National Conference on Advances in Mechanical Engineering Science (NCAMES-2016)
Modeling Stepper Motor Control System with
Micro-Stepping Excitation Mode
Navya Thirumaleshwar, Hegde1Dr. S. Meenatchi Sundaram2, , Aldrin Vaz3
1
Assistant Professor, Department of Mechanical Engineering,
Srinivas Institute of Technology,Valachil, Mangaluru, Karnataka State, India – 574143
2
Associate Professor, Department of Instrumentation & Control Engineering
Manipal Institute of Technology, Manipal, Karnataka, India
Abstract - This paper aims at providing an detailed exposure
to the basic operation of a stepper motor, its drive and logic.
The modeling and simulation of the electromechanical
behavior of step motors are of high importance because they
are often used in satellite and sub satellite systems. After
having presented the mathematical modeling which leads to
the stepper motor running’s solution, using the Runge-Kutta
numerical integration method. This paper results in designing
a driver circuits for full step, half step, micro stepping of
bipolar permanent magnet stepper motor of given
requirements. The full-step and half-step motors tend to be
slightly jerky in their mode of operation as the motor moves
from step to step. The amount of resolution is increasing, in
contrast we can reduce the resonance, vibration problems
using micro-stepping at a low step rate. The micro-stepping
with step motor is used in large number of applications like
pointing an antenna towards a desired direction in order to
minimize de-pointing losses or moving the telescope to track a
star/planet motion.
Key Words - Stepper motor, full step, half step, micro-step.
I. INTRODUCTION
A stepper motor is a marvel in simplicity and reality. Motor
has no brushes or contacts and it is a synchronous motor with
the magnetic field electronically switched to rotate the
armature magnet. The essential function of a step motor is to
translate switching excitation changes into precisely defined
increments of rotor position. A stepper motor is an electro
mechanical device, which converts electrical pulses into
discrete mechanical movements. The name stepper is used
because this motor rotates through a fixed angular step in
response to each input current pulse received by its controller.
A.Types of Step Motors
First type is the variable reluctance motors given. The
second type of step motor is the permanent magnet motor,
which
utilizes
permanent
magnets
to
perform
electromechanical rotation. Finally, the hybrid step motors
combine mechanical and electromagnetic properties of other
two types to achieve higher torque. Each coil around a single
stator tooth belongs to a single phase in both motor types. This
is called the monofilar winding scheme. Same voltage polarity
ISSN: 2231-5381
applied to monofilar windings will create a magnetic flux
always in the same direction. The stator tooth around which
the coil is wound will have a single magnetic polarity dictated
by the winding orientation. This kind of excitation is called the
unipolar drive of the winding.
First of all, the basic method of wave drive excitation is
given and it is followed by two-phase on excitation, which is
an alternative to produce full steps. The discussion continues
with half step excitation, which doubles the effective step
number and thus increases the positional accuracy. Finally,
micro-stepping excitation, which is the most important of all
regarding this paper, is explained.
The details of stepper motor modeling are given in section
2. The stepper motor specifications and simulation results are
presented in section 4.
II. STEPPER MOTOR MATHEMATICAL MODEL
In order to investigate the dynamics of mechanisms driven
by stepper motors a model had to be created[2]. With a
minimum background of basic laws of electromagnetism and
motor physics, this section provides a brief derivation of a
nonlinear model of the 2-phase PM stepper motor shown in
Figure 1. As explained earlier, when the windings of a phase
are energized, a magnetic dipole is generated on the stator
side. If for example phase 2 is active (phase 1 is switched off),
winding 3 produces an electrical north pole and winding 4 a
South Pole. Alternatively powering the windings of the stator
commands the rotor flux to follow the stator field.
Figure 1.Block diagram of stepper motor.
Va = voltage applied to the winding A.
ia = winding current.
ea = flux induced voltage in the winding.
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National Conference on Advances in Mechanical Engineering Science (NCAMES-2016)
ic = winding current.
θ= motor position.
D = Viscous friction constant.
Kc = motor torque constant.
ec = flux induced voltage in the winding.
State variable form:
Vc = voltage applied to the winding C.
