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## Dither in Systems with Hysteresis (1995)

### Citations

343 |
Non Homogeneous Media and Vibration Theory
- Sanchez-Palencia
- 1980
(Show Context)
Citation Context ...ypothesis (essentially a persistence hypothesis on the limit solution plus an incremental sector inequality) provides convergence on R + . This case is solvable with the classical averaging principle =-=[23, 8]-=- when the hysteresis operator is singlevalued. A very interesting property of the preceding model is that it is linear for small velocities, and this linearization is indeed exact if the dither is cho... |

172 |
Differential Models of Hysteresis
- Visintin
- 1994
(Show Context)
Citation Context ... been proposed, concerning systems with memoryless nonlinearities [27, 28], backlash [12] or a special class of hysteresis [12] (a particular subclass of Duhem model, according to the nomenclature in =-=[25]-=-). For a recent bibliography on experiments (resp. theory), see [24] (resp. [12]). For details on hysteresis operators, see [18, 25]. Qualitatively, the key idea for using dither is the following: if ... |

152 |
Asymptotic Methods in the Theory of Nonlinear Oscillations,” Internat.
- Bogoliubov, Mitropolsky
- 1961
(Show Context)
Citation Context ...ypothesis (essentially a persistence hypothesis on the limit solution plus an incremental sector inequality) provides convergence on R + . This case is solvable with the classical averaging principle =-=[23, 8]-=- when the hysteresis operator is singlevalued. A very interesting property of the preceding model is that it is linear for small velocities, and this linearization is indeed exact if the dither is cho... |

137 |
Almost periodic differential equations
- Fink
- 1974
(Show Context)
Citation Context ...f: As g is an AAPF and g 0 is uniformly continuous, g 0 is an AAPF, and jg 0 (t)j also [9]. Hence, the following limit exists (Lemma 19)sg(0) = lim T!+1 1 T Z T 0 jg 0 (s)j ds and one may prove as in =-=[13]-=- that it is strictly positive if g 0 6j 0. Moreover, as (14) is satisfied, thenss(0) defined by (22) exists (Lemma 20). We denote '(T ) = sup TT 0 fi fi fi fi fisg(0) \Gamma 1 T 0 Z T 0 0 jg 0 (s)j ds... |

89 | Multivalued Differential Equations. Walter de Gruyer. - Deimling - 1992 |

36 |
Easy-to-use realistic dry friction models for automatic control. In:
- Bliman, Sorine
- 1995
(Show Context)
Citation Context ...) ) (0) = ( u 0 ; u 1 ; : : : u l\Gamma1 ) (1) where L and M are real coprime polynomials of order l and m respectively, H(u) is a nonlinear operator of hysteresis type proposed to model dry friction =-=[5, 6, 7], f is a c-=-ontrol input term and d a so-called dither function of "high frequency" (see Figure 1). Due to the differential and possibly multivalued nature of H, equation (1) may indeed be considered as... |

23 |
Normal Vibrations and Friction Under Harmonic Loads: Part II—Rough Planar Contacts,"
- Hess, Soom
- 1991
(Show Context)
Citation Context ... to increase stability, in particular to quench limit cycles, or to smoothen or linearize the nonlinearities. Concluding experiments have been conducted in systems with relays [19], with dry friction =-=[4, 14, 15, 16]-=-, with rotative amplifiers [1], with DC motors [24]. Rigorous statements have also been proposed, concerning systems with memoryless nonlinearities [27, 28], backlash [12] or a special class of hyster... |

20 |
Dither in Nonlinear Systems,"
- Zames, Shneydor
- 1976
(Show Context)
Citation Context ... with relays [19], with dry friction [4, 14, 15, 16], with rotative amplifiers [1], with DC motors [24]. Rigorous statements have also been proposed, concerning systems with memoryless nonlinearities =-=[27, 28]-=-, backlash [12] or a special class of hysteresis [12] (a particular subclass of Duhem model, according to the nomenclature in [25]). For a recent bibliography on experiments (resp. theory), see [24] (... |

19 |
periodic functions in abstract spaces
- Zaidman
- 1985
(Show Context)
Citation Context ...R have F -repetitive derivative and satisfy all the desired properties. RR n2690 26 Pierre-Alexandre Bliman, Alexander M. Krasnosel'skii, Michel Sorine 4.4 Asymptotic almost-periodic dither Following =-=[9, 26], we -=-define: Definition 16 (Asymptotic almost-periodic functions) A continuous function q(t) defined on the half-line (ts0) is called asymptotic almost-periodic (AAPF for short) if for every " ? 0 the... |

