A method for determining a friction to be adjusted (F) in a power steering system, the method comprising the following steps:
- determining a speed (v), from a measurement of a speed (v) of a part of the power steering system and/or from a measurement of a steering wheel torque (T3) applied to a steering wheel of the power steering system;
- determining the friction to be adjusted (F) on the basis of a modified LuGre model (LM),
- said modified LuGre model (LM) determining the friction to be adjusted (F) as a function of a state (z) of the system, a time derivative (ż) of the state (z) being determined as a function of said state (z) of the system, the speed (v), a first gain (σ0), a second gain (β), and a coulomb friction (Fc), according to an equation of the form:
- z
- .
- =
- v
-
- (
- 1
- -
- α
-
- (
- z
- ,
- v
- )
-
- σ
- 0
-
- z
- F
- c
-
- sign
-
- (
- v
- )
- )
-
- in
-
- which
- :
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- Math
-
- 1
- ]
- α
-
- (
- z
- ,
- v
- )
- =
- {
- α
-
- (
- z
- )
- if
-
- sign
-
- (
- z
- )
- =
- sign
-
- (
- v
- )
- 0
- if
-
- sign
-
- (
- z
- )
- ≠
- sign
-
- (
- v
- )
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- where sign (z) is the sign of the quantity z and sign (v) is the sign of the quantity v, and in which,
- α
-
- (
- z
- )
- =
- {
- 0
- if
-
- ❘
- "\[LeftBracketingBar]"
- z
- ❘
- "\[RightBracketingBar]"
- ≤
- z
- b
-
- a
- 1
- 2
-
- (
- sin
- (
- π
-
- ❘
- "\[LeftBracketingBar]"
- z
- ❘
- "\[RightBracketingBar]"
- -
- z
- max
- (
- 1
- +
- β
- )
- 2
- z
- max
- (
- 1
- -
- β
- )
- )
- +
- 1
- )
- if
-
- z
- b
-
- a
- ≤
- ❘
- "\[LeftBracketingBar]"
- z
- ❘
- "\[RightBracketingBar]"
- ≤
- z
- max
- 1
- if
-
-
- ❘
- "\[LeftBracketingBar]"
- z
- ❘
- "\[RightBracketingBar]"
- ≥
- z
- max
-
- with
- ,
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- ]
- z
- max
- =
- F
- c
- σ
- 0
-
- and
-
- with
- ,
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-
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- ]
- z
- b
-
- a
- =
- β
- ·
- z
- max
- .
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- ]