Showing posts with label Friction Model. Show all posts
Showing posts with label Friction Model. Show all posts
Monday, March 23, 2009
Model and Friction Compensation
1. Model and Friction Compensation
2. Actuators Friction Compensation
3 Friction Compensation algorithms 1
4. Friction Compensation in position and speed control
5. Friction Modelling near Striebeck Velocities
Wednesday, March 18, 2009
Friction Modelling near Striebeck Velocities
Many models were developed to explain the friction phenomenon.
These models are based on experimental results rather than
analytical deductions and generallydescribe the friction force (Ff)
in function of velocity (v). The classical static + kinetic + viscous
friction model is the most commonly used in engineering. This
model has three components: the constant Coulomb friction
term ( ) (v sign FC ), which depends only on the sign of velocity,
the viscous component ( v FV ), which is proportional with the
velocity and the static term ( S F ), which represents the force
necessary to initiate motion from rest and in mostof the cases its
value is grater than the Coulomb friction: (see Figure 1.)
These models are based on experimental results rather than
analytical deductions and generallydescribe the friction force (Ff)
in function of velocity (v). The classical static + kinetic + viscous
friction model is the most commonly used in engineering. This
model has three components: the constant Coulomb friction
term ( ) (v sign FC ), which depends only on the sign of velocity,
the viscous component ( v FV ), which is proportional with the
velocity and the static term ( S F ), which represents the force
necessary to initiate motion from rest and in mostof the cases its
value is grater than the Coulomb friction: (see Figure 1.)
The servo-controlled machines are generally lubricated with oil
or grace (hydrodynamic lubrication). Tribological experiments
showed that in the case of lubricated contacts the simple
static +kinetic + viscous model cannot explain some
phenomena in low velocity regime, such as the Striebeck effect.
This friction phenomenon arises from the use of fluid lubrication
and gives rise to decreasing friction with increasing velocities.
or grace (hydrodynamic lubrication). Tribological experiments
showed that in the case of lubricated contacts the simple
static +kinetic + viscous model cannot explain some
phenomena in low velocity regime, such as the Striebeck effect.
This friction phenomenon arises from the use of fluid lubrication
and gives rise to decreasing friction with increasing velocities.
To describe this low velocity friction phenomenon, four regimes
of lubrications can be distinguished (see Figure 2). Static Friction: (I.)
the junctions deform elastically and there is no excursion until the
control force does not reach the level of static friction force.
Boundary Lubrication: (II.) this is also solid to solid contact, the
lubrication film is not yet built. The velocity is not adequate to build
a solid film between the surfaces. A sliding of friction force occurs
in this domain of low velocities. The friction force decreases with
increasing velocity but generally is assumed that friction in boundary
lubrication is higher than for fluid lubrication (regimes three and four).
Partial Fluid Lubrication: (III.) the lubricant is drawn nto the contact
area through motion, either by sliding or rolling. The greater the
viscosity or motion velocity, the thicker the fluid film will be. Until the
fluid film is not thicker than the height of aspirates in the contact
regime, some solid-to-solid contacts will also influence the motion.
Full Fluid Lubrication: (IV.) When the lubricant film is sufficiently
thick, separation is complete and the load is fully supported by fluids.
The viscous term dominates the friction phenomenon, the
solid-to-solid contact is eliminated and the friction is 'well behaved'.
The value of the friction force can be considered as proportional with
the velocity. From these domains results a highly nonlinear behavior
of the friction force. Near zero velocities the friction force decreases
in function of velocity and at higher velocities the viscous term will
be dominant and the friction force increases with velocity. Moreover
it also depends on the sign of velocity with an abrupt change
when the velocity pass through zero.
For the moment no predictive model of the Striebeck effect is
available. Several empirical models were introduced to explain the
Striebeck phenomena, such as the Tustin model [2]:
of lubrications can be distinguished (see Figure 2). Static Friction: (I.)
the junctions deform elastically and there is no excursion until the
control force does not reach the level of static friction force.
Boundary Lubrication: (II.) this is also solid to solid contact, the
lubrication film is not yet built. The velocity is not adequate to build
a solid film between the surfaces. A sliding of friction force occurs
in this domain of low velocities. The friction force decreases with
increasing velocity but generally is assumed that friction in boundary
lubrication is higher than for fluid lubrication (regimes three and four).
Partial Fluid Lubrication: (III.) the lubricant is drawn nto the contact
area through motion, either by sliding or rolling. The greater the
viscosity or motion velocity, the thicker the fluid film will be. Until the
fluid film is not thicker than the height of aspirates in the contact
regime, some solid-to-solid contacts will also influence the motion.