Stator winding A,
Va
di
L a
dt
Ria
ea
Stator winding C,
Vc
a
Ric
and
L
c
dic
dt
ec
Are the magnetic flux in the stator windings A and
C,
a
m
m
cos n
= maximum stator flux.
d
dt
dw
dt
dia
dt
dic
dt
w
T
Jr
1
Va
L
1
Vc
L
windings given by,
ea
ec
m
d(4.6)
c
dt
d
mn m sin n
dt
mn
m
cos n
d
dt
Kc w sin n
K c w cos n
m=number of turns on the stator windings.
Conservation of energy:
Mechanical power out = electrical power in
wTa
ia ea
wTc
ic ec
Ta
ia K c sin n
Tc
ic
Kc
cos n
Jr
III. STEPPER MOTOR MODEL SPECIFICATIONS
The voltages ea andec that are induced in the stator
d
m a
dt
K
Dr
w ia c sin n
Jr
Jr
K
R
ia w c sin n
L
L
Kc
R
ib w
cos n
L
L
ic K c cos n
Complete model using equations:
SSM motor
parameter
Rotor inertia
Power
Resistance
Time const
Voltage
Inductance
Load inertia
Holding
torque
Gear ratio
Step size
Torque
constant
Maximum
rate current
Table 1.Motor specifications
values
SAGEM
values
motor
parameter
1e-07kgm2
Rotor inertia
500e-07kgm2
11w
Power
8w
48 ohms
Resistance
42 ohms
2msec
Time const
2msec
28v
Voltage
13v
96mH
Inductance
105mH
1e-07kgm2
Load inertia
5kgm2
0.7Nm
Holding
0.7Nm
torque
157
Gear ratio
200
1 degree
Step size
15degree
1.489Nm
Torque
0.12Nm
constant
0.47A
Maximum
0.31A
rate current
IV. METHODOLOGY
Algorithms can be implemented with the help of
MATLAB. The common methodology in implementing
algorithms consists of the following steps
Define the initial and final conditions.
Define the motor specifications along with the initial
and final time of the motor to run.
Define Pulse width in PPS depending on the step size of
motor chosen.
Find the acceleration/deceleration, speed and position
for different excitation modes of the motor.
Plot the results.
d2
d
J r 2 Dr
T Ta Tc
dt
dt
T ia K c sin n ic K c cos n
di
Va Ria L a wKc sin n
dt
dic
Vc Ric L
wK c cos n
dt
Where,
ia , ic = currents in phases a and c.
L , R = self-inductance and resistance of each phase winding
ea , ec = currents phases a and c.
n = number of rotor teeth on each of the two rotor poles.
Jr = rotor inertia.
W = Rotor speed.
ISSN: 2231-5381
V. STEP MOTOR EXCITATION MODES
SIMULATION AND RESULTS
Mathematical modeling of the two phase stepper motor is
derived and the equation in the state variable form is solved
using Runge-Kutta numerical integration method. Solutions for
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Ia, Ib, w, Theta are calculated, simulated. Initial time and final
time for operation of motor and step size are defined. Total
inertia of the motor is calculated as JT=Jm+ (Jl / N2) when the
motor is connected to the load of inertia J l .The value of w and
Theta is found and the graph is plotted where calculation done
with load connected to the motor by a gear ratio of 1:157 from
the equations of stepper modeling.
A.Full Step Mode Excitation
1. Full step (single coil excitation)
Motor operated with only one phase energized at a time.
This mode used when torque versus speed performance not
important where motor operates at fixed speed and load
conditions. This mode requires least amount of power from the
power supply of any of the excitation modes.
Table 2.Full step sequence.
A
C
B
D
Figure 3.Plot of pulse generated by ABCD coils.
1
1
0
0
0
2
0
1
0
0
3
0
0
1
0
winding A current
0.6
0.4
0
0
0
1
When input voltage is applied then coil AC gets energies
so BD de - energizes. Coil A generates positive pulse and
same way when the coil C energies, then also positive pulse
are generated as shown in figure 3.
