High Precision and Low-cost Stepper Motor Control for Industrial Implementation

(1)

IN

DEGREE PROJECT ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS

,

STOCKHOLM SWEDEN 2018

High Precision and Low-cost

Stepper Motor Control for

Industrial Implementation

CHUYAO ZHOU

KTH ROYAL INSTITUTE OF TECHNOLOGY

(2)

TRITA TRITA-EECS-EX-2018:528 ISSN 1653-5146

(3)

KTH R

OYAL

I

NSTITUTE OF

T

ECHNOLOGY

M

ASTER

T

HESIS

High Precision and Low-cost Stepper

Motor Control for Industrial

Implementation

Author: Chuyao Zhou Supervisor: Dr. Bin Liu Examiner: Dr. Oskar Wallmark August 24, 2018

(4)

(5)

iii

Abstract

The industry is calling for a low-cost drive solution. The hybrid stepper motor is considered as a good candidate since it has much larger production than traditional servo motor. In this thesis, the author comes up with a control solution of a hybrid stepper motor based on a low-cost sensor, which reaches a high control resolution with a low cost. In the design, vector control is chosen and modified to be the con-trol strategy of the motor. An extended kalman filter (EKF), neural network (NN) and linear regression harmonic compensation (LRHC) are evaluated to improve the performance of the low-cost sensor. In the experiments, the solution is tested by running the motor to simulate an industrial implementation. The experiments give a positive outcome so that the feasibility of the low-cost solution for the industrial drive has been proved.

Sammanfattning

I industrin finns det ett behov av en lågkostnadslösning för motorstyrning. Den hybrida stegmotorn anses vara en bra kandidat eftersom den produceras i mycket högre utsträckning än den traditionella stegmotorn. I detta examensarbete har för-fattaren föreslagit en kontrollösning för en hybrid stegmotor baserad på en lågkost-nadssensor, vilken når en hög upplösning med en låg kostnad. Designen använ-der sig av vektorstyrning för att reglera motorn. Ett EKF (Extended Kalman Filter), ett NN (Neural Network) och LRHC (Linear Regression Harmonic Compensation) har utvärderats för att förbättra prestandan av lågkostnadssensorn. I experimenten testades lösningen genom att köra motorn för att simulera användning i industrin. Experimenten gav positiva resultat, så möjligheten för att använda lågkostnadslös-ningen för industriell styrning har bevisats.

(6)

(7)

v

Acknowledgements

Foremost, I would like to express my sincere gratitude to my supervisor Dr. Bin Liu for the continuous support of my master thesis project and research, for his patience, motivation, enthusiasm, and immense knowledge. His guidance helped me in all the time of research and writing of this thesis.

Besides my supervisor, I would like to thank my examiner associate professor Dr. Oskar Wallmark for his expertise on electrical machines, the continuous following of my project progress and his valuable advice on my thesis draft.

My sincere thanks also go to my ABB colleges, especially to Peter Fransson, who helped me a lot in the laboratory, and to Pietro Falco, who offered me many critical suggestions on signal processing.

Last but not least, I would like to thank my family who is always the most solid backing of me. And to my loved J.M.Walker, with whom I have spent the happiest time in Sweden.

(8)

(9)

vii

List of Abbreviations

EKF Extended Kalman Filter HSM Hybrid Stepper Motor

LRHC Linear Regression Harmonic Compensation MRPS Magnetic Rotary Position Sensor

NN Neural Network

(12)

(13)

xi

List of Symbols

uaub phase voltage of the motor V

iaib phase current of the motor A

ωr angular speed of the rotor rad/s

θr position of the rotor rad

R phase resistance of the motor Ω L phase inductance of the motor H Km torque constant V s/rad

Kv coefficient of viscous friction N m s/rad

J system inertia kg m2

τ load torque N m

(14)

(15)

1

Chapter 1

Introduction

1.1 Purpose

This purpose of this research project is to develop a high precision position control solution for a hybrid stepper motor based on a low-cost sensor, and investigate the feasibility of the solution for the high-end industrial implementation.

1.2 Challenge and Scope

The challenge of this project is how to properly control the motion of the motor with the low-quality signal from the low-cost sensor. Thus, the main task of this project will be divided into two section. First, a motion control strategy of the stepper mo-tor should be developed. Second, the signal from the low-cost sensor needs to be processed to meet the demand of the control strategy.

1.3 Background

Nowadays, the industrial automation becomes more and more popular. There will be more demand for high-end industrial implementations not only in the traditional manufacture such as autonomous industry but also in small business such as food package. The food package implementation may not need as high precision as that in the autonomous industry but it calls for a cheaper solution with a fairly high precision. The main cost of an industrial implementation locates at its driving motor and the gearbox. A common solution is using a servo motor. A servo motor is fairly expensive and it usually operates at high speed with a gearbox, which increases its bulk and the cost as well. If a cheaper motor can be used without a gearbox, the cost will decrease by a large margin. From this sense, the stepper motor will be a proper candidate. The stepper motor is widely used in industrial implementation such as motor roller conveyor and tape feeder. It can be easily controlled with an open loop and achieves a fairly high torque volume ratio. However, for an industrial implementation, the precision of a stepper motor under open loop control is not high enough. Thus, a new control strategy needs to be developed.

In the last two years, two research projects have been conducted at ABB Corpo-ration Research Center and the results have been published as master theses [Ron-quist et al.,2016], [Wallin and Varagnolo,2017], some solutions had been proposed in these research projects. Unfortunately, only a few practical results came out due to various reasons. Thus, this thesis will be the follow-up work of the previous research projects.