Full Fluid Lubrication: (IV.) When the lubricant film is sufficiently
thick, separation is complete and the load is fully supported by fluids.
The viscous term dominates the friction phenomenon, the
solid-to-solid contact is eliminated and the friction is 'well behaved'.
The value of the friction force can be considered as proportional with
the velocity. From these domains results a highly nonlinear behavior
of the friction force. Near zero velocities the friction force decreases
in function of velocity and at higher velocities the viscous term will
be dominant and the friction force increases with velocity. Moreover
it also depends on the sign of velocity with an abrupt change
when the velocity pass through zero.
For the moment no predictive model of the Striebeck effect is
available. Several empirical models were introduced to explain the
Striebeck phenomena, such as the Tustin model [2]:
The model introduced in this paper is based on Tutin friction model
and on its development, the following aspects were taken into
consideration:
- allows different parameter sets for positive and negative velocity regime
- easily identifiable parameters
- the model clearly separates the high and low velocity regimes
- can easily be implemented and introduced in real time control algorithms
For the simplicity, only the positive velocity domain is considered,
but same study can be made for the negative velocities. Assume
that the mechanical system moves in 0 … vmax velocity domain.
Consider a linear approximation for the exponential curve represented
by two lines: d1+ which cross through the (0,Ff(0)) point and it is
tangent to curve and d2+ which passes through the (vmax, Ff(vmax)
point and tangential to curve. (see Figure 3.) These two lines meet
each other at the vsw velocity. In the domain 0 … vsw the
d1+ can be used for the linearization of the curve and d2+ is used
in the domain vsw… vmax. The maximum approximation error
occurs at the velocity vsw for both linearizations.
If the positive part of the friction model (2) is considered (v>0),
the obtained equations for the d1+ and d2+, using Taylor expansion,
are:
and on its development, the following aspects were taken into
consideration:
- allows different parameter sets for positive and negative velocity regime
- easily identifiable parameters
- the model clearly separates the high and low velocity regimes
- can easily be implemented and introduced in real time control algorithms
For the simplicity, only the positive velocity domain is considered,
but same study can be made for the negative velocities. Assume
that the mechanical system moves in 0 … vmax velocity domain.
Consider a linear approximation for the exponential curve represented
by two lines: d1+ which cross through the (0,Ff(0)) point and it is
tangent to curve and d2+ which passes through the (vmax, Ff(vmax)
point and tangential to curve. (see Figure 3.) These two lines meet
each other at the vsw velocity. In the domain 0 … vsw the
d1+ can be used for the linearization of the curve and d2+ is used
in the domain vsw… vmax. The maximum approximation error
occurs at the velocity vsw for both linearizations.
If the positive part of the friction model (2) is considered (v>0),
the obtained equations for the d1+ and d2+, using Taylor expansion,
are:
Thus the linearization of the exponential friction model with bounded
error can be described by two lines in the 0 … vmax velocity domain:
error can be described by two lines in the 0 … vmax velocity domain:
Same study can be made for negative velocities. Based on
linearization, the friction can be modelled as follows:
linearization, the friction can be modelled as follows:
It can be seen that the model is linearly parameterized and it
can be implemented with low computational cost.
Source
http://bmf.hu/journal/Marton_Lantos_7.pdf
can be implemented with low computational cost.
Source
http://bmf.hu/journal/Marton_Lantos_7.pdf
Monday, March 16, 2009
Model and Friction Compensation
Friction Models and Friction Compensation
H. Olsson† K.J. Åström† C. Canudas de Wit‡
M. Gäfvert† P. Lischinsky††
Introduction
Friction occurs in all mechanical systems,e.g. bearings,
transmissions, hydraulic and pneumatic cylinders, valves, brakes
and wheels. Friction appears at the physical interface between
two surfaces in contact. Lubricants such as grease or oil are often
used but the there may also be a dry contact between the
surfaces. Friction is strongly influenced by contaminations. There
is a wide range of physical phenomena that cause friction, this
includes elastic and plastic deformations, fluid mechanics and
wave phenomena, and material sciences
Friction phenomena
Static models
Dynamic models
Comparison of the Bliman-Sorine and the LuGre
Models
Control Systems Applications
Friction Compensation
There are many ways to compensate for friction. A very simple
way to eliminate some effects of friction is to use a dither signal,
that is a high frequency signal that is added to the control signal.
