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BACHELOR’S THESIS Electronic Engineering (Karl Lantz) Computer Engineering (Martin Johansson) Department of Technology, Mathematics and Computer Science
2006:E12
Modeling of a step motor for position feedback in a climate system Karl Lantz Martin Johansson
BACHELOR’S THESIS
Modeling of a step motor for position feedback in a climate system
Summary
The goal of this project was to build a model of the actuator used in the climate system in a
Volvo car and to investigate alternative feedback control strategies. The model of the
actuator is a physical model built in Matlab/Simulink with SimMechanics toolbox and it
consists of a step motor and a gear train. The result is a well working actuator that shows
the known characteristics of "loosing steps" when the load gets too high.
Today the step motor is controlled by a Hall Effect Sensor (HES) which senses the pole
transitions of the step motor rotor. Two different alternatives to the step motor position
feedbacks are studied, resolver and back-EMF. Back-EMF is an alternative to the HES
because they both get their position from the rotor. The resolver on the other hand is an
external hardware which is mounted directly on the outgoing axle after the gear train. Since
the resolver can not be used to control the commutation of the step motor it can not
replace the HES. But it is a good complement to the HES to increase the precision for the
position feed-back of the outgoing axle.
Author: Karl Lantz, Martin Johansson Examiner: PhD Anna-Karin Christiansson Advisor: Jonas Jange & Andreas Harder, Volvo Car Corporation Programme: Electronic Engineering Computer Engineering Subject: Electrical/ Computer Engineering Level: Bachelor Date: February 25, 2007 Report Number: 2006:E12 Keywords Actuator, BLDC, step motor, climate system, modeling
Publisher: University West, Department of Technology, Mathematics and Computer Science,
S-461 86 Trollhättan, SWEDEN Phone: + 46 520 22 30 00 Fax: + 46 520 22 32 99 Web: www.hv.se
Modeling of a step motor for position feedback in a climate system
Preface
We would like to thank everyone at Volvo Car Corporation who helped us in our work,
especially Andreas Harder and Jonas Jange who helped us a lot. We also like to thank
Anna-Karin Christiansson for her help and support.
Modeling of a step motor for position feedback in a climate system
Contents
Summary............................................................................................................................................. ii
Preface ............................................................................................................................................... iii
Contents ............................................................................................................................................iv
List of symbols ..................................................................................................................................v
1 Introduction ................................................................................................................................1
1.1 Background.......................................................................................................................1
1.2 Goal....................................................................................................................................1
2 Existing system description ......................................................................................................1
3 Actuator modeling .....................................................................................................................3
3.1 Actuator.............................................................................................................................3
3.1.1 BLDC...................................................................................................................3
3.1.2 Gear train.............................................................................................................4
3.2 Matlab with Simulink and SimMechanics.....................................................................4
3.3 Modeling............................................................................................................................5
3.3.1 Mathematical .......................................................................................................5
3.3.2 DC-motor model in Simulink...........................................................................6
4 Feedback alternatives.................................................................................................................8
5 Results..........................................................................................................................................8
5.1 Actuator modeling ...........................................................................................................8
5.1.1 Gear train...........................................................................................................15
5.1.2 Conductive load................................................................................................17
5.1.3 Simulations ........................................................................................................19
5.2 Feedback alternatives.....................................................................................................23
5.2.1 Resolver .............................................................................................................23
5.2.2 Back-EMF .........................................................................................................25
6 Conclusions...............................................................................................................................26
6.1 Actuator modeling .........................................................................................................26
6.2 Feedback alternatives.....................................................................................................26
7 Recommendation for further work .......................................................................................27
References ........................................................................................................................................28
Appendices
A. Values for conductive load, forward
B. Values for conductive load, backward
C. M-file for actuator.mdl
Modeling of a step motor for position feedback in a climate system
List of symbols
ASIC Application Specific Integrated Circuit. An integrated circuit
design for a unique purpose
BLDC Brushless Direct Current
CCM Climate Control Module
EMF ElectroMotive Force
EPM Extreme Position Maintainable
FAM Flap Actuator Module
HES Hall Effect Sensor. The hall effect was discovered by Edwin
Hall 1879. It is an electrical voltage that originates across a thin
plate, when a current is applied along it and it is exposed to a
magnetic field perpendicular to the plate.[1]
HVAC Heating Ventilation Air Condition
Kirchoff's current law The sum of the currents flowing towards any point in an
electrical circuit is equal to the sum of currents flowing away
from that point.[2]
LIN Local Interconnect Network. Communication and networking
serial bus between intelligent sensors and actuators operating at
12 volts.
Newton's laws First Law:
A particle originally at rest, or moving in a straight line with
constant velocity, will remain in this state provided the particle
is not subjected to an unbalanced force
Second Law:
A particle acted upon by an unbalanced force F experiences an
acceleration a that has the same direction as the force and a
magnitude that is directly proportional to the force. If F is
applied to a particle of mass m, this law may be expressed
mathematically as F = ma.
Third Law:
The mutual forces of action and reaction between two particles
are equal, opposite, and collinear. [3]
PH Phase
Modeling of a step motor for position feedback in a climate system
POS Position = 2 steps = 1 pole on the rotor
PWM Pulse Width Modulation
VCC Volvo Car Corporation
Modeling of a step motor for position feedback in a climate system
1
1 Introduction
Volvo Car Corporation (VCC) produces seven different cars. The S40, V50, C30, S60,
V70, XC90 and the new S80. VCC is a part of Ford Motor Company. For more
information visit http://www.volvocars.com.
1.1 Background
Volvo Car Corporation wants to examine potential variants for feedback strategies for
step motors in a climate system application. This is done in order to obtain both
increased performance for the position feedback and a more cost effective solution
than the existing solution.
1.2 Goal
The thesis is done in two main assignments, the goal of the first assignment is to get
an understanding for the solution used today and build a model of the actuator in
Matlab/Simulink. The goal for the second assignment is to find out which the
possible alternatives for the Hall Effect Sensor (HES) are and pick out the ones which
are best suited to improve the position feedback of the outgoing axle.
2 Existing system description
The climate system in a Volvo car today has actuators which control flaps in a
Heating Ventilation Air Condition (HVAC) system. See figure 1. The actuators are of
a Brushless Direct Current (BLDC) type and are consisting of a step motor with HES.
There are five actuators in the HVAC. The actuators control the air mix flap which
mixes hot and cold air, the defroster, front floor- and rear floor outlet, ventilation-
and recirculation flaps. The HVAC and the flaps are made of plastic, which is a
material that changes its characteristics depending on for example temperature and
aging. Therefore the end positions of the actuators can change during the component
life time.
Modeling of a step motor for position feedback in a climate system
2
Figure 1. Heating Ventilation Air Condition system. The flaps that are controlled by the actuators are green marked.
The actuator flap position is stored in the Flap Actuator Module (FAM) software. To
get the position the actuator needs to be calibrated. This is done by running an End
Of Line (EOL) command. The actuator then moves the flap to its two end positions,
one at a time. The Climate Control Module CCM then gets the range of how many
steps the actuator needed to get from one end position to the other. If the actuator
looses its position information, the CCM commands the actuator to go to one end
position and then the CCM calculates where the other end position is by knowing
how many steps it took to go from one end position to the other. If the end position
changes, this calibration looses its accuracy.
Pollenfilter
Evaporator Core Heater Core
Blower Motor (not shown)
Temperature Door
Ventilation outlet
Air Inlet (Fresh/Recirc/ Speed Compensation)
Drainage
Electr. Power Heater (PTC) (not shown)
Defroster outlet
Rear Floor outlet
Front Floor outlet
Modeling of a step motor for position feedback in a climate system
3
3 Actuator modeling
The first assignment was to understand the step motor solution of today and build a
simulation model of it which catches the dynamic and static characteristics for feed
back strategies and to investigate where the costs lie.
3.1 Actuator
The actuator consists of a step motor with HES, Application Specific Integrated
Circuit ASIC with software that drives it like a BLDC, and a gear train.
3.1.1 BLDC
The BLDC motor is designed to move and control the position of several HVAC
flaps [4]. The motor consists of two coils with two windings on each coil around two
external stators. The rotor consists of a 10-pole permanent magnet. When the rotor is
positioned so that one of the coils has a whole north pole (N) and a south pole (S) in
front of the coil surface, the other coil surface has half of the N/S in front. See figure
2.