(16)

2 Chapter 1. Introduction

1.4 Previous Work

Thought the study of stepper motor has been done for years, no reference was found considering the stepper motor and low-cost sensor together. One reason may be the limited usage of the stepper motor in high-end applications. It has its significant drawback such as low precision and detent torque, which results in its less usage than the permanent magnet synchronous motor (PMSM) and brushless direct cur-rent (BLDC) motor. However, in recent years, some industrial research projects such as [Karlsson,2016] had been done to investigate the feasibility of replacing the exist-ing solutions with stepper motor solutions.

As for the control of stepper motor, research works have been taken in different aspects. For many years, references such as [Zhang, He, and Sheng,2005], [Baluta,

2007] focused on improving the microstepping algorithm to increase the precision of the open-loop control of the stepper motor. Some following works such as [Der-ammelaere et al.,2014], [Derammelaere et al.,2017] have made progress in the load angle compensation, trying to reach a higher precision in open-loop mode. Inspired by this, a research in ABB [Liu et al.,2017] implemented the load compensation algo-rithm in a close-loop mode. In another way, some researchers tried to implement the close-loop control based on a sensorless control strategy using estimation algorithm such as Linearization [Zribi and Chiasson,1991], neural network(NN) [Feng,2000] and extended kalman filter(EKF) [Persson and Perriard,2003a], [Persson and Per-riard,2003b]. And different damping strategies have been developed to eliminate the detent torque of the stepper motor [Schweid, McInroy, and Lofthus,1995], [Le, Hoang, and Jeon,2017]. In general, many projects have been done to overcome the nature drawback, low precision and detent torque. These works will offer a lot of valuable information for this thesis, the details will be further discussed in Chapter 2.

In previous research projects at ABB, a low-cost Magnetic Rotary Position Sen-sor (MRPS) was selected to provide the position information of the rotor. However, its signal quality can not meet the requirement of the control strategy so it needs to be compensated. The previous student theses had already given a good summary for this specific MRPS and some compensated methods were proposed. For exam-ple, [Ronquist et al., 2016] proposed methods such as linear regression and adap-tive notch filter, but this research did not totally eliminate the variation problem of the MRPS signal. The next student thesis [Wallin and Varagnolo,2017] proposed a method using EKF, however, the result is not so reliable. In this thesis, these meth-ods will be reevaluated and new methmeth-ods such as neutral network will be tested. Further details will be discussed in Chapter 3 and Chapter 4

1.5 Thesis Contribution

Based on the previous work, this thesis proposed a complete solution of a stepper motor control for high-end industrial implementations, combining the stepper mo-tor and a low-cost sensor. This solution improves the precision of the low-cost sensor by linear regression harmonic compensation, and control the motor’s motion by a Vector Control strategy through a properly designed controller. The final solution greatly reduces the cost of the drive system of a stepper motor and keeps a fairly high precision of position control.

(17)

1.6. Thesis Outline 3

1.6 Thesis Outline

The following contents will begin with the system modeling and go on with the theories of controller design and signal processing. Some simulation results related to method choice will be shown with the theories. In the end, there are experimental results followed by the conclusion and discussion.

(18)

(19)

5

Chapter 2

System Modeling and Control

Strategy

2.1 Hybrid Stepper Motor

Stepper motor is a kind of motor which can translate switched excitation changes into precisely defined increments (‘Step’) of rotor position [Acarnley, 2002]. The stepper motor can be divided into two basic types: hybrid stepper motor (HSM) and the variable-reluctance motor (VRM). The main difference is that the magnetic flux in VRM is purely excited by the exciting current that applied to the stator wind-ing. However, for the HSM, magnetic flux is mainly induced by the permanent magnet. In this thesis, a two-phase hybrid stepper motor is used on the test rig. (All the ‘stepper motor’ refers to the hybrid stepper motor in the following text if not specified). This stepper motor has two phase winding perpendicular to each other, which are referred as a and b phase, respectively. The coordination based on these two phases is called αβ frame. The schematic of a hybrid stepper motor can be seen in Fig.2.1. A disassembled stepper motor provided by ABB is shown in Fig.2.2.

2.2 Open-loop Control and Microstepping

Conventionally, stepper motors were always controlled by a series of step signals on each phase, which induced a series of magnetic force on the stator to attract the rotor to a certain position. Since it is open-loop control, this control strategy needs a large number of rotor teeth to achieve a high resolution. Typically, a stepper motor has

FIGURE2.1: Schematic

of Hybrid Stepper Mo-tor Structure [Ronquist

et al.,2016].

FIGURE 2.2:

Disas-sembled Stepper Mo-tor From ABB

(20)

6 Chapter 2. System Modeling and Control Strategy 200 teeth with the resolution of 1.8◦mechanical degrees. However, this discrete step control will naturally induce a cogging problem, i.e. the detent torque, which may affect the performance of the motor in some implementation. This phenomenon is an essential drawback of the stepper motor.

To reach a higher position resolution, the size of exciting steps can be reduced, for example, the half-step algorithm can reach a double resolution. The step size can be reduced even further by an algorithm named microstepping [Zhang, He, and Sheng,

2005], [Baluta,2007]. The microstepping algorithm uses sinusoidal excitation current to generate flux and torque. The more steps the controller generates, the higher resolution it will reach and more sinusoidal the control signals will be. The position reference information is provided by the excitation current as shown in (2.1).

ia = I0cos(θe) = I0cos(Nrθ_{re f})

ib= I0sin(θe) = I0sin(Nrθre f)

(2.1) Note that even with microstepping algorithm, the effect of detent torque can not be totally eliminated. Usually, the magnitude of detent torque is only 10% of the holding torque. Thus, most of the references neglect it in the system model and consider it as a disturbance of the system [Bellini et al.,2007].