In next sequence when input voltage is applied then coil BD
gets energies so AC de - energizes. Where coil B generates
negative pulse of that of A and same way when the coil D
energies, then negative pulse of coil are generated as shown in
fig 3. Pulse generated by the all windings of the motor ABCD
as shown in below figure 2.
Current from the coil A, from the equation as same as the
voltage in the winding A, where the first pulse started from the
zero as same to controller design. Current from the coil C,
from the equation as same as the voltage in the winding C,
where the first pulse is missing as same to controller design as
shown in figure 4 and 5.
pulse generated by coil ABCD
30
0
-0.2
-0.4
-0.6
-0.8
0
0.01
0.02
0.03
0.04 0.05 0.06
time in msec
0.07
0.08
0.09
0.1
Figure 4.Plot of Current generated by A coil
winding C current
0.6
0.5
0.4
Icp in amps
4
Iap in amps
0.2
0.3
0.2
0.1
20
0
V in volts
10
-0.1
0
0.01
0.02
0.03
0.04 0.05 0.06
time in msec
0.07
0.08
0.09
0.1
Figure 5.Plot of current generated by C coil.
-10
Two phase SSM stepper motor, which is used in
ASTROSAT SATELLITE having high resolution and high
accuracy where theta measured to be of step angle of 1deg as
shown in the below figure 7.
-20
-30
0
0
0.01
0.02
0.03
0.04
t msec
0.05
0.06
0.07
Figure 2.Plot of pulse generated by ABCD coils.
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1
2
3
4
A
1
0
0
1
C
1
1
0
0
B
0
1
1
0
D
0
0
1
1
Figure 6.Plot of motor speed motor rotation.
Figure 9.Plot of pulse generated by ABCD coil.
Pulse generated by the all windings of the motor ABCD as
shown in above figure 9.
Current generated by the A and C coils in dual phase
excitation is √2*I the current as in case of single coil excitation
in figure 10 and 11.
Figure 7.Plot of motor speed motor rotation.
Figure 10.Plot of current generated by A and C coil.
Figure 8.Plot of torque generated by motor.
Torque generated by SSM motor is as sown in figure 8 for
single coil excitation.
2. Full step (dual phase coil excitation)
Motor operated with two phases energized at a time. This
mode provides good torque and speed performance with a
minimum of resonance problems. Dual excitation provides 3040% more torque than single excitation. Motor requires twice
power from driver power supply.
Table 3.Full step dual phase sequence
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Figure 11.Plot of current generated by A and C coil.
Motor position is having less resonance and vibration as
compared to single coil excitation as shown in figure 12. This
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National Conference on Advances in Mechanical Engineering Science (NCAMES-2016)
mode gives better speed and torque performance. Motor
position is half way to that of a single coil excitation as shown
in below figure 13.
resolution. Complete freedom from resonance problems.
Motor operate at wide range of speeds. This mode used to
drive almost any load commonly encountered. This mode also
used in less torque applications.
Table 4.Half step sequence.
1
2
3
4
5
6
7
8
A
1
1
0
0
0
0
0
1
C
0
1
1
1
0
0
0
0
B
0
0
0
1
1
1
0
0
D
0
0
0
0
0
1
1
1
Pulse generated by the all windings of the motor ABCD as
shown in below figure 15:
Figure12.Plot of motor speed.
Figure13. Plot of motor rotation.
Torque generated by SSM motor is as sown in figure 14
for double coil excitation.
Figure 14.Plot of torque generated by motor.
Figure 15.Plot of pulse generated by ABCD coils.
Figure 16.Plot of pulse generated by ABCD coils.
B.Half Step Mode Excitation
It is alternate single and dual phase operation results in half
of normal step. This mode provides twice the full step
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Figure 17.Plot of current generated by A coil.
Current generated by the A and C coils in half step
excitation is same the current as in case of full step excitation
as shown in figures 17 and 18.
Figure 20.Plot of motor rotation.
Figure 21.Plot of torque generated by motor.
Power generated by the coils A and C is more as
compared to the full step as shown in figures 22 and 23.
Figure 18.Plot of current generated by c coil.
