Modeling of a step motor for position feedback in a climat )214944/FULLTEXT01.pdf · Modeling of a step motor for position feedback in a climate system Summary The goal of this project

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


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.


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


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


POS Position = 2 steps = 1 pole on the rotor

PWM Pulse Width Modulation

VCC Volvo Car Corporation


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.


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


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


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].


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.


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)


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


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)


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)


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)


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)


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.


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


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.


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


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


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.


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.


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


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


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.


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


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


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.


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.


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


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.


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]


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


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


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


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


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


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


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


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


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


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


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];

Documents

Modeling of a step motor for position feedback in a climat )214944/FULLTEXT01.pdf · Modeling of a step motor for position feedback in a climate system Summary The goal of this project