J.-P. Hauschilda, G. R. Hepplerb and J. J. McPheeb
Abstract
Friction models and methods of friction compensation as
applied to harmonic drive servo-actuators are investigated.
In the absence of output torque measurements and
output shaft encoder data nearly complete friction compensation
is achieved. Simulation and experimental results showing
the application of the friction compensation are given.
Friction compensation
The methods of friction compensation to be discussed here
are restricted to those that are applicable to HD actuators
without output torque measurements or encoders
mounted on the output shaft. The simplest way to compensate
friction in servo drives is a feed-forward element as shown
in Figure 1 (with the feed-back part removed). A friction
torque f () is added to the input torque as an offset to
the input signal for the motor depending on the sign of the
input. In the ideal case, this offset should be exactly the friction
torque but in practice the offset should always under compensate
the real friction to avoid instabilities. Feed-forward compensation
is limited to the reduction of the Coulomb friction. It cannot
compensate stiction effects nor viscous friction, does not
provide back drivability to the motor, would not prevent large
steady state errors and it would increase the non-linearities
of the motor[4]. Compensation based on Coulomb friction
based models has an infinite slope for a zero input which can
cause an undesirable chattering when the friction compensation
is used in a direct feedback loop. A remedy would be
a decreased slope at zero input[5], but the steady-state error
of the system can still increase due to the under compensation
of the friction at low velocities. An extension of the feed-forward
friction compensation is shown in Figure 1 where there is now
an additional feed-back element which provides a compensation
for viscous friction and can include the Stribeck effect.
A compensation of the stiction
The methods of friction compensation to be discussed here
are restricted to those that are applicable to HD actuators
without output torque measurements or encoders
mounted on the output shaft. The simplest way to compensate
friction in servo drives is a feed-forward element as shown
in Figure 1 (with the feed-back part removed). A friction
torque f () is added to the input torque as an offset to
the input signal for the motor depending on the sign of the
input. In the ideal case, this offset should be exactly the friction
torque but in practice the offset should always under compensate
the real friction to avoid instabilities. Feed-forward compensation
is limited to the reduction of the Coulomb friction. It cannot
compensate stiction effects nor viscous friction, does not
provide back drivability to the motor, would not prevent large
steady state errors and it would increase the non-linearities
of the motor[4]. Compensation based on Coulomb friction
based models has an infinite slope for a zero input which can
cause an undesirable chattering when the friction compensation
is used in a direct feedback loop. A remedy would be
a decreased slope at zero input[5], but the steady-state error
of the system can still increase due to the under compensation
of the friction at low velocities. An extension of the feed-forward
friction compensation is shown in Figure 1 where there is now
an additional feed-back element which provides a compensation
for viscous friction and can include the Stribeck effect.
A compensation of the stiction
force is theoretically possible, but in practice not applicable
because an infinite slope of both compensators for zero velocity
would cause chattering. Reducing this slope would result in a zero
velocity reading and therefore prevent any feed-back
compensation. This type of friction compensation introduces
an increased non-linearity as in the pure feed-forward case.
more
SUBMICROMETER FRICTION COMPENSATION USING
VARIABLE-GAIN SLIDING MODE CONTROL
Paul I. Ro
ABSTRACT
The paper discusses a sliding mode control suitable
for compensation of nonlinear microdynamic friction
and parameter changes in a ball-screw driven slide
system. The conventional, fixed-gain sliding mode
control has a limited range of performance in the
presence of varying nonlinear friction in submicrometer
trajectory tracking. In this work, an
algorithm that effectively calculates variable
switching gain based on the observation of parameter
variation and friction disturbance is proposed. To
verify the effectiveness of the proposed algorithm, the
comparison with the conventional slide mode control
is presented and experimentally verified. It is shown,
from the result of this work, that a variable switching
gain was critically important in compensating for
varying nonlinear friction in the sub-micrometer
motion range for ball-screw driven systems.
because an infinite slope of both compensators for zero velocity
would cause chattering. Reducing this slope would result in a zero
velocity reading and therefore prevent any feed-back
compensation. This type of friction compensation introduces
an increased non-linearity as in the pure feed-forward case.
more
SUBMICROMETER FRICTION COMPENSATION USING
VARIABLE-GAIN SLIDING MODE CONTROL
Paul I. Ro
ABSTRACT
The paper discusses a sliding mode control suitable
for compensation of nonlinear microdynamic friction
and parameter changes in a ball-screw driven slide
system. The conventional, fixed-gain sliding mode
control has a limited range of performance in the
presence of varying nonlinear friction in submicrometer
trajectory tracking. In this work, an
algorithm that effectively calculates variable
switching gain based on the observation of parameter
variation and friction disturbance is proposed. To
verify the effectiveness of the proposed algorithm, the
comparison with the conventional slide mode control
is presented and experimentally verified. It is shown,
from the result of this work, that a variable switching
gain was critically important in compensating for
varying nonlinear friction in the sub-micrometer
motion range for ball-screw driven systems.
A simple conceptual model for the system was
developed in Figure 1 that shows the idealized model
of the mechanical components of the system. In the
current system setup, as seen in Figure 1, the slide
position, 2 x , is the only state measured by a laser
interferometer. The slide velocity, 2 x& , is gathered
digitally by first order difference of 2 x . The nut
position and its velocity, 1 x and 1 x& , are not
measurable. The built-in tachometer can be used for
measuring the angular velocity of the ball-screw but
the signal output is very noisy. The tachometer
signal is usually good for motor speeds orders of
magnitude greater than that used in submicrometer
motion. The ball-screw rotation and its angular
velocity, and & , are thus estimated. The
unmeasurable state variables, x1 and 1 x& , are estimated
by a Kalman filter (Ro, Shim and Jeong, in press).
more
developed in Figure 1 that shows the idealized model
of the mechanical components of the system. In the
current system setup, as seen in Figure 1, the slide
position, 2 x , is the only state measured by a laser
interferometer. The slide velocity, 2 x& , is gathered
digitally by first order difference of 2 x . The nut
position and its velocity, 1 x and 1 x& , are not
measurable. The built-in tachometer can be used for
measuring the angular velocity of the ball-screw but
the signal output is very noisy. The tachometer
signal is usually good for motor speeds orders of
magnitude greater than that used in submicrometer
motion. The ball-screw rotation and its angular
velocity, and & , are thus estimated. The
unmeasurable state variables, x1 and 1 x& , are estimated
by a Kalman filter (Ro, Shim and Jeong, in press).
more
