36 publications

(26 citation statements)

References 43 publications

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“…Liu (2004) proposed an algorithm for state observer design of two-dimensional linear shift-invariant systems via using the well-known one-dimensional system results. Röbenack and Lynch (2006) proposed two methods for nonlinear observer design which are based on a partial nonlinear observer canonical form. Moreover, Sliding Mode Observer (SMO) design of an uncertain system is an important issue of recent discussion.…”

Section: X(t) = (A + δA)x(t) + (A D + δA D )X(t − τ ) + (B + δB)u(t) mentioning

confidence: 99%

Variable structure observer design for a class of uncertain systems with a time-varying delay

Liu

2012

International Journal of Applied Mathematics and Computer Science

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Design of a state observer is an important issue in control systems and signal processing. It is well known that it is difficult to obtain the desired properties of state feedback control if some or all of the system states cannot be directly measured. Moreover, the existence of a lumped perturbation and/or a time delay usually reduces the system performance or even produces an instability in the closed-loop system. Therefore, in this paper, a new Variable Structure Observer (VSO) is proposed for a class of uncertain systems subjected to a time varying delay and a lumped perturbation. Based on the strictly positive real concept, the stability of the equivalent error system is verified. Based on the generalized matrix inverse approach, the global reaching condition of the sliding mode of the error system is guaranteed. Also, the proposed variable structure observer will be shown to possess the invariance property in relation to the lumped perturbation, as the traditional variable structure controller does. Furthermore, two illustrative examples with a series of computer simulation studies are given to demonstrate the effectiveness of the proposed design method.

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Section: X(t) = (A + δA)x(t) + (A D + δA D )X(t − τ ) + (B + δB)u(t) mentioning

confidence: 99%

Variable structure observer design for a class of uncertain systems with a time-varying delay

Liu

2012

International Journal of Applied Mathematics and Computer Science

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“…Approximations of nonlinearities in the canonical form (which results in ELO) have already been suggested (Bestle & Zeitz, 1983), and this approach can be extended to higher order approximations (Röbenack & Lynch, 2004). An observer using a partial nonlinear observer canonical form (POCF) (Röbenack & Lynch, 2006) has weaker observability and integrability existence conditions than the well-established non-linear observer canonical form (OCF). Non-linear sliding mode observers use a quasi-Newtonian approach, applied after pseudo-derivations of the output signal (Efimov & Fridman, 2011).…”

Section: Introductionmentioning

confidence: 99%

Resistance to Noise of Non-linear Observers in Canonical Form Application to a Sludge Activation Model

Schwaller¹,

Ensminger²,

Dresp-Langley³

et al. 2017

JMR

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The aim of this study was to increase the resistance to noise of an observer of a non-linear MISO system transformed into canonical regulation form of order n. For this, the principle idea was to add n observers on the output equations of the main observer. By adjusting the time scale of the output observers, the resistance to noise of the final estimates is considerably increased. The proposed method is illustrated by model simulations based on a non-linear Sludge Activation Model (SAM)

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“…There exists a sustained error between the steady state values of the actual and the observed states. Different types of such observers, like Luenberger observers, reduced order Luenberger observers [6]- [13], sliding mode observers [14]- [18] are mentioned in literatures. To minimize the steady state observer error in presence of disturbances, full order observers with integral action have been proposed in literatures [1]- [5].…”

Section: Introductionmentioning

confidence: 99%