2.3 Close-loop and Vector Control

Since the microstepping algorithm can only reduce the error but not eliminate the error in open-loop mode, a close-loop control algorithm may be taken into account. However, if the control is done directly under αβ frame, a PI controller can not con-trol the current without a static error in close-loop mode, which has been proven by the previous thesis work [Wallin and Varagnolo,2017]. This problem can be solved by the Vector Control algorithm.

Vector control, sometimes known as field oriented control (FOC), allows the con-trol process to be performed on a synchronous rotation coordination aligning with the rotor position, which names dq frame. A schematic of dq coordination is shown in Fig.2.3. The currents and voltages under dq frame can be easily derived from the

αβ frame by applying a transformation call Park transformation as shown in (2.2).

After applying Park transformation, both AC current and voltage are changed into DC current and voltage, which can be easily controlled by a simple PI controller without static error. The mathematical dynamic model of the hybrid stepper motor in dq frame can be commonly described [Bendjedia et al., 2012] as (2.3). It could be remarked that the equation is similar with the one of non-salient PMSM due to the existence of the permanent magnet rotor. Another point is that there is no mu-tual inductance in this two-phase HSM due to the orthogonality between the two phases. In this case, this HSM can be controlled as a PMSM through vector control. Conventionally, the reference of d-axial current will be set as zero, trying to reach the maximum power output of the machine [Fitzgerald,2003, p.583-587]. And the torque will be proportional to the q-axial current output of the machine with coeffi-cient Km. This control algorithm will also be used in this thesis project.

i_d(t) iq(t) = cos(θe(t)) sin(θe(t)) −sin(θe(t)) cos(θe(t)) ia(t) ib(t) (2.2)

(21)

2.4. Different Controller Structures 7

FIGURE2.3: Coordination Rotation of dq frame based on αβ frame.

ud= Rid+L di dt−LNωriq uq= Riq+L di dt−LNωrid+Kmωr Kmiq−τ= Jdω dt +Kvωr dθr dt = ωr (2.3)

The drawback of this method is that a very accurate position information should be provided for the Park transformation. Otherwise, the transformation will not be beneficial to the position control. Hence, it calls for a high-resolution position signal from the sensor. This is the main challenges of signal processing for this thesis.

2.4 Different Controller Structures

There can be different structures of the controller design. Intuitively, the first struc-ture is a simple PID controller with position feedback as shown in (2.4), where KP,

KI and KD are PID controller parameters. The torque reference τre f can be

calcu-lated based on the position reference θre f and the position measurement θr. Since the

torque is proportional to the q-axial current by a coefficient Km, the iqre f can be given

as the input of the current controller.

τ_{re f} =Kmiqre f = KP(θre f −θr) +KI t Z 0 (θ_{re f} −θr)dt+KD( . θ_{re f}− · θr) (2.4)

Also, an additional speed feedback controller as (2.5) may improve the perfor-mance. KPωis the proportional gain of the controller.

τ_{re f} =Kmiqre f =KP(θre f −θr) +KI t Z 0 (θ_{re f}−θr)dt+KD( . θ_{re f}− · θr) +KPω(ω_{re f} −ωr) (2.5) However, as a mechanical system, the other important variables such as friction and moment of inertia should be considered. Thus, the controller structure pro-posed in reference [Kim, Yang, and Chung,2011] is interesting to be discussed and

(22)

8 Chapter 2. System Modeling and Control Strategy compared with other simpler controllers. Expect the PID component, this controller structure has other two additional terms to compensate for the viscous friction and the torque induced by acceleration. It has been proved in the same reference that this controller structure is stable and will converge to zero error when the time in-crease to infinite. The equation of the controller is (2.6), where KP, KI and KD can

be determined by a stability analysis of the control matrix. Kv is the coefficient of

friction. J is the inertia of the motor.

τre f =Kmiqre f =KP(θre f−θr) +KI t Z 0 (θre f −θr)dt+KD( . θre f− · θr) +Kvωre f +J . ωre f

Moreover, it is possible to add a speed controller on this structure as (2.6). The speed controller may contribute to the control of transience.

τre f =Kmiqre f =KP(θre f−θr) +KI t Z 0 (θre f −θr)dt+KD( . θre f− · θr) +KPω(ωre f −ωr) +Kvωre f +J . ωre f

These four controller structures will all be tested on the test rig and the results will be evaluated in Chapter 5.

2.5 Reverse Challenge and Friction Compensation

For the dynamic process in industrial implementations, one of the most important challenges is the compensation of the position error in the reverse process, i.e, when the motor changes its rotation direction in a short time. The reverse process is similar to the restart-up of the machine. For example, the q-axial current will vanish from a positive value to zero and then increase in the negative direction or vise versa. Thus, the motor will lose the driving force in an instant and regain it after. The largest error in the whole running period of the motor will be induced by this reverse process (see Chapter 5). This problem may be eliminated in different ways, such as high-order compensator [Krishnamurthy and Khorrami, 2004] to overcome the disturbance, optimized controller bandwidth to shorten the reverse time, etc. Due to the time limit, a simple friction compensation is proposed in this thesis instead of other advanced methods.

The term of in Kvω in (2.6) is for the compensation of friction. However, this

term only considers the common running process. According to the Coulomb’s law, the friction needed to start a motion is larger than that needed to maintain it, i.e, the friction will change from the static friction to the kinetic friction when a mass starts its motion [“Friction” 2011]. A schematic illustration is shown in Fig.2.4. Thus, the controller design should take static friction into account.

