By Shankar Sastry

ISBN-10: 0130043265

ISBN-13: 9780130043269

ISBN-10: 0130043672

ISBN-13: 9780130043672

This quantity surveys the most important effects and strategies of study within the box of adaptive keep watch over. targeting linear, non-stop time, single-input, single-output structures, the authors supply a transparent, conceptual presentation of adaptive equipment, allowing a severe overview of those options and suggesting avenues of extra improvement. 1989 variation

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**Additional resources for Adaptive control : stability, convergence, and robustness**

**Example text**

38) dr1 r1 =− . 39) and We will make a third hypothesis: 3) The derivative of r2 with respect to z can be obtained in an identical manner: dr2 r2 =− . 41) z 1 where, for the case of two plates of identical material (in other words two identical contact angles), F =− 2πγ 2 r cos θ. 42) If we take into consideration the lateral area Σ, the above hypotheses are replaced by the following ones: 1) approximation of a cylindrical meniscus of radius r and height z; 2) liquid volume exactly equal to V = πr2 z.

9. Illustration of the Young-Dupré equation Another important parameter in the capillary force model is the contact angles formed by the liquid and the object (θ1 ), and the liquid and the probe (θ2 ). This angle is determined by the tangent at the liquid-gas interface and the tangent to the solid at the triple interface line (the line defining the intersection of the liquid-gas, liquid-solid and solid-gas interfaces). 9 this triple line reduces to a point that is its intersection with the plane of the figure.

The transition between the DMT and JKR models has been studied analytically by [MAU 92]. Introduced is a parameter λ known as the elasticity parameter: λ = 2σ0 R πW K 2 1/3 , with σ0 = W and h ≈ 1Å. 81) It should be noted that a suitable ratio exists to qualify both the adhesion and the rigidity of the solid. This is [FRÉ 03] r= W . 82) The pull-off force is then P = 2σ0 a2 m2 arctan m2 − 1 + m2 − 1 .

### Adaptive control : stability, convergence, and robustness by Shankar Sastry

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