Page 224 - Electric Drives and Electromechanical Systems

220 Electric Drives and Electromechanical Systems

where K is the stiffness at the rotor position under consideration and I tot is the sum of
the motor inertia and the load inertia reflected back to the motor. The oscillating
behaviour can be damped out, if required, for single-step operations by the use of
mechanical (that is, viscous) or electrical damping. Excessive vibration of the
mechanical system will result in wear, leading to premature mechanical failures.
This resonance behaviour results in a loss of torque at well-defined stepping rates, as
shown in the pull-out torque-speed characteristic in Fig. 8.6. These stepping rates can be
determined from the natural frequency of the system, and they are given by,

f n
f k ¼ ðfor k ¼ 1; 2; . Þ (8.7)
k
Hence, if the motor and load have a natural resonance frequency of 120 Hz, the dips
1
in the speed-torque curve will occur at 40, 60, 120, steps s .

8.4 Control of stepper motors
The design of a drive system that incorporates a stepper motor should start with
consideration of the steady-state performance; the choice of the type and step angle of
the stepper motor is dictated largely by the maximum allowable positional error and by
the maximum stepping rate which is required. While a stepper motor can be operated
under either an open-loop or a closed-loop control system, this chapter will primarily
discuss the open-loop approach. Closed-loop stepper-motor drives are no different
from any other closed-loop drive, which are discussed in Chapter 10. Due to the
inherent operation of a stepper motor, one change of phase excitation will result in the
motor moving a specified, and accurately known, distance. The stepper motor’s
position is controlled by generating a pulse train of known length, which is converted
into the correct sequence of winding excitations by a translator, the winding power
being switched by the drive circuit. A block diagram of a typical open-loop-stepper
drive system is shown in Fig. 8.8. While the pulse generator and translator can be
implemented in discrete logic, it is the current practice to use a microprocessor to
control the whole process.
During the design process, information is required on the restrictions that have to
be placed on the timing of the pulse train to ensure satisfactory operation. These
restrictions can be summarised as:
The maximum step rate permitted for the required load torque. This can be deter-
mined from the motor’s pull-out characteristic.
The motor’s transient performance. If the load has a high inertia, the motor’s
speed must be ramped up to ensure that the motor remains in synchronism with
the step demand.