15 |
A system-theoretic Approach of Systems With Hystereis: Application to Friction Modelling and
- Bliman, Sorine
- 1993
(Show Context)
Citation Context ...) ) (0) = ( u 0 ; u 1 ; : : : u l\Gamma1 ) (1) where L and M are real coprime polynomials of order l and m respectively, H(u) is a nonlinear operator of hysteresis type proposed to model dry friction =-=[5, 6, 7], f is a c-=-ontrol input term and d a so-called dither function of "high frequency" (see Figure 1). Due to the differential and possibly multivalued nature of H, equation (1) may indeed be considered as... |

13 |
Almost Periodic Functions, Chelsea Pub
- Bohr
- 1947
(Show Context)
Citation Context ...R have F -repetitive derivative and satisfy all the desired properties. RR n2690 26 Pierre-Alexandre Bliman, Alexander M. Krasnosel'skii, Michel Sorine 4.4 Asymptotic almost-periodic dither Following =-=[9, 26], we -=-define: Definition 16 (Asymptotic almost-periodic functions) A continuous function q(t) defined on the half-line (ts0) is called asymptotic almost-periodic (AAPF for short) if for every " ? 0 the... |

13 |
Vibration Reduces Metal to Metal Contact and Causes an Apparent Reduction in Friction,"
- Godfrey
- 1967
(Show Context)
Citation Context ... to increase stability, in particular to quench limit cycles, or to smoothen or linearize the nonlinearities. Concluding experiments have been conducted in systems with relays [19], with dry friction =-=[4, 14, 15, 16]-=-, with rotative amplifiers [1], with DC motors [24]. Rigorous statements have also been proposed, concerning systems with memoryless nonlinearities [27, 28], backlash [12] or a special class of hyster... |

11 |
Hysteresis Operators and Tyre Friction Models: Application to Vehicle Dynamic Simulation
- Bliman, Bonald, et al.
- 1995
(Show Context)
Citation Context ...) ) (0) = ( u 0 ; u 1 ; : : : u l\Gamma1 ) (1) where L and M are real coprime polynomials of order l and m respectively, H(u) is a nonlinear operator of hysteresis type proposed to model dry friction =-=[5, 6, 7], f is a c-=-ontrol input term and d a so-called dither function of "high frequency" (see Figure 1). Due to the differential and possibly multivalued nature of H, equation (1) may indeed be considered as... |

9 | Structural stabilization and quenching by dither in nonlinear systems - Zames, Shneydor - 1977 |

8 |
Application of a method of averaging to the study of dither in non-linear systems
- Mossaheb
- 1983
(Show Context)
Citation Context ...er operator. However, we show that this operator is smoother (in particular, it is singlevalued): the hysteresis operator has been smoothed. The convergence holds on every compact set of R + , (as in =-=[20]-=-, where periodic dithers and memoryless nonlinearities are considered), but an additional hypothesis (essentially a persistence hypothesis on the limit solution plus an incremental sector inequality) ... |

7 |
Couplage entre frottement de glissement et frottement de pivotement dans la théorie de la toupie
- Contensou
- 1963
(Show Context)
Citation Context ... is singlevalued. A very interesting property of the preceding model is that it is linear for small velocities, and this linearization is indeed exact if the dither is chosen adequately. In the paper =-=[10]-=- by P. Contensou or in the book [21, chapter IV] by Ju.I. Neimark and al., same kind of results are presented in the context of gyroscopic motion, where the dither is created by combining sliding and ... |

7 |
Reduction of Static Friction by Sonic Vibrations
- Fridman, Levesque
- 1959
(Show Context)
Citation Context ... to increase stability, in particular to quench limit cycles, or to smoothen or linearize the nonlinearities. Concluding experiments have been conducted in systems with relays [19], with dry friction =-=[4, 14, 15, 16]-=-, with rotative amplifiers [1], with DC motors [24]. Rigorous statements have also been proposed, concerning systems with memoryless nonlinearities [27, 28], backlash [12] or a special class of hyster... |