Figure 2. Step motor design
When one of the coils has a whole N and S pole in front of the coil surface the HES
is either just on transition between 2 poles or in the middle of one pole. The HES
detects pole transitions in that it can feel the motor running, but not in which
direction.
The smallest move the motor can make is from match N/S on one coil surface to
match N/S on the other coil surface (movement = ½ pole = 1 step). The smallest
move allowed is 1 POS = 2 steps. The reason for this is that if the rotor only moved 1
step it could stop so that the HES would be on the transition of two poles and that
could generate a signal change only due to vibration of the car. If it instead moves two
steps the HES will always get a complete pole in front. When running full speed and
torque, two half coils or two phases (2PH) are fed with voltage at the same time. A
Modeling of a step motor for position feedback in a climate system
4
sequence of commutation of the four half coils creates rotation in clock-wise direction
or counter-clock-wise direction. This is handled by the ASIC. To start the actuator
only one winding is powered at first and then the other on opposite coil is powered.
See figure 3. The most common step motors use an input signal to the winding with a
defined pattern, for example PWM or sinusoidal waveform. The logic for how the
windings are powered in this motor is programmed in an ASIC and it uses the pulses
from the HES to determine the timing for the powering of the windings. If the timing
is not right the motor can start to rotate in the opposite direction without the ASIC
knowing it, since the HES can not feel in which direction the rotor is moving.
Figure 3. Shows when one phase (1PH) and two phases (2PH) are powered when running the motor in different speeds.
3.1.2 Gear train
The gear train consists of eight plastic cog wheels in various sizes. The first cog wheel
is mounted directly on the step motor rotor and the last one is mounted directly on
the outgoing axle. The gear ratio of the gear train is 1:209,14 which means that 36˚
movement of the rotor correspond to 0,17˚ on the outgoing axle. The angular play,
which is the difference between the ingoing and outgoing angle, for the gear train is
1,5˚ +/- 0,5˚ measured at +23˚C with +/- 10Ncm load on the outgoing axle [4].
3.2 Matlab with Simulink and SimMechanics
Matlab is a computing language and interactive environment for algorithm
development, data visualization, data analysis, and numeric computation. It can be
used in a many applications, for example signal processing, communications, control
design, test and measurement [5].
Simulink is a platform for simulation and model-based design for dynamic systems. It
provides an interactive graphical environment and a set of block libraries that is
customizable [6].
SimMechanics extends Simulink with tools for modeling and simulating mechanical
systems. The model of the mechanical system can then be tested in real time [7].
Modeling of a step motor for position feedback in a climate system
5
3.3 Modeling
By modeling a system questions can be answered without making any physical experiment. The models can be of various types for example conceptual, mental, physical and mathematical [8].
3.3.1 Mathematical
A mathematical model states different mathematical relations between parameters in a system. The mathematical models can be divided into three different categories.
• Black box is a model where no attentions to the physical factors which affect the system are taken into consideration. The only thing of interest is the correlation between incoming and outgoing signals. Therefore there is no need for a deeper understanding in the process itself. The model is instead based on statistical data.
• White box is a model which is built on good knowledge of the process that is to be modeled. The connection between different variables in the system and its process are well known and described thoroughly.
• Grey box is a mix of black box and white box modeling where the connection between cause and effect in a more complex system is hard or impossible to find.
The first phase in building a model is often the hardest and most time demanding. This is the phase where the complexity of the model is determined. The questions that should be answered in the first phase are as follows:
• Which are the outgoing signals from the system? • What external signals are incoming to the system? • Which quantification in the system is of importance to describe what takes
place? • Which of these are time variable and should apprehend as internal variables
(states)? • Which are approximately time invariant and can apprehend as constants? • Which system connections can come off as static and dynamic respectively?
A block diagram of the result from the questions is usually formed.
In the second phase the block diagram from phase one is translated into a
mathematical model. This is done by stating the relations between in signal and out
signal in the different blocks in a block scheme. The different relations between the
system variables can be either of natural kind, given as known equations, an
experimentally produced connection, given by for example testing, or a connection
which is based on approximations, but which can give the relation its characteristics.
In phase three the system of equations which describes the model is written in a state-
space form.
Modeling of a step motor for position feedback in a climate system
6
3.3.1.1 Physical model
The physical model is in general a nonlinear model based on physical equations. This
type of modeling gives a good understanding in which of the ingoing factors that have
some kind of influence on the system that is to be modeled. The flexibility of a
physical model is one of the advantages, as it has the possibility to change
components and then change the characteristics in part models.
It is recommended to find possible approximations to keep the complexity of the
model low.
3.3.2 DC-motor model in Simulink
To get started and to get an understanding in how Matlab/Simulink works a physical
model of a DC-motor was built. See figure 4. The model provides the angular rotor
position from a DC-motor [9].
Figure 4. Model of a DC-motor. Left the electrical part and right the mechanical part
The following values were used as the physical parameters in the simulation [9]
* moment of inertia of the rotor (J) = 3.2284 10-6 kg.m2/s2 * damping ratio of the mechanical system (b) = 3.5077 10-6 Nms * electromotive force constant (K=Ke=Kt) = 0.0274 Nm/A * electric resistance (R) = 4 Ω * electric inductance (L) = 2.75 10-6 H * input (V): source Voltage * output (θ): position of shaft * the rotor and shaft are assumed to be rigid
The motor torque, T, is related to the armature current, i, by a constant factor Kt. The
back-EMF, e, is related to the rotational velocity by the constant factor Ke. These
facts give the following equations (1), (2).
iKTt*= (1)
dt
dKe
e
θ*=
(2)
Modeling of a step motor for position feedback in a climate system
7
Newton's law and Kirchoff's law give the following equations (3), (4) which later on
are translated into boxes in Simulink.
)**(1
**2
2
2
2
dt
dbiK
Jdt
d
dt
dbT
dt
dJ
t
θθθθ−=⇒−=
(3)
)**(1
**dt
dKViR
Ldt
dieViR
dt
diL
e
θ−+−=⇒−+−=
(4)
After translating the equations above (3), (4) into boxes the following structure was
given. See figure 5.
Figure 5. Simulink model of DC-motor corresponding to equations (3), (4).
After running the simulation with step as in signal and then opening the Scope box a result was given showing how the motor first moves its position in a slow pace and then accelerates to stable speed. See figure 6.
Figure 6. Position output angle theta after running simulation of DC-motor
Modeling of a step motor for position feedback in a climate system
8
4 Feedback alternatives
The second assignment was to look at alternative strategies for controlling the
position of the step motor outgoing axle and compare these strategies to the solution
used today and then draw a conclusion of what to recommend in the future.
5 Results
5.1 Actuator modeling
To understand how to model a step motor in Simulink the web was searched in order
to find simulation models that could be helpful in the progress of building up a
model. One paper of a study that was found included a step motor with controlled
phase currents. This model was built on a physical model structure. Since the study
was missing a few but vital parameters much time was put into understanding the
model and its parameters [11]. The things that made it most difficult was the lack of
declaration of what was to be the input signal and that there was lack of declarations
of some of the variables used in the equations.
The model can be described with the following mathematical equations (5), (7), (10),
(11):
Electrical equations:
)sin(rrr
aa
aaaNkw
dt
diLiRV θ−+=
(5)
This equation (5) was rewritten so it could be converted into Simulink boxes , see
figure 7, and then integrated to get the winding current ia (6).
))sin((1
rrraaa
a
a
aNkwiRV
Ldt
dii θ+−==
•
(6)
Modeling of a step motor for position feedback in a climate system
9
Subsystem dot_ia
1
dot_ia
k/La
wr*(k/La)
Nr
thetar*Nr
sin
sin(thetar*Nr)
Ra/La
ia*(Ra/La)
1/La
Va/La
(wr*k/La)*(sin(thetar*Nr))
4
wr
3
thetar
2
Va
1
ia
Figure 7. Subsystem dot_ia
The same thing was done with the equation (7) for the current in the other winding.
)2
sin(n
Nkwdt
diLiRV
rrr
bb
bbb
πθ −−+=
(7)
By using the following relationship (8) where n is the number of stator phases.
)cos()2
sin(rrrr
Nn
N θπ
θ −=− (8)
The equation (7) could be written into this form (9) and also converted into Simulink
boxes. See figure 8.