An interesting form of this was used in gyroscopes for auto pilots
in the 1940s. There the dither signal was obtained simply by
a mechanical vibrator, see J41K. The effect of the dither is that it
introduces extra forces that makes the system move before the
stiction level is reached. The effect is thus similar to removing
the stiction. A modern version is the Knocker, introduced in J32K,
for use in industrial valves. The effects of dither in systems with
dynamic friction HLuGreI was recently studied in J43K.
more
Model Based Friction Compensation in a DC Motor
Tegoeh Tjahjowidodo, Farid Al-Bender, Hendrik Van Brussel
1 Introduction
Friction modeling and identification is a prerequisite for
the accurate control of electromechanical systems. In the
literature, identification of friction in a motor system
usually considers only classical friction models, such as
Coulomb and Viscous friction. Presliding motion, which is
apparent in many friction investigations, is usually
neglected. The presliding regime is taken into account in
some advanced models, such as LuGre model and the most
recent Generalized Maxwell-Slip (GMS) model.
Unfortunatelly, LuGre does not accommodate the unique
behavior of presliding faithfully. The GMS model manages
to overcome those difficulties by modeling friction as a
Maxwell-Slip model where the slip elements satisfy a
certain, new state equations [1,2].
Once the friction models have been optimized, position
control incorporating friction compensation is performed
[1,3]. For this purpose, the inertial force and friction
behavior are compensated for using a feedforward control,
while a simple (PID) feedback part is included to track setpoint
changes and to suppress unmeasured disturbances.
2 Modeling and Results
more
H. Olsson† K.J. Åström† C. Canudas de Wit‡
M. Gäfvert† P. Lischinsky††
Introduction
Friction occurs in all mechanical systems,e.g. bearings,
transmissions, hydraulic and pneumatic cylinders, valves, brakes
and wheels. Friction appears at the physical interface between
two surfaces in contact. Lubricants such as grease or oil are often
used but the there may also be a dry contact between the
surfaces. Friction is strongly influenced by contaminations. There
is a wide range of physical phenomena that cause friction, this
includes elastic and plastic deformations, fluid mechanics and
wave phenomena, and material sciences
Friction phenomena
Static models
Dynamic models
Comparison of the Bliman-Sorine and the LuGre
Models
Control Systems Applications
Friction Compensation
There are many ways to compensate for friction. A very simple
way to eliminate some effects of friction is to use a dither signal,
that is a high frequency signal that is added to the control signal.
An interesting form of this was used in gyroscopes for auto pilots
in the 1940s. There the dither signal was obtained simply by
a mechanical vibrator, see J41K. The effect of the dither is that it
introduces extra forces that makes the system move before the
stiction level is reached. The effect is thus similar to removing
the stiction. A modern version is the Knocker, introduced in J32K,
for use in industrial valves. The effects of dither in systems with
dynamic friction HLuGreI was recently studied in J43K.
Friction Models and Friction Compensation
Karl J. Åström
Slide Content
1. Introduction
2. Friction Models
3. The LuGre Model
4. Effects of Friction on Control Systems
5. Friction Compensation
6. Summary
Friction Models and Friction Compensation
1. Introduction
2. Friction Models
3. The LuGre Model
4. Effects of Friction on Control Systems
5. Friction Compensation
6. Summary
Static Models
Karl J. Åström
Slide Content
1. Introduction
2. Friction Models
3. The LuGre Model
4. Effects of Friction on Control Systems
5. Friction Compensation
6. Summary
Friction Models and Friction Compensation
1. Introduction
2. Friction Models
3. The LuGre Model
4. Effects of Friction on Control Systems
5. Friction Compensation
6. Summary
Static Models
more
Model Based Friction Compensation in a DC Motor
Tegoeh Tjahjowidodo, Farid Al-Bender, Hendrik Van Brussel
1 Introduction
Friction modeling and identification is a prerequisite for
the accurate control of electromechanical systems. In the
literature, identification of friction in a motor system
usually considers only classical friction models, such as
Coulomb and Viscous friction. Presliding motion, which is
apparent in many friction investigations, is usually
neglected. The presliding regime is taken into account in
some advanced models, such as LuGre model and the most
recent Generalized Maxwell-Slip (GMS) model.
Unfortunatelly, LuGre does not accommodate the unique
behavior of presliding faithfully. The GMS model manages
to overcome those difficulties by modeling friction as a
Maxwell-Slip model where the slip elements satisfy a
certain, new state equations [1,2].
Once the friction models have been optimized, position
control incorporating friction compensation is performed
[1,3]. For this purpose, the inertial force and friction
behavior are compensated for using a feedforward control,
while a simple (PID) feedback part is included to track setpoint
changes and to suppress unmeasured disturbances.
2 Modeling and Results
more
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