Page 104 - Servo Motors and Industrial Control Theory -

5.6 Stepping Motors for Position Control Applications 97

The natural frequency gives the speed of response and it can be seen that as the iner-
tia increases the natural frequency reduces and as K increases the natural frequency
θ
increases. The damping ratio is
ξ C C 1
2 : = : ξ = ⋅ (5.12)
ω n K θ 2 KJ ⋅
θ

If the mechanical damping coefficient C is zero, the rotor will oscillate continuous-
ly. In practice, there is some mechanical friction that increases the damping ratio.
It means that the rotor moves one step and will oscillate little and the teeth become
aligned with the stator. Both K and J reduce the damping ratio.
θ
For a better mathematical model, the inductance of the stator windings must be
taken into account. This only changes the voltage equation and the transfer function
becomes third order which means that the motor might become unstable.

5.5 Speed–Torque Characteristic Behavior of Stepping
Motors

In the previous section, the dynamic behavior of stepping motors was studied. In
many applications the stepping motor is required to move several steps. In this case
the motor is moved one step at a time. It is interesting to study that how fast the
motor can be moved one step at a time. It obvious that when the motor is moved
one step the next step must be applied when the rotor has reached at least 80 or
90 % of the previous step. This is shown for a typical stepping motor in Fig. 5.7. It
shows the speed-torque characteristic of a typical stepping motor. The stepping rate
depends on the applied torque and implicitly depends on the rotor inertia. At zero
torque, maximum stepping rate defined by manufacturer can be used which means
the motor can be moved by maximum speed and then decelerate so the rotor has
moved to the required position.
There are two curves on the diagram; one for pull-in torque and one for pull-out
torque. It means that once the rotor has accelerated to the near maximum speed the
switching rate can be increased further. This diagram must be provided by manu-
facturers.

5.6 Stepping Motors for Position Control Applications

When stepping motors are used for position control applications, they can be oper-
ated in open loop. The danger is that the stepping motors may lose steps when they
have to be moved several steps. In open loop, the switching rate must be sufficiently
small so that correct positioning is achieved. To overcome this problem, they must
be operated in closed loop. The output position is usually measured by a position