))cos((1
rrrbbb
b
b
bNkwiRV
Ldt
dii θ−−==
•
(9)
Modeling of a step motor for position feedback in a climate system
10
Subsystem dot_ib
1
dot_ib
k/Lb
wr*(k/Lb)
Nr
thetar*Nr
Rb/Lb
ib*(Rb/Lb)
cos
cos(thetar*Nr)
1/Lb
Vb/Lb
(wr*k/Lb)*(cos(thetar*Nr))
4
thetar
3
wr
2
Vb
1
ib
Figure 8. Subsystem dot_ib
)cos()sin(
rrbrramNkiNkiC θθ +−= (10)
Mechanical equations (11), (12), (13),(15):
rr
r
dt
dw
•
== θθ
(11)
l
rr
mC
dt
Bd
td
JdC ++=
θθ
2
2
(12)
lrrmCBJC ++=
•••
θθ (13)
lrrmCBwwJC ++=
•
(14)
To get the equation for rotor speed wr equation (10) is set to equal equation (14). See
equation (15)
)*)*cos(**)*sin(**(1
lrrrbrrarCwBNikNik
Jw −−+−=
•
θθ (15)
Modeling of a step motor for position feedback in a climate system
11
Subsystem dot_wr
1
dot_wr
B/J
wr*(B/J)
sin
sin(Nr*thetar)
k/J
ib*(k/J)
k/J
ia*(k/J)
cos
cos(Nr*thetar)
Nr
Nr
1/J
Cl/J
(ib*k/J)*(cos(thetar*Nr))
(ia*k/J)*(sin(thetar*Nr))
5
Cl
4
ia
3
ib
2
wr
1
thetar
Figure 9. Subsystem dot_wr
The equations translated into state space model (16).
+
−−
−−
−
=
•
•
•
•
0
0000
01
00
001
0
0001
0100
0)sin()sin(
0)cos(0
0)sin(0
l
b
a
a
a
r
r
b
a
rrrr
rr
bb
b
rr
aa
a
r
r
b
a
C
V
V
J
L
L
w
i
i
J
BN
J
kN
J
k
NL
k
L
R
NL
k
L
R
w
i
i
θθθ
θ
θ
θ
(16)
Modeling of a step motor for position feedback in a climate system
12
The three equation models, dot_ia, dot_ib and dot_wr, are then inserted and
connected together as sub blocks in the step motor model. See figure 10. The angle of
the rotor θ r is converted from radians to degrees.
dot_wr
dot_thetar
dot_ib
dot_ia
Step motor
4
ib
3
ia
2
wr
1
thetar
thetar
wr
ib
ia
Cl
dot_wr
Subsystem dot_wr
ib
Vb
wr
thetar
dot_ib
Subsystem dot_ib
ia
Va
thetar
wr
dot_ia
Subsystem dot_ia
180/pi
Radians to degrees
1
s
1
s
1
s
1
s
3
Vb
2
Va
1
Cl
Figure 10. Step motor model with Va, Vb, Cl as inputs and ia, ib,thetar and wr as outputs.
Modeling of a step motor for position feedback in a climate system
13
Figure 11 shows the actuator model. The step motor’s two windings are fed by PWM signals. The constant 12 is subtracted from the signals to have the signals centered on the zero axes. When the signal is positive one phase is powered and when negative the other phase on the coil is powered. Both signals got a period time of 1 s and amplitude of 24 V and Vb has an offset of 0.25 s. The output signals that can be viewed are voltages winding A and B, the position of the rotor and of the shaft, rotor speed, currents winding A and B and the conductive load.
Current winding A
Current winding B
Rotor position
Rotor speed
Voltage winding A
Voltage winding B
Shaft position
Conductive load
wr
thetas
thetar
ib
iaVb
Va
V
Cl
Va
Vb
thetar
wr
ia
ib
Step motor
thetarthetas
Gear train
thetasCl
Conductive loadCl
12
Figure 11. Actuator model
Modeling of a step motor for position feedback in a climate system
14
Declaration of terms:
Va , Vb are the windings voltages [V]
ia , ib are the windings currents [A]
Ra , Rb are the windings resistance [Ω]
La , Lb stator winding inductance [H]
k constant of torque do motor [Nm/A]
wr rotor speed [rad/s]
Nr number pair of poles of the rotor
θ r rotor position [˚]
J motor inertia [kgm²]
B motor viscous friction [Nms]
Lm mutual inductance of stator and rotor windings [H]
n number of stator phases
The declaration of Cm and Cl was missing in the declaration of terms in [11] but the
most likely declaration is:
Cm conductive moment [Nm]
Cl conductive load [Nm]
Tests with input of different values on Cl gave the characteristics that indicated that Cl
was the conductive load. More information in chapter [5.1.2].This was seen when
looking at the output signal for the angle on the rotor axle. When the load was too
high the step motor took one step forward and three steps back which is a known
characteristic of a step motor. According to tests done by VCC.
Modeling of a step motor for position feedback in a climate system
15
5.1.1 Gear train
To model the gear train SimMechanics was used. The cog wheel cogs where counted
to get the circumference of the cog wheels. Except from the gear on the outgoing axle
and the gear on the rotor every gear contains two set of cogs, one big and one small.
This is to save space in the gear train and still get the wanted ratio. The amount of
cogs per gear is shown in table 1.
Type Amount of cogs (Big) Amount of cogs (Small)
Gear shaft 48 - Gear3 65 13 Gear2 71 23 Gear4 59 11 Gear rotor - 19 Table 1. Amount of cogs for the cog wheels in the gear train
The gear train consists of a base body, which is welded to the ground so that it won't
move. Five gears are attached upon the body with revolutes. A revolute is a rotation
between two bodies. The angle from the step motor is used as an input to the revolute
that is attached to the rotor gear to start a motion. The joint actuator is used to
transform a regular Simulink signal, in this case the rotor angle, into a motion. The
joint sensor transforms a motion into a Simulink signal. The gears are attached by a
gear constraint which determines the ratio between them. See figure 12.
1
thetas
BF
Weld
B
F
Revolute6
B F
Revolute4
B F
Revolute3
B F
Revolute2
B
F
Revolute1
EnvMachine
Environment
Joint Sensor
Joint Actuator
Ground
CS1
CS2CS3
Gear4
CS1
CS2CS3
Gear3
CS3CS1
CS2
Gear2
CS2 CS1
Gear shaft
CS1 CS2
Gear rotorCG
CS1
CS2
CS3
CS4
CS5
Base body
BF
23:65
BF
19:71B
F
13:59
BF
11:48
1
thetar
Figure 12. Subsystem gear train modeled in SimMechanics
Modeling of a step motor for position feedback in a climate system
16
5.1.1.1 Parameter settings
CG (center of gravity) is a parameter where settings are done to move the bodies in a
three dimensional room. This is done to set the distance between the cog wheels to be
sure that the cog wheels are attached to each other. See table 3. The parameter that
decides which CG to use is the gear ratio set in the gear constraints. On the body
block the CS (coordinate system) for each port is set according to the CG for the
connected bodies. See table 2. In the gear constraints the size of the attached cog
wheels are set. The size of the cog wheels in the gear constraint should be defined by
the radius, but since the amount of cogs would be more precise this is used instead.
The relationship between the radius and the amount of cogs will make the ratio of the
two cases equal. The machine environment block determines the settings for the
machine to which it is connected. It has parameter settings that control how the
machine is simulated. It also has settings to control how constrains are interpreted
and setting to control how linearization is implemented and whether the machine is
displayed in SimMechanics visualization.
Name Origin position
[x y z] CS1 [0 0 0] CS2 [90 0 0] CS3 [178 0 0] CS4 [240 0 0] CS5 [299 0 0] Table 2. CS on ports of base body
Name Origin position
[x y z] Base body [0 0 0] Gear rotor [0 0 0] Gear2 [90 0 0] Gear3 [178 0 0] Gear4 [240 0 0] Gear shaft [299 0 0] Table 3. CG for bodies in gear train
Modeling of a step motor for position feedback in a climate system
17
Figure 13 shows how the gears move during a simulation. The gear in origin is the gear on the rotor.
