A simple improved velocity estimation for low-speed regions based on position measurements only

Su, Yu; Zheng, Chunhong; Mueller, Peter C.; Duan, Baoyan

doi:10.1109/tcst.2006.876917

Cited by 94 publications

(50 citation statements)

References 27 publications

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“…3 For some recent references in the control literature, see, e.g., Braci & Diop (2001); Busvelle & Gauthier (2003); Chitour (2002); Dabroom & Khalil (1999); Diop, Fromion & Grizzle (2001); Diop, Grizzle & Chaplais (2000); Diop, Grizzle, Moraal & Stefanopoulou (1994) ;Duncan, Madl & Pasik-Duncan (1996); Ibrir (2003Ibrir ( , 2004; Ibrir & Diop (2004); Kelly, Ortega, Ailon & Loria (1994); Levant (1998Levant ( , 2003; Su, Zheng, Mueller & Duan (2006). The literature on numerical differentiation might be even larger in signal processing and in other fields of engineering and applied mathematics.…”

Section: General Overviewmentioning

confidence: 99%

Non-linear estimation is easy

Fliess¹,

Join²,

Sira‐Ramírez³

2008

IJMIC

308

183

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Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line estimations, are illustrating our viewpoint.

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Section: General Overviewmentioning

confidence: 99%

Non-linear estimation is easy

Fliess¹,

Join²,

Sira‐Ramírez³

2008

IJMIC

308

183

View full text Add to dashboard Cite

show abstract

“…If the discretization (15) into (24) is nonpathological in that the sampling period is selected to ensure that the controllability of (17), (22), and (24) is preserved and the pair [Φ, Γ 1 ] is controllable.…”

Section: Resultsmentioning

confidence: 99%

“…To attenuate quantization error, the use of the inversetime method [23,17,16], adaptive fir filters [12], Kalman filtering [3], or else observers such as that in [21,22] have been advocated both for control purposes and for virtual reality applications. All of these methods involve tradeoffs.…”

Section: Introductionmentioning

confidence: 99%

Ineluctability of oscillations in systems with digital implementation of derivative feedback

2011

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Differentiation in the feedback is common practice in digital control. Yet, the fundamental behavior of the universally employed backward difference of quantized signals has not been studied thus far. We show that velocity always oscillates when this type of feedback is applied to a forced, linear second-order system for any system parameter. We then compute a bound for the oscillation amplitude which can be easily computed given the parameters of the system. Experimental results are in close agreement with the theory. If the system has dry friction, our study yields a sufficient condition for the quenching of spontaneous oscillations.

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“…Methods based on observer design may be found in the control literature [7], [6], [18]. See also [19,22,34] for other approaches from the control litterature. In signal processing, it is very common to cast the problem in terms of frequency domain digital filter design [31], [29], [5].…”

Section: Introductionmentioning

confidence: 99%

Numerical differentiation with annihilators in noisy environment

2008

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Numerical differentiation in noisy environment is revised through an algebraic approach. For each given order, an explicit formula yielding a pointwise derivative estimation is derived, using elementary differential algebraic operations. These expressions are composed of iterated integrals of the noisy observation signal. We show in particular that the introduction of delayed estimates affords significant improvement. An implementation in terms of a classical finite impulse response (FIR) digital filter is given. Several simulation results are presented.

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A simple improved velocity estimation for low-speed regions based on position measurements only

Cited by 94 publications

References 27 publications

Non-linear estimation is easy

Non-linear estimation is easy

Ineluctability of oscillations in systems with digital implementation of derivative feedback

Numerical differentiation with annihilators in noisy environment

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