(23)

2.5. Reverse Challenge and Friction Compensation 9

FIGURE2.4: Schematic of Static Friction and Kinetic Friction (

“Fric-tion” 2011).

The friction can be modeled in different ways, for the simplest as Morin’s model, the static friction is assumed to be a constant value [Morin,1833]. In this case, the friction model can be described by (2.6).

f(v, τ) =      τ ωr=0,|τ| < fs fssgn(τ) ωr=0,|τ| > fs Kvωr ωr6=0, (2.6)

where fsis the static friction and the sign function is defined as (2.7):

sgn(x) =      1 x<0 0 x=0 −1 x>0 (2.7)

From the control aspect, if the compensation term is constructed by the simple model, the discontinuity of the reference signal at the original point will induce a large step of reference, which will result in a larger error. Thus, a tanh function is considered to construct the compensation term Kvω. The modified model is shown

as (2.8). f(v) = ( m·tanh(v) |ωr| <ωth Kvωr |ωr| >ωth (2.8) where m is the magnitude of the tanh function and ωth is the speed threshold

to limit the implementation range of the tanh term. These two parameters can be determined if the material and running scenario of the motor is known. However, in engineering application, it can be tuned through trial-and-error method.

The experimental results of this friction compensation algorithm can be seen in Chapter 5.

(24)

(25)

11

Chapter 3

Extended Kalman Filter

Extended kalman filter (EKF) and unscented kalman filter (UKF) have been pro-posed in a previous student thesis [Wallin and Varagnolo,2017] for the sensor fusion solution, i.e, fusing two position signals (MRPS+back-emf), to improve the signal quality from the low-cost sensor MRPS. However, the outcome of that student thesis seems to be unreasonable. Thus, the EKF algorithm will be reexamined in this thesis.

3.1 EKF Algorithm

Kalman Filter (KF) is a recursively calculation algorithm to predict a signal and filter the white noise. In the original paper of R.E.Kalman [R.E,1960], he only raised up the algorithm on the linear system. In the later works such as [Persson and Perri-ard,2003a] and [Zawirski, Janiszewski, and Muszynski, 2013], people applied this algorithm on non-linear systems by linearizing the system, which is the so-called extended kalman filter (EKF).

Usually, a system can be modeled in state space as (3.1). xk+1=Φxk+Γuk+wk

zk+1= Hxk+vk

w_k ∼ N(0, Qk)

v_k ∼ N(0, R_k)

(3.1)

where the subscripts k+1 and k stand for the sample time instant in a discrete system. The other symbols are listed in Table.3.1.

In this stepper motor implementation, based on the system model of stepper motor in Chapter 2, the (2.3) can be discretized in a matrix form as (3.2).

      idk+1 iqk+1 ωrk+1 θrk+1 τ_k+1       =        1−TsR_L 0 0 0 0 0 1−TsR_L TsK_Lm 0 0 0 TsK_Jm 1− K_Jv 0 −T_Js 0 0 Ts 1 0 0 0 0 0 1              idk iqk ωrk θrk τ_k       +        Ts_/L ₀ 0 Ts_/L 0 0 0 0 0 0        " u∗_d k u∗_q_k # (3.2) where u∗_d k and u ∗

qk are the decoupled voltage as described in (3.3). This method

is proposed in reference [Persson and Perriard,2003b], which make it easier to build the EKF model and avoid the coupling problem between d and q axis.

udk =u ∗ dk−LNωrkiqk uqk =u ∗ qk+LNωrkidk (3.3)

(26)

12 Chapter 3. Extended Kalman Filter

Symbol Meaning Content

x state of interest h id iq ωr θr τ

iT

z measurement matrix h id iq θr1 θr2 · · · θrS

iT

Φ system matrix see 3.2

Γ control input matrix see 3.2

H measurement input matrix see 3.9

u control matrix h u∗_d u∗_q

iT

w system modeling error matrix Need to be tuned v measurement error matrix Need to be tuned

Q covariance of w Need to be tuned

R covariance of v Need to be tuned

Ts sample time 5e−5(s)

TABLE3.1: Symbols in state space modeling and EKF algorithm

Thus, the system model can be easily written in the way of (3.1) and perform the EKF algorithm as follows.

First, compute the predicted state estimate and measurement: ˆx_k|k−1=Φkˆxk−1|k−1ΦTk +Γk−1uk−1

ˆzk = Hkˆxk|k−1

(3.4) Then compute the prior covariance matrix, Kalman gain and the posterior co-variance matrix:

Pk|k−1 =ΦkPk−1|k−1ΦTk +Qk

K_k =P_k_|_k₋₁H_kT(H_kP_k_|_k₋₁H_kT+R_k)−1

P_k_|_k = (I−K_kH_k)P_k_|_k₋₁

(3.5)

At last, correct the predicted estimate on the measurement:

ˆx_k_|_k = ˆx_k_|_k₋₁+Kk(zk−ˆzk) (3.6)

3.2 Implementation of EKF

3.2.1 Introduction of the signal

There will be two signals(MRPS+back-emf) involved in the implementation of EKF. The MPRS signal and the other is back-emf position signal. The MRPS sensor is introduced in a previous student thesis [Wallin and Varagnolo,2017], it provides a position signal with some variation as shown in Fig.3.5. The challenge is to eliminate this variation as much as possible to provide accurate position information to the controller.