6 |
A.V.: Systems with Hysteresis
- Krasnosel’skiĭ, Pokrovskiĭ
- 1983
(Show Context)
Citation Context ...(a particular subclass of Duhem model, according to the nomenclature in [25]). For a recent bibliography on experiments (resp. theory), see [24] (resp. [12]). For details on hysteresis operators, see =-=[18, 25]. Qualitat-=-ively, the key idea for using dither is the following: if d is e.g. a "fast" periodic function, one expects the input-output map f 7! u to be closely related to the corresponding map for the... |

5 |
Aström K.J., Lischinsky P., A new model for control of systems with friction
- C, Olsson
- 1995
(Show Context)
Citation Context ...f H for small values ofsu is given by the following linear time-invariant operator 6 Formulas like (6), deriving from a differential model of friction, have been proposed by C. Canudas de Wit and al. =-=[2]-=- to model steady state Stribeck effect. In our case,sg(su) \Gammasus(su) ! 0 for somesu would be necessary to have such decreasing friction with increasing velocity: this is impossible (becausesg(su)s... |

3 | Asymptotics of nonlinearities and operator equations (Birkhäuser - Krasnoselskii - 1995 |

2 |
Fufaev N.A.,Dynamics of Nonholonomic Systems
- I
- 1972
(Show Context)
Citation Context ...may consider it as a viscous linearization of H. Notice also that for large values of the input velocity,sH behaves like H (assg(ff) = jffj andss(ff) = sgn ff for large jffj): this may be linked with =-=[10, 21]-=-, where the averaging (which is spatial in these works rather than temporal) gives rise to viscous behavior for low steady state values of the velocity, and Coulomb friction for high values. Proof: ff... |

2 |
Experimental and analytical studies of the sinusoidal dither signal in a DC motor system
- Tung, Chen
- 1993
(Show Context)
Citation Context ...or to smoothen or linearize the nonlinearities. Concluding experiments have been conducted in systems with relays [19], with dry friction [4, 14, 15, 16], with rotative amplifiers [1], with DC motors =-=[24]-=-. Rigorous statements have also been proposed, concerning systems with memoryless nonlinearities [27, 28], backlash [12] or a special class of hysteresis [12] (a particular subclass of Duhem model, ac... |

1 |
Dithering as a factor in hysteresis elimination in rotating amplifiers
- Alexandrovitz, Rootenberg
- 1968
(Show Context)
Citation Context ...uench limit cycles, or to smoothen or linearize the nonlinearities. Concluding experiments have been conducted in systems with relays [19], with dry friction [4, 14, 15, 16], with rotative amplifiers =-=[1]-=-, with DC motors [24]. Rigorous statements have also been proposed, concerning systems with memoryless nonlinearities [27, 28], backlash [12] or a special class of hysteresis [12] (a particular subcla... |

1 |
Sethna P.R., A generalization of the method of averaging for systems with two time scales
- Balachandra
- 1975
(Show Context)
Citation Context ...1\Gammafl g 0 (t)) In the case where fl = 1 (which corresponds to bounded dithering velocity), this writes assx = "f (x; "; t; "t) where " = 1=n, a form which is classical in the c=-=ontext of averaging [23, 3, 8]-=-. In view of the classical results, we then define the operatorsH: 8u 2 W 1;1 loc (0; +1);sH(u) \Delta = Cx + Ds(su);sx = Axg(su) + Bsu; x(0) = x 0 2 R N (4) where we suppose the existence of the foll... |

1 |
Applying vibrators to eliminate nonlinearities in automatic regulators
- Bersekerskii
- 1947
(Show Context)
Citation Context |

1 |
Shahruz S.M., Stability of non-linear systems with backlash or hysteresis, Int
- Desoer
- 1986
(Show Context)
Citation Context ...with dry friction [4, 14, 15, 16], with rotative amplifiers [1], with DC motors [24]. Rigorous statements have also been proposed, concerning systems with memoryless nonlinearities [27, 28], backlash =-=[12]-=- or a special class of hysteresis [12] (a particular subclass of Duhem model, according to the nomenclature in [25]). For a recent bibliography on experiments (resp. theory), see [24] (resp. [12]). Fo... |

1 |
Fundamentals of servomechanisms
- MacColl
- 1945
(Show Context)
Citation Context .... This technique is used to increase stability, in particular to quench limit cycles, or to smoothen or linearize the nonlinearities. Concluding experiments have been conducted in systems with relays =-=[19]-=-, with dry friction [4, 14, 15, 16], with rotative amplifiers [1], with DC motors [24]. Rigorous statements have also been proposed, concerning systems with memoryless nonlinearities [27, 28], backlas... |