Figure 13. Machine for gear train
5.1.2 Conductive load
When a flap, which is connected to the actuator, gets to an end position the
conductive load increases. To get the characteristics for this VCC have performed
tests where they moved the flap in a distinct pattern back and forth between the end
positions. A torque measurement equipment was used to measure the torque that the
actuator was exposed to during this test. The result of this test, which can be seen in
the appendices A and B, where later used in the simulation of the step motor to get
the right characteristics of the conductive load. By implementing these characteristics
into two lookup tables, one for when the motor moves forward and one when it
moves backwards, the load can change depending on direction and distance to end
positions.
Modeling of a step motor for position feedback in a climate system
18
5.1.2.1 Parameter settings
The block, table constant, is used to make sure that the model starts in the middle of
the look-up tables. This is done to get the model to simulate that the actuator starts in
the middle between the end positions. The new value is then sent into the look-up
tables where the torque value for that input signal is sent out. The parameters for the
look-up table are stored as a vector in an m-file. The vector values are taken from the
VCC test.
The Cl chooser consists of the following program code.
function Cl = f(forward,backward)
Cl = (forward + backward)/2;
This block adds the values from the backward table to the forward table and the
divide the result by two to get the mean value. See figure 14.
1
Cl90 Table constant
Lookup Table Forward
Lookup Table Backward
f orward
backward
Clf
Cl chooser
Add
1
thetas
Figure 14. Subsystem conductive load.
Modeling of a step motor for position feedback in a climate system
19
5.1.3 Simulations
Simulation of two different cases where the actuator was simulated for two seconds
and one when it was simulated for 114 seconds.
5.1.3.1 Two seconds simulation
After running the model (figure 11) for two seconds the following result was given. As seen in figure 15 the input voltages are two PWM signals where one of them has an offset.
Figure 15. Voltage PWM input signal. The yellow shows Va and the purple line is Vb, which has an offset of a quarter of the period time.
The current, ia and ib, follows the PWM signals. It also shows that there are some jitter when the other winding is powered. See figure 16.
Figure 16. Winding currents left ia and right ib
Modeling of a step motor for position feedback in a climate system
20
The conductive load torque changes with time. See figure 17
Figure 17. Conductive load, Cl
The pikes in figure 18 shows that the motor accelerates every time it makes a step. The small deacceleration is caused by the small backward movement that the rotor does after each step.
Figure 18. Rotor velocity, wr
Modeling of a step motor for position feedback in a climate system
21
The steps are well defined with overshoot at the end of every step movement. See figure 19.
Figure 19. Angular position, left rotor, thetar and right shaft, thetas.
Modeling of a step motor for position feedback in a climate system
22
5.1.3.2 114 seconds simulation
The simulation time is 114 seconds because that is the time it takes for the actuator to
get to its end position when using an input signal of ±12V. When the actuator reaches
its end position the torque will increase causing the actuator to bounce against the end
position. This is called Extreme Position Maintainable (EPM) [4] and in the real
actuator a fault code will be set in the built-in software. The input signals are the same
as in figure 15 only this time it is runned for 114 seconds.
Figure 21 shows the currents through the windings. The big peaks occur when the
actuator gets to an end position. This is because the current correlates with the torque.
Figure 20. Current through the windings, left ia and right ib
When the actuator reaches its end position the conductive load is at its highest which causes the actuator to "loose steps" and drop back three steps. The actuator then continues to run which will cause the actuator to bounce against the end position. This is shown in figure 22 when the load increases and then decreases in a short period of time.
Figure 21. Conductive load
Modeling of a step motor for position feedback in a climate system
23
The velocity, wr (to the left in figure 23), decreases when the torque, Cl (figure 22), increases. The end positions are seen in figure 23 by being the highest shaft angle before the shaft angle decreases. When the actuator loses its steps the velocity becomes negative and negative peaks are given.
Figure 22. Velocity and shaft angle
5.2 Feedback alternatives
The environment in a HVAC is tough and sets high demands on the position feed
back sensors that can be used to increase the position feedback of the outgoing axle
of the actuator. Optical sensors are sensitive to dirt and moist and will therefore not
be suitable for this purpose. Another alternative is to mount temperature sensors in
the mix box of hot and cold air to measure the temperature and control the actuator
to get this temperature right. The problem with this is that it is not enough with only
this temperature sensor. There is also a need for one after every flap that regulates
where the air is to be blown out. This increases the costs. Therefore this thesis
concentrates on alternatives with position feedback of the axle on the actuator. Two
alternatives have been chosen.
5.2.1 Resolver
A resolver is an electrical angle measuring organ [12]. It is used in many different areas
where demands on maintenance, durability towards vibration, chock and high
temperature is required. A resolver can be found in automotive applications, such as
power-assisted steering system, industrial applications where there are large
temperature variations. Comparing with optical absolute encoders, resolvers are more
mechanically reliable, and easy to be integrated with motor systems.
The resolver is an analog angle sensor which translates rotation to an electrical
sinusoidal signal. The resolver consists of a stator and a rotor, similar to an electric
motor/generator. The stator consists of two windings which are placed perpendicular.
See figure 24. Its function is similar to a transformer, but changes its characteristics
when rotating. When the rotor windings are fed with a signal, induced voltage is
produced in the stator windings. The phase displacement between the stator windings
Modeling of a step motor for position feedback in a climate system
24
voltage and the rotor windings voltage is a linear measure of the rotor angle position,
which is what you are looking for. A resolver can only detect the angle of one
revolution but it can sense the rotor position even when the motor is standstill. If the
motor is standstill the relation between the amplitude for the signal and the reference
signal is constant. To transform sinus and cosines signals to an angle position of the
rotor, the signals must be dealt with in a suitable manner. One alternative is to sample
the reference, sinus and cosines signals and from that sampled information get the
relation between the amplitudes. Another solution is to use a resolver-to-digital
converter. The converter converts the reference, sinus and cosines signals into an
absolute position value in binary form. The resolution of the angle position can be
adjusted depending on the accuracy of the resolver. The position errors are mainly
caused by third harmonics and the non-effective EMFs existing in the signals.
Figure 23. Resolver signals.
Modeling of a step motor for position feedback in a climate system
25
5.2.2 Back-EMF
When the step motor windings are supplied with a voltage and starts to rotate, an
electromotive force called back-EMF is generated in the windings. The back-EMF
polarity is in opposite direction to the supplied voltage to the winding. Back-EMF
depends mainly on three factors:
• Angular velocity of the rotor • Magnetic field generated by rotor magnets • The number of turns in the stator windings
The last two factors become constants after that the motor has been designed. So it is
only the angular velocity or the speed of the rotor that changes the back-EMF and as
the speed increases, the back-EMF increases. There is often a constant called back-
EMF constant in the technical specification of the motor. It can be used to calculate
an estimated back-EMF for a given speed. If you subtract the back-EMF value from
the supply voltage you get the potential difference across a winding. The motors are
designed with a back-EMF that will make the potential difference sufficient to draw
the rated current and deliver the rated torque.
5.2.2.1 Sensor less control
In the step motor used today in the HVAC, commutation based on rotor position is
given by a HES. An alternative is to manage the commutation by monitoring the
back-EMF signal, instead of using the pole change as with the HES. The zero-
crossing when a winding switches from being energized positive to negative and vice
versa is used to handle the commutation. See figure 25. One problem with this
method is when the motor is running at low speed. The back-EMF is proportional to
the speed of the rotor. So at very low speed the back-EMF will have very low
amplitude, which makes it hard to detect the zero-crossing. Because of this the motor
has to be started in open loop, until there is sufficient back-EMF to detect the zero-
crossing.
Figure 24 Example of back-EMF curve. X-axis time, Y-axis voltage.
Modeling of a step motor for position feedback in a climate system
26
Using back-EMF instead of HES simplifies the construction of the motor and
reduces the cost, because it’s a natural part of the motor which requires no extra
hardware. This is an advantage when used in dusty or oily environments where the
HES needs occasional cleaning to sense properly [13].
6 Conclusions
6.1 Actuator modeling
The actuator model is built on mathematical formulas which makes it realistic. It is a
well working actuator that shows the known characteristics of "losing steps" when the
load gets too high. The gear train is an ideal gear train with possibility to implement
hysteresis in further work.
6.2 Feedback alternatives
Since the first assignment took much more time and was more extensive than the first
plan, the second assignment was to be concentrated on looking at two specific
alternatives for position feedback of the step motor.
