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Ch67-I044963.fm Page 331 Tuesday, August 1, 2006 5:54 PM
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5:54 PM
Tuesday, August
Ch67-I044963.fm
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amplifier to the level that the current command reaches saturation. After its saturation, output of the
integrating amplifier is still increased, but it no longer matters. Then, when motor velocity reaches the
desired velocity, the velocity loop is generally used to maintain motor velocity at the desired velocity.
However, in this case, it could not do so since output of the integrating amplifier is so high that it could
not be reduced fast enough. Therefore, overshoot occurs as shown in Figure 2(a) and 3(a). In order to
prevent integral windup, anti-windup must be added to the integrating amplifier. It can reduce
overshoot and settling time of step responses as shown in Figure 2(b) and 3(b). However, the velocity
loop with anti-windup still degrades some dynamic characteristics of the servo motor. The frequency
responses at high frequency are degraded, as demonstrated in Figure 4, especially, when high-level
input is fed into the system due to saturation of the current limiter.

POSITION CONTROL WITH CURRENT LOOP
A position control must drive a servo motor so as to hold the position of the motor at the desired
position commanded by an external source. The position amplifier amplifies the position error between
the measured position and the desired position, and, then, this amplified position error is used to drive
the servo motor to minimize the position error. The typical position loop is shown in Figure l(c). The
simulation results of the position loop are shown in Figure 5 and 6. The simulation parameters are set
as follow. The position gain, VH, is 100. The step position commands are 0.04, 0.16, and 0.63 radian,
respectively. Other parameters are the same as that of the previous section. From the simulation results,
this positioning system has underdamped responses, large overshoot, ringing and long settling time
because of effects of high position gain and saturation.

DEVELOPMENT OF HIGH SPEED AND HIGH ACCURACY POSITIONING SYSTEM

For the purpose of development of the high-speed and high-accuracy positioning system, the position
loop controller has been modified to work in either the velocity control mode or the position control
mode. Therefore, the position amplifier, V H in Figure l(c), has been replaced with a non-linear
amplifier in the case of velocity control mode and linear amplifier in the case of position control mode.
Functionality of the modified position amplifier is described below. The linear region of position error
is set to [-s,+s], and the initial mode of the position amplifier is position mode, with a linear gain (VH).
Then, the condition for switching between the position mode and velocity mode is described below.
For condition 1, if the initial position error is not in the region of [-s,+s], the amplifier mode is
changed to the velocity mode with input-output characteristic functions as demonstrated in Eqn. 2. For
condition 2, if the current mode of the amplifier is the velocity mode, and the current motor velocity is
approximated zero, the amplifier mode is set to the position mode (linear mode) with a linear gain VH-

V(x) = V Hl^ n J.v-sgn(.v ( , fr(n )x£ where x > sgn(.v m. (n)x£, V(x) = -f' Hj . v; , Jsgn(x , <ru))x £- x where.v < sgn(x <,^ ln)x t" v /
where VH(NLJ is non-linear gain, x is the motor position, and x errfi) is the initial position error.
Simulation of a positioning system with a modified position amplifier is studied, the simulation
parameters are set as follows. The linear gain, VH, is 100. The non-linear gain, VHINL), is 6. The e is
0.01. The step position commands are 0.04, 0.16, and 0.63 radian, respectively. Other parameters are
the same as that of the previous section. By choosing VH(NL) and s, a trial and error technique has been
used as shown in Figure. 10. It shows that 6 of VH(NL) and 0.01 of s give the best system responses.
The simulation results of the modified position loop are shown in Figure 7 and 8. Phase plan diagrams
of the modified system and the transfer characteristics of the modified position amplifier are shown in
Figure 9. Comparing step responses in Figure 7 with that of the pervious system in Figure 5, it could
be understood that the modified positioning system can reduce overshoot, ringing and settling time.