(27)

3.2. Implementation of EKF 13 The back-emf is the abbreviation of back electromotive force, which is induced by the inductance in the winding of the motor by Lenz’s law. As shown in Fig.2.3, the back-emf is always aligning with the q axis. Thus, it can be easily derived from the figure that the projection of back-emf in αβ frame as (3.7).

ea = −Kmωrsin(θe) = −Kmωrsin(Nθr)

eb=Kmωrcos(θe) =Kmωrcos(Nθr)

(3.7) Since ea, eb can be measured, so that the position θr can be calculated through

(3.8).

θr= _N1 arctan(−_ee_ba) (3.8)

3.2.2 Sensor Fusion Algorithm

Senor fusion is a good solution if a better output of the system is expected when several inputs are available simultaneously. Basically, the information contained in different input signals are fused together to generate a better output signal. Thus, sensor fusion is frequently used in robotics’ implementations [Li et al.,2012], [Zhou and Liu,2016]and the optimization of localization problems [Lee et al.,2012], [Yoon, Park, and Kim,2015] as well.

Sensor fusion algorithm is an extension implementation of EKF, the key point on this implementation is the number of position measurement signal. In general cases, considering there are S measurements of position, then the measurement equation, i.e, the second one in (3.1) will be rewritten as:

         idk+1 iqk+1 θr1k+1 θr2k+1 .. . θrSk+1          =          1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 .. . 0 0 .. . 0 0 .. . 0 1 .. . 1 0 .. . 0                idk iqk ωrk θrk τk       (3.9)

In this way, several position signals can be fused by the EKF algorithm. If the available position signals can calibrate each other, the outcome of EKF will be better then the one which has single position input. Note that the number of position input depends on the specific implementation but at least one position signal is needed. In this thesis S=2 so that the back-emf signal will be taken into account besides the MRPS signal.

3.2.3 Tuning of EKF Parameters

Once the EKF is formulated according to the algorithm described before, the matrix w and v need to be tuned based on the real system parameters. The tuning method are described in many references such as [M et al.,2015] and [Bendjedia et al.,2012]. The system error matrix can be tuned based on the measurements and the EKF es-timation results, i.e, the eses-timation results should be as close to the measurements as possible. In this sense, if a measurement is available, a larger coefficient should be put on the corresponding place in the system error matrix rather then the mea-surement error matrix. It can be explained as the error from system modeling is larger than the error from measurement, thus, the measurement should be given

(28)

14 Chapter 3. Extended Kalman Filter more credit. However, the difference of the coefficients can not be too large. Other-wise, the estimation results can not gain benefits from both the system model and the measurements.

The effect of the EKF parameters can be easily observed by tuning the system modeling error matrix w and the measurement error matrix v. If the system mod-eling error of Id and Iq is in w are set to be 1 and the corresponding value in v is

set to be 0.001, 0.1, 1, respectively. The result is shown in Fig.3.1. Note that in this experiment, the Encoder signal is taken as the position signal and only one position signal is involved (no sensor fusion).

FIGURE3.1: EKF tuning of single position input(Encoder); Error of

system modeling is 1 and measurement is 0.001, 0.1, 1, respectively.

3.3 Experimental Results

(29)

3.3. Experimental Results 15

FIGURE3.2: EKF system work flow chart.

A estimation result of EKF is shown in Fig.3.3 and the error of estimation is shown in Fig.3.4. It can be seen from the figures that EKF can give a good estimation of current and position but have a relatively large error for the speed estimation. This error may result in problems when a speed close-loop controller is applied, see experiment result in Chapter 5. And this will be an important further work to do, see discussion in Chapter 6.

(30)

FIGURE3.3: EKF estimation result and reference when the speed is

(31)

3.3. Experimental Results 17

FIGURE3.4: EKF estimation error between result and reference when

the speed is -300rpm, Controlled in open-loop mode.

The sensor fusion result is shown in Fig.3.5. Note that the Encoder signal is taken as the true reference here. It can be seen that from the figure that the matrix v can be further tuned when sensor fusion is applied. The principle is the same with the basic EKF tuning described before, i.e, when a larger error is put in the corresponding place of a signal, that signal gain less ‘’credit” in EKF algorithm. However, it can be clearly observed that the fusion signal is not better than the back-emf position signal, which means that the fusion signal can only provide a signal as best as back-emf position signal rather than taking advantage from both signals. Thus, the EKF sensor fusion algorithm is not an appropriate choice to improve the MRPS signal quality in this situation.

(32)

FIGURE3.5: Sensor fusion result of EKF; The p-p value of position

error of fusion signal is 0.51, 0.61, 0.71 corresponding to 0.1, 0.5, 1 of emf error value in matrix v with MRPS error value as 1, respectively.

3.4 Conclusion

EKF algorithm has its advantage in the signal filtering and observation/estimation. And it has been proved in many references and this thesis that it is very robust and easy to implement. If it is formulated properly, it can contribute a lot to the sensor-less control of speed and torque. However, the EKF algorithm is very sensitive to the parameters and need to be properly tuned. Otherwise, it will lose its accuracy and can only be used for rough observation. As for the sensor fusion, the MRPS signal can not get many benefits from the back-emf signal. There is no evidence that the fusion signal is better than both of the original signals. Moreover, the back-emf has its nature that it will vanish at the low-speed region. Thus, the sensor fusion algo-rithm will not valid in the low-speed region. Besides, there should be a realignment between the MRPS and back-emf signal when the motor accelerates. Due to the low quality of the MRPS signal, the realignment problem severely reduces the feasibility of this solution in industrial implementations.