The resolver is usually used to get the position of the outgoing axle. The back-EMF
alternative on the other hand is used to count the amount of steps the step motor
takes. These are two strategies that are used to control the step motor. When looking
at the resolver the step motor runs to get the outgoing axle to the wanted position by
knowing the position of the outgoing axle.
When comparing the back-EMF to the HES, advantages show that back-EMF will
provide a less complex design where no extra hardware has to be added which will
lower the costs. Back-EMF is a maintenance-free solution which also can be used, not
only as a replacement for the HES but as a compliment to it. Disadvantages for back-
EMF are that there is no detection during start up and when the motor is at standstill.
This will generate problems when moving the motor close to its end positions.
The resolver is an external component for position feedback which can be a good
compliment to the HES solution used today to increase the accuracy of the position
feedback of the actuator. By mounting the resolver on the outgoing axle a more exact
position feedback will be given since that is the wanted position of the actuator in the
HVAC. The resolver can fit into small spaces which also makes it suitable for the
HVAC. It can also detect when the motor is in standstill which can be useful when
the position is changed by external stress. On its disadvantages it is an extra hardware
which will increase the costs.
Both alternatives can detect in which direction the motor is running. But the biggest
problem with the actuator today is when some external force moves the actuator
causing it to stop and even go backwards. The backwards phenomenon can appear
Modeling of a step motor for position feedback in a climate system
27
when the rotor is set in such a position that the forward commutation sequence
makes it go backwards without the motor knowing it. The resolver would solve this
problem since it detects the angle of the outgoing axle and has nothing to do with the
commutation. The back-EMF on the other hand will still have this problem because
the back-EMF from the coils is of the same characteristics as when the motor moves
forward.
7 Recommendation for further work
The model today has a few things that can be improved in the future. This is to get a
more realistic model of the actuator.
• The parameter values in the m-file for the step motor are not the correct
values for the Eaton actuator used in the HVAC. The values used today in the
model are taken from the article where the mathematical formulas were first
found [11].
• The conductive load algorithm is a very simplified model of how it actually
works. For more realism the conductive load should be generated by
implementing an algorithm for when the actuator moves forward the forward
lookup-table should be used and when the actuator moves backwards the
backwards lookup-table should be used. If the actuator starts to move
backwards when going forward, an algorithm that switches table smoothly
should be used.
• In the model today the conductive load is calculated from the angle on the
outgoing axle and then it goes directly into the motor. The conductive load
should instead go back trough the gear train and then into the motor, as in the
real actuator.
• In the real world the actuator is exposed to different types of hysteris that
should be implemented for realistic modeling.
o Voltage drop – battery voltage in a car changes and the actuator is
required to move between the voltages of 9-16V. This means that the
speed and torque of the motor will vary.
o Temperature shifting – since the cog wheels are made of plastic, the
temperature changes its characteristics. Temperature shifting will also
have an effect on the ageing.
o Ageing – when plastic gets old it become brittle and the mechanical
play increases.
o Mechanical play – natural factor for gear trains.
Modeling of a step motor for position feedback in a climate system
28
References
1. Nationalencyklopedin [Electronic]. Accessible http://www.ne.se [2007-01-12]
2. Bergström, Lars; Nordlund, Lars (2002). Ellära – Kretsteknik och fältteori Partille: Studentlitteratur
3. Hibbeler, R.C. (2004). Statics and mechanics of materials. Singapore: Student literature
4. Zeraffa, P; Sanamder, E (2003). LIN bus 082 BLDC actuator [Electronic]. EATON SAM Actuator & Sensor Division. Accessible [2007-01-10]
5. Pärt-Enander, Eva; Sjöberg, Anders (2003). Användarhandledning för MATLAB® 6.5 Uppsala: Avd. för teknisk databehandling
6. The mathworks/products/matlab description. [Electronic]. Accessible http://www.mathworks.com/products/matlab/description1.html [2006-11-29]
7. The matworks/products/simmmechanichs [Electronic]. Accessible http://www.mathworks.com/products/simmechanics/ [2006-12-21]
8. Jung, Lennart; Glad, Torkel (2003). Modellbygge och simulering Lund: Studentlitteratur
9. Lennartson, Bengt (2002). Reglerteknikens grunder Lund: Studentlitteratur
10. Control Tutorials for Matlab and Simulink DC motor position in modeling in Simulink. [Electronic]. Accessible http://www.library.cmu.edu/ctms/ctms/simulink/examples/motor2/motor2s.htm [2006-12-28]
11. Freitas, M.A.A.; Andrade, D.A.; Borges, T.T.; Azevedo, H.R.; Power Electronic Drives and Energy Systems for Industrial Growth, 1998. Proceedings. 1998 International Conference on Volume 2, 1-3 Dec. 1998 Page(s):493 - 498 Vol. 2 Digital Object Identifier 10.1109/PEDES.1998
12. Göransson, Linus; Lund, Magnus (2002) Driftsättning av artemis mätplattform [Electronic] Örebro University department of technology Accessible http://www.oru.se/oru/upload/Institutioner/Teknik/Dokument/Exjobb%202002/Oru-Te-AUT067-Mag106-02.pdf [2007-01-28]
13. Motor geek [Electronic]. Accessible http://www.harmonfamily.us/Motor_Geek.htm
[2006-12-29]
Modeling of a step motor for position feedback in a climate system
Appendix A:1
A. Values for conductive load, forward
Shown below are the values from the measuring done by VCC showing how the load
changes when moving the flaps forward.
Degrees Ncm
53,7 -0,718
53,7 -0,718
53,7 -0,713
53,7 -0,708
53,7 -0,705
53,7 -0,708
53,7 -0,711
53,7 -0,715
53,7 -0,714
53,7 -0,710
53,7 -0,710
53,7 -0,703
53,7 -0,696
53,7 -0,693
53,7 -0,692
53,7 -0,691
53,7 -0,690
53,7 -0,686
53,7 -0,679
53,7 -0,674
53,7 -0,673
53,7 -0,669
53,7 -0,663
53,7 -0,658
53,7 -0,653
53,7 -0,646
53,7 -0,641
53,7 -0,640
53,7 -0,640
53,7 -0,642
53,7 -0,645
53,7 -0,645
53,7 -0,642
53,7 -0,634
53,7 -0,623
53,7 -0,610
53,7 -0,603
53,7 -0,601
53,7 -0,601
53,7 -0,602
53,7 -0,604
53,7 -0,604
53,7 -0,602
Degrees Ncm
53,7 -0,597
53,7 -0,589
53,7 -0,575
53,7 -0,554
