February 1994 Hewlett-Packard Journal 75
Stepper Motor Simulation Model
The model used to simulate a permanent magnet stepper motor for the simulations
described in the accompanying article originated from a classic control systems
point of view. The model includes simple position and velocity feedback control
algorithms. Fig. 1 is a block diagram of the model.
A nonlinear block in the model allows the nonlinear characteristics of the stepper
to be included. This block makes the stepper torque output match the desired
torque for a given error signal.
The resultant nonlinear system was linearized by running it at a very high sample
rate of 40,000 samples per second. At this sample rate, speeds, positions and
currents are changing very slowly. Hence linear control systems analysis is valid.
The model was used to compute velocity profiles with several different motor
resistances, inductances, and so on. The lowest-resistance motor available in a
permanent magnet motor at this time was an 8-ohm motor. Fig. 2* shows that the
simulated velocity clearly does not reach the desired 1400 steps per second. This
motor fails and stalls in the real system. In Fig. 3,* the simulated velocity of a
2-ohm motor is shown. In this successful run, it appears that the motor has no
trouble reaching the desired 1400 steps per second. This motor was built and is
now the motor being used in the DeskJet 1200C printer.
The currents in a failing stepper motor are shown in Fig. 4* and the currents in a
stable, running stepper motor are shown in Fig. 5.* In the failing stepper motor, the
currents do not even reach their normal operating levels before they are switched
again. The characteristic hook in the graph of these currents reflects reality very
well for the case of insufficient voltage used to drive the motor.
Stephen B. Witte
Development Engineer
San Diego Printer Division
Fig. 1. Block diagram of the theoretical stepper motor model.
Reference
Generator
Reference
Position
+
S
Error
(Torque
Desired)
–
Nonlinear Stepper Simulator:
Coil Resistance and Inductance
Current Level Maximum
Holding Torque Maximum
Back EMF Feedback
Optimum Switching Time to Match Desired Torque
Half-Stepping and Full-Stepping Modes
Torque
Delivered
Linear Plant Differential Equations:
Moment of Inertia of Motor and Gears
Acceleration and Velocity of Rotor
Friction
Position
Response
Digital Filter:
Position and
Velocity
Feedback
Sample Time 25 Microseconds
* See top of next page for Figs. 2, 3, 4, and 5.
The term traction was used to define media slippage with the
drive surface to avoid preconceptions of friction behavior.
(Paper has a composite surface of fibers and fillers that cause
its frictional characteristics to be nonlinear with normal
forces beyond a relatively low surface shear stress.)
The characterization efforts revealed interactions with printer
components not previously considered. Affected components
were redesigned and the traction surface successfully devel-
oped in concert with these components. Analytical tools to
measure system and component performance were devel-
oped or enhanced by this project. This greatly improved cor-
relation of print quality goals with measured performance
and design specifications.
High-volume processes at multiple suppliers for this assembly
were characterized with proven process margins. Supplier
inspection processes were improved to fit part requirements
and inspection metrics.
Media Motor and Antibacklash Device
The goal for selecting the Deskjet 1200C media axis drive
was to design a motor and gearing system that is simple and
compact and has better speed and accuracy than we had
ever achieved before. Not only did this new gear drive system
have to have improved performance, but it also had to be
less expensive.
One key element of the media drive system is the motor
selection. The HP PaintJet, PaintJet XL, and PaintJet XL 300
printers use a hybrid stepper motor to drive gear trains that
control two roller media drive systems. These systems have
relatively high inertia and are limited in speed. They also
have multiple idler gears for the purpose of transferring
position control to a different location in the machine. For
the HP DeskJet 1200C printer, a decision was made to use a
double-pinion approach to eliminate the idler gears.
For low cost, we believed that a permanent magnet stepper
combined with an antibacklash device would be as accurate
as the hybrid stepper system. The key issues were: How do
we design a low-cost anti-backlash device? and, How do we
get the speed and torque that we need out of this low-cost
stepper motor?
To determine whether the permanent magnet stepper would
work, a theoretical model was developed that allows the
simulation of the motion of a stepper motor from a standing