Motor speed and position is as shown below figures 19
and 20, where motor steps through an angle half of the normal
step.
Figure 22.Plot of motor power generated by A coil.
Figure 19.Plot of motor speed.
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Figure 23.Plot of motor power generated by C coil.
C.Micro Step Mode Excitation
Micro-stepping mode that controls the current in the
motor windings. Micro stepping is typically used in
applications that require accurate positioning and a fine
resolution over a wide range of speeds. Smooth movement at
low speeds. Increased step positioning resolution as a result of
smaller step angle.
Va
sin
n
2kv
Vc
cos
n
2k v
Figure 25. Plot of pulse generated by C coil.
In Micro stepping mode the currents in the winding are
continuously varying as shown in figure 26 and 27.
Plots of motor speed and motor rotation of step angle 1deg
as shown in the figures 28 and 29.Motor position for microstepping is highly accurate and linear, smooth. So microstepping is used in all space application.
Where,
n = 0, 1, 2, - - - - - - - - (4Kv-1)
Kv = number of steps.
Sine and cosine of the input voltage divided into given number
of steps here Kv = 8 and n= 31 as shown in the below figures
24 and 25.
Figure 26.Plot of current generated by A coil.
Figure 24. Plot of pulse generated by A coil.
Figure 27.Plot of current generated by C coil.
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National Conference on Advances in Mechanical Engineering Science (NCAMES-2016)
Figure 28.Plot of motor speed.
The major disadvantage of the micro step drive is the cost
of implementation due to the need for partial excitation of the
motor windings at different current levels. If static friction is in
the system, the angular precision is limited. Cost of
implementation is high. In wave-drive and two-phase on
excitation, step size is equal to the natural step size.
In half-step excitation, step number is doubled and step size
is halved. Non-linear factors of the system bring limitations on
the number of micro-steps achievable and introduce
difficulties in achieving constant current and torque outputs.
Micro-stepping method can significantly improve system
performance.
motor allow for realistic simulation conditions, resembling
commercially available devices. All these highlight the
pertinence and usefulness of the elaborated mathematic model
of the stepper motor. The model and the simulation program
can be used in the optimization process of the design and in
elaborating an efficient control strategy in order to improve the
performances of the motor in study. Simulation is carried out
and compared to realistic motor called SSM and SAGEM used
in ASTRTOSAT satellite and its data, specifications. There
are different driver topologies for step motor control, each
having advantages and disadvantages for certain needs. Microstepping can be enabled using the H-bridge topology. Stepper
motor is modeled using differential equations and then
numerically solved by “Runge Kutta” method. Stepper motor
performances for different step rates are tested. Step motors
provide fine control of rotation angle and speed through
discrete excitation signals. Micro-stepping enables higher
precision through fractional excitation of step motor windings.
REFERENCES
[1] P.P.Acarnley, stepping motors: A Guide to Modern Theory and Practise.
Stevenge, UK: P.Peregrinus, Ltd., 1982.
[2] M.Bodson and J.Chiasson, “Application of nonlinear control methods to
the positioning of a permanent magnet stepper motor,” in Proc.28th IEEE
Conf.DecisionContr.,Tampa,FL 1989.
[3] J. Chiasson and M. Zribi,“Position control of a PM stepper motor by exact
linearization,” IEEE Trans Automat Contr., vol.36, no, 5, May 1991.
[4] M.Aiello, R,Rekowski, M.Bodson, J.Chiasson, and D.Schuerer,
“Experimental results of using an exact linearization controller on a PM
stepper motor,” in Proc. IEEE Int, Conf. Syst. Eng., Aug.1990, Pittsburg, PA.
[5] M. Zribi, Mohamed, “Control of a PM stepper motor using modern
nonlinear control techniques” M.S.E.E.thesis, Purdue University 1987.
Figure 29.Plot of motor rotation.
Maximum torques at both low and high step rates is as
shown in the figure 21.
Figure 21.Plot of torque generated by motor.
VI. CONCLUSIONS
The quantative results found during the simulations fit
well with the expected behaviour of an electric stepper motor.
In particular, the proposed solutions to simulating real stepper
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