(33)

19

Chapter 4

Experimental Test Result

5.1 Test Rig Setup

The test rig is developed by previous thesis students and ABB [Ronquist et al.,2016, Wallin and Varagnolo, 2017, Liu et al., 2017]. The test system contents following sections:

• i) Matlab/Simulink (host computer)

• ii) Speedgoat Real-time Target Machine (Link:Speedgoat) • iii) MOSFET driving board

• iv) Motor test rig (Fig.5.1).

The principle of the test system is presented in Fig.5.2.

FIGURE 5.1: Test Rig Setup (ABB); The hysteresis brake is used to

(40)

26 Chapter 5. Experimental Test Result

FIGURE5.2: Working Principle of the Test System.

5.2 Controller Design Test

In this section, the design of the controller is evaluated using the encoder signal for the dq transformation and providing the position information. For the current controller, a step will act as the reference. For the position controller, in general, if a machine will be implemented on the high-end industrial purpose at least it needs to be qualified through the test of following movements: a) Acceleration b) Constant speed (usually with it maximum speed) c) Reverse Direction. As an initial trial, a series of steps from 50rpm to 250rpm are assigned to test a) and b), a sinusoidal reference with frequency _2π10rad/s is assigned to test c). In the end, a test trajectory named cubic test provided by ABB will be run.

As mentioned in Chapter 2, several methods have been proposed for the posi-tion controller design. Thus, different designs will be tested in both steady mode and dynamic mode. The position controller designs that will be tested are listed as follows:

• i) position feedback with PID controller (2.4)

• ii) position feedback (PID) + speed feedback (P) (2.5)

• iii) position feedback (PID) + speed feed forward + acceleration feed forward (2.6)

• iv) position feedback (PID) + speed feed forward + acceleration feed forward + speed feedback (2.6)

and the friction compensation will be tested in sinusoidal and cubic case of the iii) and iv) method to prove its advantage in the motion dynamic process.

5.2.1 Current Controller

The current controller is tested with a q-axial current step from Iq = 0.5A to Iq =

0.3A, the test result is shown in Fig.5.3. As the figure shows, the current controller can respond to the step within a short dynamic period and induce zero error at steady state.

5.2.2 Position Controller with Position Feedback

The test results are shown in Fig.5.4, Fig.5.5 and Fig.5.6. In the step response, a zero error can be seen at the steady state. However, an oscillation appears at the dynamic

(41)

5.2. Controller Design Test 27

FIGURE5.3: Current response to step.

state, which is induced by the well-known trade-off between the fast convergence and the stability in PID controller design. The PID parameters can be tuned accord-ing to the specific implementation. In an industrial implementation, the fast con-vergence has higher priority and the oscillation can be avoided by optimizing the trajectory, speed, acceleration in the top layer optimization algorithm. In the sinu-soidal response, the error is reduced at the running period and the maximum error appears at every reverse instant due to the vanishing of current and speed. This problem will be compensated by the following design. In the cubic test, a dynamic process in the initial state induces a large error, in the common running process, the error increases at every reverse instant as it is in the sinusoidal test.

(42)

FIGURE 5.4: Design(i): position response to a series steps from

50rpm to 250rpm; The peak-peak position error of initial dynamic is

1.07◦;The maximum peak-peak position error during running period

(43)

FIGURE 5.5: Design(i): position response to a sinusoidal reference

with frequency _2π10rad/s; The maximum peak-peak position error

(44)

FIGURE5.6: Design(i): position response to ABB cubic test reference;

The peak-peak position error of initial dynamic is 2.68◦ (not fully

shown);The maximum peak-peak position error during running pe-riod is 2.08◦.

5.2.3 Position Controller with Position Feedback and Speed Feedback

The test results are shown in Fig.5.7, Fig.5.8 and Fig.5.9. For the step reference, a reduction of the dynamic process can be seen from the error waveform, which is the advantage of the speed feedback compared with the single position feedback. However, there is a large steady state error at high-speed range due to the absence of integral controller. Actually, if an integral controller is applied, the position error will increase. As it has been discussed in Chapter 3, one reason for this may be the inaccuracy of rotor speed estimation from EKF. Another reason is the detent torque is not considered in the controller structure. For the sinusoidal reference, a larger position error can be seen compared with the single position feedback. The same phenomenon can be seen from the cubic test as well. Thus, this kind of controller may not be a proper choice for the industrial implementation.

(45)

FIGURE 5.7: Design(ii): position response to a series steps from

(46)

FIGURE 5.8: Design(ii): position response to a sinusoidal reference

with frequency _2π10rad/s ; The maximum peak-peak position error

(47)

FIGURE 5.9: Design(ii): position response to ABB cubic test

refer-ence; The peak-peak position error of initial dynamic is 2.46◦ (not

fully shown);The maximum peak-peak position error during running

period is 4.03◦.

5.2.4 Position Controller with Position Feedback, Speed Feed Forward and Acceleration Feed Forward

The test results are shown in Fig.5.10, Fig.5.11 and Fig.5.12. A significant decrease in error can be observed from all the dynamic process in these three tests. Hence, this kind of controller is more suitable for the industrial implementation.

(48)

FIGURE 5.10: Design(iii): position response to a series steps from

(49)

FIGURE5.11: Design(iii): position response to a sinusoidal reference

(50)

FIGURE5.12: Design(iii): position response to ABB cubic test

period is 1.11◦.

5.2.5 Position Controller with Position Feedback, Speed Feedback, Speed Feed Forward and Acceleration Feed Forward

The test results are shown in Fig.5.13, Fig.5.14 and Fig.5.15. For the step reference, a decrease of error can be seen in the dynamic process due to the use of speed feed-back. For the sinusoidal reference, an error is eliminated more than the controller without speed feedback. For the cubic reference, the error is larger than the one without speed feedback. The effect of speed feedback can be concluded to be help-ful to the dynamic process of position control.