53,7 -0,525
53,7 -0,491
53,7 -0,457
53,7 -0,429
53,7 -0,387
53,7 -0,361
53,7 -0,330
53,7 -0,296
53,8 -0,259
53,8 -0,221
53,8 -0,186
53,8 -0,156
53,9 -0,130
53,9 -0,110
53,9 -0,095
54,0 -0,082
54,0 -0,067
54,0 -0,052
54,1 -0,041
54,1 -0,032
54,1 -0,023
54,2 -0,013
54,2 -0,006
54,2 0,003
54,2 0,003
54,3 0,012
54,3 0,021
54,3 0,032
54,3 0,042
54,4 0,050
54,4 0,057
54,4 0,065
54,4 0,072
54,5 0,077
54,5 0,084
54,5 0,097
54,5 0,104
54,6 0,110
54,6 0,118
Degrees Ncm
54,6 0,126
54,7 0,130
54,8 0,132
54,9 0,135
55,0 0,137
55,1 0,136
55,3 0,136
55,5 0,135
55,7 0,132
55,9 0,128
56,1 0,125
56,3 0,124
56,4 0,123
56,6 0,124
56,7 0,124
56,9 0,125
57,0 0,126
57,1 0,127
57,1 0,127
57,3 0,126
57,5 0,125
57,6 0,124
57,8 0,123
57,9 0,123
58,1 0,121
58,3 0,120
58,4 0,120
58,6 0,121
59,0 0,121
59,2 0,123
59,3 0,123
59,5 0,124
59,7 0,126
59,9 0,128
60,1 0,128
60,3 0,128
60,5 0,130
60,7 0,131
60,9 0,133
61,0 0,134
61,2 0,135
61,4 0,136
61,6 0,137
Modeling of a step motor for position feedback in a climate system
Appendix A:2
Degrees Ncm
61,8 0,137
61,9 0,137
62,1 0,137
62,3 0,137
62,5 0,137
62,7 0,136
62,7 0,136
62,9 0,136
63,1 0,136
63,3 0,135
63,5 0,135
63,6 0,134
63,8 0,134
64,0 0,134
64,2 0,134
64,4 0,133
64,6 0,133
64,8 0,132
64,9 0,132
65,3 0,133
65,4 0,133
65,6 0,134
65,8 0,134
66,0 0,135
66,1 0,136
66,3 0,137
66,5 0,136
66,7 0,137
66,9 0,137
67,1 0,138
67,3 0,138
67,4 0,139
67,6 0,139
67,9 0,139
68,1 0,139
68,3 0,139
68,5 0,139
68,5 0,139
68,7 0,140
68,9 0,140
69,1 0,140
69,4 0,140
69,6 0,139
69,8 0,139
70,1 0,140
70,3 0,140
70,5 0,141
70,7 0,140
Degrees Ncm
70,9 0,141
71,2 0,141
71,4 0,141
71,6 0,142
71,9 0,142
72,1 0,142
72,3 0,143
72,6 0,143
73,1 0,143
73,4 0,143
73,6 0,144
73,8 0,144
74,1 0,144
74,3 0,144
74,6 0,144
74,8 0,144
75,1 0,145
75,3 0,146
75,6 0,145
75,8 0,146
76,0 0,147
76,0 0,147
76,2 0,147
76,5 0,147
76,7 0,148
76,9 0,149
77,1 0,148
77,4 0,148
77,6 0,148
77,8 0,148
78,1 0,147
78,3 0,148
78,6 0,149
78,8 0,150
79,0 0,149
79,3 0,149
79,5 0,149
79,7 0,150
80,0 0,149
80,2 0,149
80,5 0,150
80,7 0,150
80,9 0,150
81,2 0,153
81,4 0,153
81,6 0,152
81,9 0,154
82,1 0,155
Degrees Ncm
82,3 0,155
82,6 0,156
82,8 0,156
83,1 0,156
83,4 0,156
83,7 0,155
84,0 0,155
84,2 0,155
84,5 0,155
84,8 0,154
85,0 0,154
85,3 0,152
85,5 0,152
85,8 0,151
86,0 0,151
86,3 0,150
86,5 0,150
86,8 0,149
87,0 0,149
87,3 0,150
87,5 0,149
87,8 0,149
88,0 0,150
88,2 0,150
88,5 0,150
88,7 0,151
88,9 0,152
89,2 0,153
89,4 0,155
89,6 0,155
89,8 0,157
90,0 0,158
90,2 0,159
90,4 0,159
90,4 0,159
90,6 0,161
90,8 0,161
91,0 0,162
91,2 0,164
91,4 0,164
91,6 0,164
91,8 0,165
92,0 0,167
92,4 0,167
92,6 0,168
92,8 0,168
93,1 0,168
93,3 0,168
Modeling of a step motor for position feedback in a climate system
Appendix A:3
Degrees Ncm
93,5 0,168
93,7 0,169
93,9 0,171
94,1 0,171
94,4 0,171
94,6 0,172
94,8 0,173
95,0 0,173
95,4 0,173
95,7 0,172
95,9 0,169
96,2 0,169
96,5 0,166
96,8 0,168
97,1 0,166
97,3 0,167
97,5 0,168
97,8 0,168
97,8 0,168
98,0 0,169
98,2 0,169
98,4 0,168
98,6 0,167
98,9 0,166
99,2 0,164
99,5 0,164
99,7 0,165
99,9 0,165
100,3 0,167
100,5 0,166
100,7 0,165
100,9 0,164
101,1 0,162
101,3 0,162
101,6 0,161
101,8 0,161
102,0 0,159
102,2 0,158
102,4 0,159
102,6 0,158
102,8 0,159
103,0 0,159
103,3 0,157
103,5 0,156
103,7 0,155
104,0 0,154
104,2 0,153
104,4 0,151
Degrees Ncm
104,7 0,151
104,7 0,151
104,8 0,152
105,0 0,154
105,2 0,153
105,4 0,153
105,6 0,152
105,8 0,150
106,0 0,151
106,2 0,149
106,4 0,149
106,8 0,149
107,0 0,151
107,2 0,148
107,4 0,149
107,6 0,150
107,8 0,147
108,0 0,149
108,3 0,146
108,5 0,147
108,7 0,148
108,9 0,149
109,1 0,151
109,2 0,153
109,4 0,151
109,6 0,151
109,7 0,155
109,9 0,152
110,1 0,151
110,2 0,157
110,4 0,151
110,6 0,151
110,8 0,153
110,8 0,153
111,0 0,149
111,2 0,153
111,3 0,155
111,4 0,152
111,6 0,155
111,7 0,160
111,9 0,152
112,0 0,150
112,3 0,162
112,5 0,143
112,7 0,154
112,8 0,161
113,0 0,141
113,2 0,149
Degrees Ncm
113,3 0,158
113,5 0,146
113,7 0,142
113,8 0,156
113,9 0,162
114,1 0,141
114,2 0,140
114,3 0,153
114,4 0,159
114,7 0,141
114,8 0,136
114,9 0,151
115,0 0,157
115,3 0,130
115,4 0,139
115,5 0,151
115,6 0,157
115,7 0,147
115,9 0,133
115,9 0,133
116,0 0,149
116,0 0,155
116,1 0,162
116,1 0,167
116,3 0,166
116,5 0,129
116,7 0,153
116,7 0,160
116,8 0,167
116,8 0,171
117,0 0,150
117,2 0,133
117,3 0,150
117,4 0,156
117,4 0,163
117,5 0,169
117,5 0,172
117,8 0,146
117,9 0,133
118,0 0,152
118,0 0,155
118,1 0,163
118,1 0,169
118,2 0,173
118,3 0,171
118,6 0,126
118,7 0,147
118,8 0,153
Modeling of a step motor for position feedback in a climate system
Appendix A:4
Degrees Ncm
118,8 0,153
118,9 0,159
119,2 0,127
119,3 0,146
119,4 0,154
119,5 0,160
119,7 0,125
119,8 0,139
120,0 0,152
120,3 0,125
120,4 0,138
120,5 0,151
120,6 0,157
120,9 0,136
121,1 0,133
121,2 0,150
121,3 0,156
121,6 0,121
121,7 0,139
121,8 0,150
121,9 0,158
122,1 0,165
122,2 0,170
122,3 0,173
122,5 0,176
122,8 0,143
123,0 0,122
123,1 0,145
123,1 0,145
123,3 0,150
123,4 0,165
123,6 0,170
123,7 0,173
123,7 0,173
123,8 0,177
123,9 0,182
124,0 0,188
124,0 0,192
124,2 0,192
124,3 0,195
124,7 0,137
124,9 0,170
125,0 0,176
125,1 0,184
125,2 0,189
125,3 0,194
125,3 0,200
125,4 0,205
Degrees Ncm
125,5 0,210
125,5 0,216
125,6 0,221
125,7 0,227
126,0 0,184
126,1 0,204
126,2 0,218
126,2 0,223
126,2 0,231
126,3 0,237
126,3 0,242
126,4 0,245
126,4 0,249
126,4 0,255
126,4 0,255
126,5 0,261
126,6 0,266
126,7 0,272
126,9 0,232
127,0 0,251
127,1 0,264
127,1 0,269
127,1 0,276
127,2 0,283
127,2 0,293
127,3 0,297
127,3 0,302
127,4 0,308
127,4 0,313
127,4 0,318
127,5 0,321
127,5 0,327
127,6 0,332
127,6 0,335
127,8 0,310
127,8 0,315
127,9 0,328
127,9 0,335
127,9 0,341
128,0 0,348
128,0 0,354
128,0 0,360
128,0 0,366
128,1 0,372
128,1 0,378
128,1 0,378
128,1 0,385
128,1 0,392
Degrees Ncm
128,2 0,401
128,2 0,410
128,3 0,420
128,3 0,428
128,3 0,437
128,3 0,444
128,4 0,450
128,4 0,468
128,4 0,479
128,5 0,491
128,5 0,503
128,5 0,516
128,6 0,526
128,6 0,537
128,6 0,537
128,6 0,547
128,6 0,560
128,6 0,564
128,7 0,563
128,7 0,560
128,7 0,560
128,7 0,563
128,7 0,568
128,7 0,576
128,7 0,583
128,7 0,588
128,7 0,592
128,7 0,594
128,7 0,594
128,7 0,593
128,7 0,592
128,7 0,592
128,7 0,598
128,7 0,603
128,7 0,608
128,7 0,615
128,7 0,619
128,7 0,620
128,8 0,621
128,8 0,626
128,8 0,634
128,8 0,643
128,8 0,650
128,8 0,655
128,8 0,660
128,8 0,667
128,9 0,671
128,9 0,676
Modeling of a step motor for position feedback in a climate system
Appendix A:5
Values from the measurment
-0,800
-0,600
-0,400
-0,200
0,000
0,200
0,400
0,600
0,800
0,0 20,0 40,0 60,0 80,0 100,0 120,0 140,0
Degrees Ncm
128,9 0,685
128,9 0,693
128,9 0,699
Degrees Ncm
128,9 0,706
Table below shows the values used in the forward look-up tables in the model.
