Recent Advances in Sliding Modes: From Control to by Xinghuo Yu, Mehmet Önder Efe

By Xinghuo Yu, Mehmet Önder Efe

This quantity is devoted to Professor Okyay Kaynak to commemorate his lifestyles time impactful learn and scholarly achievements and amazing providers to occupation. The 21 invited chapters were written by means of prime researchers who, long ago, have had organization with Professor Kaynak as both his scholars and co-workers or colleagues and collaborators. The focal subject of the amount is the Sliding Modes masking a vast scope of issues from theoretical investigations to their major functions from keep watch over to clever Mechatronics.

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Phase portrait of Plant’s states x1 and x2 , and locus of the switching curve φ = φN = 0, showing a Sliding-Like behavior of the CTSM controller Control Input and perturbation 8 u/5 μ −z 6 u, μ, z 4 2 0 −2 −4 0 2 4 6 8 10 t Fig. 12. Time behavior of the continuous control signal u2 , and (finite-time) estimation of the perturbation f by the controller state −L = −z V (x) is positive definite and radially unbounded if and only if P > 0, which is true if the following inequalities are satisfied ⎧ ⎪ ⎨ ⎪ ⎩ p1 > 0, p1 p2 > 14 p212 , p1 p2 p3 − 14 p223 + p212 − p122p3 + + p213 p124p23 − p22p13 > 0 p13 p23 4 (21) 22 L.

On robustness of sliding mode systems with discontinuous control function. Automatika i Telemechanica (Automation & Remote Control 5, 172–175 (1985) 15. : Variable Gain Super-Twisting Sliding Mode Control. IEEE Transactions on Automatic Control 57(8), 2100–2105 (2012) 16. : Inequalities, 2nd edn. Cambridge University Press, London (1988) 17. : Higher order super-twisting algorithm. In: Proc. 6881129 18. : On inequalities between upper bounds of consecutive derivatives of an arbitrary function defined on an infinite interval.

X˙ r−1 = −k1 |φr−2 | 1/2 sign (φr−2 ) + xr x˙ r = −kr sign (φr−2 ) + ρ (40) where x1 , x2 , · · · , xr represent the states, and the perturbation ρ satisfies |ρ| ≤ Δ. Variable φr−2 is defined as: • • • r R1,r−1 = |x1 | r+1 where r represents the relative degree of the algorithm with respect to x1 . q Ri,r−1 = ||x1 |r1 + |x2 |r2 + · · · + |xi−2 |ri−2 | i , where i = 2, 3, · · · , (r − 1), r1 , r2 , · · · , ri−2 , and qi is a parameter designed based on the homogeneity weight of xi+1 . S0,r−1 = x1 S1,r−1 = x2 + k2 R1,r−1 sign(x1 ) Si,r−1 = xi+1 + ki+1 Ri,r−1 sign(Si−1,r−1 ) where i = 2, 3, · · · , (r − 1) • Finally φr−2 = sr−1,r−1 .

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