(51)

FIGURE 5.13: Design(iv): position response to a series steps from

(52)

FIGURE5.14: Design(iv): position response to a sinusoidal reference

(53)

5.3. Friction Compensation Test 39

FIGURE5.15: Design(iv): position response to ABB cubic test

period is 1.76◦.

5.3 Friction Compensation Test

The test results are shown in Fig.5.16a and Fig.5.16b. The figures focus on the revers-ing motion of the motor, a slight decrease of error can be seen from the compensated model (black blocks in the figure). However, this kind of compensation can only take effect for a short instant but not contribute much to the whole dynamic process. The same phenomenon can be seen from the cases in design (iii). Another phenomenon is that the compensation works better in one direction than another(difference be-tween red and black blocks). An explanation for this phenomenon is the small un-symmetry of the motor itself or the motor support. As it has been discussed in section 2.5, the friction can be modeled in a more complex way and reach a better performance.

(54)

(A) Error Comparison of Design(iii). (B) Error Comparison of Design(iv).

FIGURE5.16: Error Comparison in Sinusoidal Case of Design (iii) and

Design(iv).

5.4 Linear Regression Compensation Test

In this section, the linear regression compensation method described in Chapter 4 will be tested with Design(iii). The position information is provided only by MRPS signal and the signal will be compensated by the linear regression algorithm. The results are shown in Fig.5.17, Fig.5.18 and Fig.5.19, for steps, sinusoidal and cubic reference, respectively. And it can be seen from the figures that the test results don’t have an obvious difference with the one with tested with the encoder signal, which proves that the linear regression method is valid for the industrial implementation.

(55)

5.4. Linear Regression Compensation Test 41

FIGURE5.17: Linear Regression Harmonic Compensation Test of

De-sign(iii): position response to a series steps from 50rpm to 250rpm;

The peak-peak position error of initial dynamic is 1.15◦;The

(56)

De-sign(iii): position response to a sinusoidal reference with frequency 10

2πrad/s ; The maximum peak-peak position error during running

(57)

5.5. Test Summary 43

De-sign(iii): position response to ABB cubic test reference; The peak-peak

position error of initial dynamic is 3.69◦(not fully shown);The

maxi-mum peak-peak position error during running period is 1.19◦.

5.5 Test Summary

The test results are summarized in Table.5.1. The position errors are given in me-chanical degrees with Peak-Peak value. Note that some of the extreme values of the initial dynamic error do not show up in the previous section since the large error in the initial transient is can be seen as a response to a big step reference. Thus the emphasis of those figures locates on the steady state.

(58)

44 Chapter 5. Experimental Test Result Except for the content that has been discussed in previous sections, there are some common rules that can be concluded from the table.

• i) The speed-feedback controller can contribute to reducing the error in the dynamic process. Even the inaccuracy of EKF speed estimation decreases the effect of the speed-feedback controller. The existence of a speed-feedback con-troller in the system can still decrease the dynamic error. Thus the speed-feedback controller may be an important component in the control system if the EKF estimation has been improved.

• ii) The more ‘’smooth” the reference signal is, the better it could be controlled by the speed-feedback controller. An outstanding example is the sinusoidal reference. If the position reference is sinusoidal, the speed and acceleration reference are also sinusoidal, which means they are all differentiable and con-tinuous. This character is essential to a well-optimized reference signal, espe-cially in an industrial implementation.

``_`` ``_`` ``_`` `` Method Reference

Steps(I/R) Sinusoidal Cubic(I/R) Sensor

θrFb 1.07/1.4 1.89 2.68/2.08 Encoder (High-end) θrFb + ωrFb 1.91/1.08 6.88 2.46/4.03 θrFb + ωrFw + α Fw 1.20/ 1.45 1.67 3.65/1.11 θrFb + ωrFw(FC) + α Fw - 1.64 4.22/1.1 θrFb + ωrFb + ωrFw + α Fw 0.8/1.01 1.29 2.67/1.76 θrFb + ωrFb + ωrFw(FC) + αFw - 1.16 2.61/1.66 θr Fb + ωr Fw(FC) + α Fw + LRHC 1.15/1.52 1.58 3.69/1.19 MRPS (Low-cost)

TABLE5.1: Test result summary: Position error shown in mechanical

degrees; (Fb = feedback, Fw = feed forward, θr= position, ωr= speed,

α= acceleration, FC=friction compensation, LRHC=linear regression

harmonics compensation, I=initial dynamic, R=running process).

5.6 Discussion

5.6.1 Response Time and Bandwidth Selection

Usually, the response time of controllers follows this sequence PositionLoop> SpeedLoop> CurrentLoop

If the position controller requires short response time, then the speed controller may be deleted. If the speed needs to be controlled, then the controller bandwidth need to be properly designed and the position controller may suffer from a slow response.

(59)

5.6. Discussion 45

5.6.2 The Effect of Detent Torque

The stepper motor has a large number of pole pairs, and the rotor has a permanent magnet component. Since the magnetic field intensity is not evenly distributed be-tween two teeth, the generated magnetic force will have a small variation that can be observed as detent torque. If an EKF estimation result is presented with a time window that is equal to the fundamental time period Tf undas:

Tf und =

2π

ωr

(5.1) where ωr is the angular speed of the rotor. An EKF estimation result taken at the

speed of 100rpm is shown in Fig.5.20. Here ωr = 100· 2π₆₀ and Tf und = 0.6s. Note

that for this motor that has 50 pole pairs, 50 regular peaks can be seen from both torque and speed error, which is a proof of the relation between the detent torque and the large pole pair number.

