Friday, March 27, 2009

System Modeling - Linear Permanent Magnet Motors

Two types of position dependent disturbances are
considered: cogging force and force ripple. Cogging is
a magnetic disturbance force that is caused by attraction
between permanent magnets and translator. The force
depends on the relative position of the translator with
respect to the magnets, and it is independent of the motor
current. Force ripple is an electro-magnetic effect and
causes a periodic variation of the force constant c. Force
ripple occurs only if the motor current is different from
zero, and its absolute value depends on the required thrust
force and the relative position of the translator to the
stator. Both disturbances are periodic functions of the
position. [9]

Cogging is negligible in motors with iron-less translators
[14]. Figure 3 shows the nonlinear block diagram of a
servo system with brushless linear motor. The nonlinear
disturbances are the velocity depended friction force
Ffriction, and the position dependent cogging force
Fcogging and force ripple

The friction force is modeled with a kinetic friction
model. In the kinetic friction model the friction force is a
function of velocity only. The friction curve is identified
with experiments at different velocities. The friction has
a discontinuity at

because of stiction. Stiction
avoid accurate measurement of the thrust force without
motion of the carriage. A survey of friction models and
compensation methods is given in [17].
Aim of the force ripple identification is to obtain a
function of the thrust force Fthrust versus the control
signal u and the position x. A possible solution to identify
this function is to measure the thrust force Fthrust at
different positions x and control signals u. In this case an
additional force sensor and a screw cylinder for manual
position adjustment is necessary. In order to measure the
force ripple accurately, without motion of the carriage, a
frictionless air bearing support is necessary [7]. A solution
to avoid frictionless air bearings is the measurement of the
thrust force with moving carriage. At constant velocities
the friction force is also constant and can be treated as
additional load force. In this case an additional servo
system is needed to achieve the movement [18].

The main idea of the proposed identification method is
to identify the force ripple in a closed position control loop
by measuring the control signal u at different load forces
Fload and positions x. Neither additional force sensor nor
device for position adjustment are necessary. In order to
avoid inaccuracy by stiction the measurement is achieved
with moving carriage. The position of the carriage is
obtained from an incremental linear optical encoder with
a measurement resolution of 0:2m. The experiment
consists of several movements at constant low velocity
(1mm=s) and different load forces (0 : : : 70N). The
output of the position controller is stored at equidistant
positions. A controller with an integral component is used
to eliminate steady position error. During motion with
constant low velocity the dynamics of the motor have no
significant effect on the control signal u.

Figure 4 shows the controller output u versus the
translator position x. In this first experiment there is no
additional load force attached to the carriage. The period
spectrum of the controller signal ui is carried out via FFT.

Source ( pdf )


Relate Posts