Degrees Ncm
53,7 -0,718
53,7 -0,673
53,7 -0,604
53,9 -0,110
54,5 0,077
56,7 0,124
60,1 0,128
63,6 0,134
67,4 0,139
71,6 0,142
76,5 0,147
81,2 0,153
86,3 0,150
90,6 0,161
95,0 0,173
99,7 0,165
104,2 0,153
108,3 0,146
111,6 0,155
114,8 0,136
117,0 0,150
119,2 0,127
122,2 0,170
125,0 0,176
126,4 0,255
127,8 0,310
128,4 0,450
128,7 0,592
128,9 0,671
128,9 0,706
Used values
-0,800
-0,600
-0,400
-0,200
0,000
0,200
0,400
0,600
0,800
0,0 20,0 40,0 60,0 80,0 100,0 120,0 140,0
Figure 25. Values from the measurements by VCC
Figure 26. Value for forward movement used in model
Modeling of a step motor for position feedback in a climate system
Appendix B:1
B. Values for conductive load, backward
Shown below are the values from the measuring done by VCC showing how the load
changes when moving the flaps backwards.
Degree Ncm
130,5 0,404
130,5 0,403
130,5 0,400
130,5 0,395
130,5 0,387
130,5 0,378
130,5 0,368
130,5 0,360
130,5 0,347
130,5 0,339
130,5 0,329
130,5 0,313
130,5 0,291
130,5 0,264
130,5 0,236
130,4 0,209
130,4 0,181
130,3 0,153
130,3 0,127
130,3 0,127
130,1 0,105
130,0 0,083
129,9 0,064
129,7 0,046
129,6 0,031
129,4 0,018
129,3 0,007
129,2 0,000
129,1 0,000
129,0 -0,005
128,9 -0,024
128,7 -0,034
128,4 -0,040
128,0 -0,041
127,6 -0,041
127,1 -0,043
126,7 -0,045
126,3 -0,048
126,0 -0,053
125,8 -0,057
125,4 -0,066
125,2 -0,070
125,1 -0,074
Degree Ncm
124,9 -0,077
124,6 -0,080
124,4 -0,083
124,0 -0,081
123,4 -0,074
122,7 -0,066
122,7 -0,066
121,9 -0,061
121,1 -0,059
120,3 -0,059
119,7 -0,060
119,2 -0,060
118,6 -0,060
118,1 -0,060
117,4 -0,059
116,7 -0,057
115,9 -0,056
115,1 -0,054
114,2 -0,054
113,3 -0,052
112,5 -0,051
111,6 -0,051
110,9 -0,051
110,3 -0,050
109,7 -0,050
109,1 -0,050
108,5 -0,051
107,9 -0,051
106,5 -0,051
105,8 -0,050
105,1 -0,050
104,3 -0,050
103,6 -0,049
102,8 -0,049
102,1 -0,050
101,5 -0,050
101,5 -0,050
100,8 -0,051
100,2 -0,052
99,5 -0,051
98,7 -0,052
98,0 -0,051
97,2 -0,051
Degree Ncm
96,4 -0,051
95,6 -0,052
94,7 -0,052
93,9 -0,052
93,1 -0,053
92,3 -0,052
91,5 -0,051
90,8 -0,050
90,0 -0,050
89,2 -0,050
88,5 -0,051
87,7 -0,051
86,9 -0,050
86,2 -0,050
85,5 -0,049
84,8 -0,049
83,6 -0,049
83,0 -0,050
82,5 -0,050
82,1 -0,050
81,6 -0,051
81,2 -0,051
80,8 -0,052
80,5 -0,052
80,5 -0,052
80,2 -0,052
79,9 -0,053
79,6 -0,053
79,3 -0,055
78,8 -0,054
78,3 -0,054
77,8 -0,054
77,4 -0,054
76,9 -0,054
76,5 -0,054
76,1 -0,055
75,7 -0,055
75,3 -0,055
74,9 -0,054
74,5 -0,054
74,2 -0,054
73,8 -0,055
73,3 -0,055
Modeling of a step motor for position feedback in a climate system
Appendix B:2
Degree Ncm
72,8 -0,056
72,3 -0,055
71,7 -0,056
71,1 -0,056
70,5 -0,055
69,3 -0,057
68,8 -0,058
68,2 -0,058
67,5 -0,058
66,9 -0,058
66,3 -0,057
66,3 -0,057
65,7 -0,058
65,1 -0,058
64,5 -0,059
63,9 -0,059
63,3 -0,059
62,7 -0,059
62,1 -0,060
61,5 -0,060
61,0 -0,062
60,4 -0,063
59,9 -0,063
59,4 -0,065
58,9 -0,066
58,3 -0,067
57,8 -0,070
57,4 -0,072
57,0 -0,077
56,7 -0,081
56,4 -0,085
56,1 -0,090
55,9 -0,095
55,7 -0,101
55,5 -0,109
55,3 -0,115
54,9 -0,126
54,8 -0,131
54,6 -0,135
54,4 -0,140
54,3 -0,145
54,1 -0,150
54,0 -0,153
53,8 -0,157
53,8 -0,157
53,7 -0,161
53,6 -0,166
53,4 -0,169
Degree Ncm
53,3 -0,173
53,3 -0,178
53,2 -0,181
53,1 -0,185
53,0 -0,190
52,9 -0,194
52,8 -0,200
52,7 -0,204
52,6 -0,209
52,6 -0,215
52,6 -0,221
52,5 -0,226
52,5 -0,232
52,5 -0,237
52,5 -0,243
52,5 -0,248
52,5 -0,253
52,5 -0,257
52,5 -0,263
52,4 -0,275
52,4 -0,282
52,4 -0,288
52,4 -0,291
52,4 -0,294
52,3 -0,299
52,3 -0,302
52,3 -0,302
52,3 -0,303
52,3 -0,305
52,3 -0,307
52,3 -0,310
52,3 -0,314
52,3 -0,319
52,2 -0,321
52,2 -0,325
52,2 -0,327
52,2 -0,328
52,2 -0,330
52,2 -0,333
52,2 -0,334
52,2 -0,337
52,2 -0,338
52,1 -0,341
52,1 -0,343
52,1 -0,344
52,1 -0,348
52,1 -0,352
52,1 -0,354
Degree Ncm
52,1 -0,356
52,0 -0,358
52,0 -0,361
52,0 -0,365
52,0 -0,366
52,0 -0,367
52,0 -0,367
52,0 -0,368
52,0 -0,368
52,0 -0,371
52,0 -0,376
52,0 -0,379
51,9 -0,381
51,9 -0,381
52,0 -0,384
51,9 -0,386
51,9 -0,388
51,9 -0,388
51,9 -0,389
51,9 -0,390
51,9 -0,393
51,9 -0,396
51,9 -0,401
51,9 -0,407
51,9 -0,410
51,9 -0,413
51,9 -0,415
51,9 -0,416
51,9 -0,420
51,9 -0,423
51,8 -0,429
51,8 -0,435
51,8 -0,440
51,8 -0,446
51,8 -0,454
51,8 -0,455
51,8 -0,454
51,8 -0,455
51,8 -0,454
51,8 -0,455
51,8 -0,455
51,8 -0,458
51,8 -0,464
51,8 -0,469
51,8 -0,473
51,8 -0,475
51,8 -0,476
51,8 -0,476
Modeling of a step motor for position feedback in a climate system
Appendix B:3
Degree Ncm
51,8 -0,475
51,8 -0,474
51,8 -0,474
51,8 -0,478
51,8 -0,482
51,8 -0,486
51,8 -0,489
51,7 -0,491
51,7 -0,493
51,7 -0,491
51,7 -0,489
51,7 -0,489
51,7 -0,490
51,7 -0,492
51,7 -0,496
51,7 -0,499
51,7 -0,503
51,7 -0,506
51,7 -0,507
51,7 -0,510
51,7 -0,510
51,7 -0,513
51,7 -0,520
51,7 -0,523
51,7 -0,525
51,7 -0,527
51,7 -0,528
51,7 -0,531
51,7 -0,531
51,7 -0,531
51,7 -0,531
51,7 -0,529
51,7 -0,529
51,7 -0,530
51,7 -0,534
51,7 -0,537
51,7 -0,540
51,7 -0,542
51,7 -0,546
51,7 -0,548
51,7 -0,549
51,7 -0,549
51,7 -0,548
51,7 -0,548
51,7 -0,550
51,7 -0,551
51,7 -0,554
51,7 -0,556
Degree Ncm
51,6 -0,558
51,6 -0,558
51,6 -0,557
51,6 -0,558
51,6 -0,558
51,6 -0,560
51,6 -0,560
51,6 -0,564
51,6 -0,564
51,6 -0,566
51,6 -0,568
51,6 -0,569
51,6 -0,569
51,6 -0,567
51,6 -0,568
51,6 -0,570
51,6 -0,574
51,6 -0,577
51,6 -0,580
51,6 -0,582
51,6 -0,581
51,6 -0,578
51,6 -0,576
51,6 -0,575
51,6 -0,576
51,6 -0,578
51,6 -0,581
51,6 -0,583
51,6 -0,586
51,6 -0,585
51,6 -0,584
51,6 -0,582
51,6 -0,578
51,6 -0,578
51,6 -0,578
51,6 -0,579
51,6 -0,580
51,6 -0,581
51,6 -0,584
51,6 -0,586
51,6 -0,588
51,6 -0,591
51,6 -0,593
51,6 -0,593
51,6 -0,596
51,6 -0,597
51,6 -0,597
51,6 -0,597
Degree Ncm
51,6 -0,598
51,6 -0,599
51,6 -0,600
51,6 -0,600
51,6 -0,602
51,6 -0,603
51,6 -0,605
51,6 -0,605
51,6 -0,606
51,6 -0,605
51,6 -0,604
51,6 -0,601
51,6 -0,600
51,6 -0,600
51,6 -0,602
51,6 -0,606
51,6 -0,608
51,6 -0,610
51,5 -0,614
51,5 -0,617
51,5 -0,618
51,6 -0,619
51,6 -0,619
51,5 -0,617
51,5 -0,616
51,6 -0,614
51,5 -0,613
51,5 -0,613
51,5 -0,613
51,5 -0,615
51,5 -0,619
51,5 -0,621
51,5 -0,622
51,5 -0,620
51,5 -0,619
51,5 -0,619
51,5 -0,619
51,5 -0,619
51,5 -0,622
51,5 -0,623
51,5 -0,625
51,5 -0,627
51,5 -0,629
51,5 -0,629
51,5 -0,630
51,5 -0,629
51,5 -0,630
51,5 -0,630
Modeling of a step motor for position feedback in a climate system
Appendix B:4
Degree Ncm
51,5 -0,630
51,5 -0,631
51,5 -0,632
51,5 -0,633
51,5 -0,634
51,5 -0,633
51,5 -0,631
51,5 -0,631
51,5 -0,630
51,5 -0,628
51,5 -0,629
51,5 -0,628
51,5 -0,628
51,5 -0,627
51,5 -0,630
51,5 -0,633
51,5 -0,636
51,5 -0,637
51,5 -0,637
51,5 -0,638
51,5 -0,639
51,5 -0,640
51,5 -0,642
51,5 -0,642
51,5 -0,644
51,5 -0,645
Degree Ncm
51,5 -0,646
51,5 -0,648
51,5 -0,648
51,5 -0,647
51,5 -0,647
51,5 -0,647
51,5 -0,648
51,5 -0,649
51,5 -0,651
51,5 -0,653
51,5 -0,654
51,5 -0,653
51,5 -0,653
51,5 -0,652
51,5 -0,653
51,5 -0,653
51,5 -0,653
51,5 -0,652
51,5 -0,651
51,5 -0,650
51,5 -0,652
51,5 -0,652
51,5 -0,653
51,5 -0,655
51,5 -0,656
51,5 -0,656
Degree Ncm
51,5 -0,655
51,5 -0,651
51,5 -0,649
51,5 -0,648
51,5 -0,650
51,5 -0,652
51,5 -0,652
51,5 -0,652
51,5 -0,651
51,5 -0,653
51,5 -0,655
51,5 -0,656
51,5 -0,657
51,5 -0,657
51,5 -0,657
51,5 -0,660
51,5 -0,661
51,5 -0,659
51,5 -0,655
51,5 -0,650
51,5 -0,650
Modeling of a step motor for position feedback in a climate system
Appendix B:5
Values used in the look-up table for backwards movement in the model.
Values from measurement
-0,800
-0,600
-0,400
-0,200
0,000
0,200
0,400
0,600
0,0 20,0 40,0 60,0 80,0 100,0 120,0 140,0
Figure 27. Values from measurements by VCC
Used values
-0,800
-0,600
-0,400
-0,200
0,000
0,200
0,400
0,600
0,0 20,0 40,0 60,0 80,0 100,0 120,0 140,0
Figure 28. Values used for backward movement in model
Degree Ncm
51,5 -0,650
51,5 -0,656
51,5 -0,652
51,5 -0,642
51,5 -0,633
51,5 -0,621
51,6 -0,601
51,6 -0,586
51,6 -0,582
51,7 -0,556
51,7 -0,531
51,7 -0,491
51,8 -0,455
51,9 -0,386
52,1 -0,343
52,4 -0,294
53,1 -0,185
56,1 -0,090
66,3 -0,057
76,5 -0,054
85,5 -0,049
100,8 -0,051
115,1 -0,054
125,4 -0,066
130,1 0,105
130,5 0,404
Modeling of a step motor for position feedback in a climate system
Appendix C:1
C. M-file for actuator.mdl %M-file for actuator %(not real values for Eaton actuator)
close all; clear all;
Ra = 4.5 ; % Ohm. A winding resistance Rb = 4.5 ; % Ohm. B winding resistance La = 20*10^-3 ; % H. A winding inductance Lb = 20*10^-3 ; % H. B winding inductance k = 0.1 ; % Nm/A. Torque of constant J = 10.1*10^-6 ; % kg m^2. Moment of inertia B = 2.4*10^-3 ; % Nms. Viscous friction Nr = 5 ; % Number pair of poles of the rotor
%Values for Cl-lookup tables %Real values for Eaton actuator thetas_f =
[53.7;53.7;53.7;53.9;54.5;56.7;60.1;63.6;67.4;71.6;76.5;81.2;86.3;90.6
;95.0;99.7;104.2;108.3;111.6;114.8;117.0;119.2;122.2;125.0;126.4;127.8
;128.4;128.7;128.9;128.9]; Cl_f = [-0.718;-0.673;-0.604;-
0.110;0.077;0.124;0.128;0.134;0.139;0.142;0.147;0.153;0.150;0.161;0.17
3;0.165;0.153;0.146;0.155;0.136;0.150;0.127;0.170;0.176;0.255;0.310;0.
450;0.592;0.671;0.706];
thetas_b =
[51.5;51.5;51.5;51.5;51.5;51.5;51.6;51.6;51.6;51.7;51.7;51.7;51.8;51.9
;52.1;52.4;53.1;56.1;66.3;76.5;85.5;100.8;115.1;125.4;130.1;130.5]; Cl_b = [-0.650;-0.656;-0.652;-0.642;-0.633;-0.621;-0.601;-0.586;-
0.582;-0.556;-0.531;-0.491;-0.455;-0.386;-0.343;-0.294;-0.185;-0.090;-
0.057;-0.054;-0.049;-0.051;-0.054;-0.066;0.105;0.404];