FIGURE5.20: EKF estimation of torque and speed error at 100rpm.

The detent torque does not only affect the speed controller but also could be the hardware limitation of the position controller. For example, when the PID param-eters are increased to a certain range, the motor will begin to shake and make a big noise, and the performance becomes worse, i.e. the peak-to-peak error increases. Thus, it should be an important future work to eliminate the effect of the detent torque.

(60)

(61)

47

Chapter 6

Conclusion and Future Work

6.1 Conclusion

In this thesis, a complete stepper motor solution is proposed based on a low-cost position sensor (MRPS). From the motor control aspect, based on a careful study of the development of stepper motor control, vector control is chosen as the control strategy. And a controller is properly designed and compared with different con-troller structure. Then a friction compensation is proposed by the author to improve the performance in the motor reverse process. In order to improve the quality of the low-cost sensor signal, the extended kalman filter (EKF) is properly implemented with the sensor fusion algorithm at the first trial. Although EKF performs well at fil-tering the signal and observing states without direct measurement, it can not show an advantage in improving the signal quality. The neural network is tested as the second trial and it has been proved that the neural network is not an appropriate method for handling the position information. Thus, linear regression harmonic compensation (LRHC) is proposed to solve the problem and it leads to a positive result.

If the motor control strategy and the signal processing method is combined, it becomes a complete low-cost solution for stepper motor control and fits for the in-dustrial implementation. Hence, the main conclusions are listed as follows.

First, the idea to combine the stepper motor and the low-cost sensor is valid for the industrial implementation. In this thesis, the solutions for the two main sec-tions of this combination design, motor control and signal processing, have been proposed and tested with real motor and sensor. The result is positive in general cases and specific cases for industrial implementations. Thus, it can be claimed that this combination idea is valid for the industrial implementation.

Second, the present design can be further optimized. For the motion control of the motor, a valid structure of controller has been tested in this thesis and a friction compensation solution is proposed to improve the reverse performance of the mo-tor. However, due to the limited time, more complex controllers are not able to be tested in the thesis. Thus, a relatively large error still exists in the start-up process of the motor. And the cogging problem (detent torque) of the stepper motor is not con-sidered in this thesis. Hence, there can be a lot of further works concerning related problems to improve the motor performance.

Third, the result of this research may be transferred to a real product with further test and validation. One of the purposes of this thesis is to validate the feasibility of transferring the theoretical scheme to the real product so that the product compe-tence will be increased and the cost will be reduced. Although those tests in this thesis show positive results, it is too far to ensure the product feasibility. There need to be more strict tests with different scenarios such as various load, changeable iner-tia and so on.

(62)

48 Chapter 6. Conclusion and Future Work

6.2 Further Work

6.2.1 Advanced Controller

Due to the time limit, there are only junior controller designs are tested in this the-sis, some good designs such as [Krishnamurthy and Khorrami, 2004] can not be tested. As discussed in Chapter 3 and Chapter 5, the cogging problem of stepper motor should be solved to build a better speed controller. And also a more adaptive controller for changeable load and inertia in industrial implementations should be considered in the future.

6.2.2 Parameter Identification

In this implementation, the EKF and the controller are both sensitive to the motor parameters (see (2.6) and (3.2)). Thus, if the parameters can be somehow identified, the performance will be further improved. If the EKF estimation is accurate enough, the speed controller may be implied as well(see section 5.2.3). Besides, consider-ing the mass production and the industrial implementation, an on-line parameter identification seems to be interesting and promising.

6.2.3 Trial of More Sensors and EKF

The idea of sensor fusion is very interesting although it is not so appropriate for this implementation. In Chapter 3, it has been discussed that the back-emf and MRPS signal can not give an advantage to each other. However, it does not deny that other sensors may be valid for sensor fusion algorithm with back-emf. Thus, more sensors should be evaluated to examine this feasibility.

(63)

49

Bibliography

Acarnley, Paul (2002). Stepping Motors: a guide to theory and practice. Institution of Engineering and Technology. URL: http : / / digital - library . theiet . org /

content/books/ce/pbce063e.

Baluta, G. (2007). “Microstepping Mode for Stepper Motor Control”. In: 2007 Inter-national Symposium on Signals, Circuits and Systems. Vol. 2, pp. 1–4.DOI:10.1109/

ISSCS.2007.4292799.

Bellini, A. et al. (2007). “Mixed-Mode PWM for High-Performance Stepping Mo-tors”. In: IEEE Transactions on Industrial Electronics 54.6, pp. 3167–3177.ISSN: 0278-0046.DOI:10.1109/TIE.2007.905929.

Bendjedia, M. et al. (2012). “Position Control of a Sensorless Stepper Motor”. In: IEEE Transactions on Power Electronics 27.2, pp. 578–587.ISSN: 0885-8993.DOI:10.1109/

TPEL.2011.2161774.

Bishop, Christopher M (2006). Pattern recognition and machine learning. eng. Informa-tion science and statistics. New York: Springer.ISBN: 978-0-387-31073-2.

Derammelaere, S. et al. (2014). “Load angle estimation for two-phase hybrid step-ping motors”. In: IET Electric Power Applications 8.7, pp. 257–266.ISSN: 1751-8660.

DOI:10.1049/iet-epa.2013.0333.

Derammelaere, Stijn et al. (2017). “Sensorless load angle control for two-phase hy-brid stepper motors”. In: Mechatronics 43, pp. 6 –17.ISSN: 0957-4158.DOI:https:

/ / doi . org / 10 . 1016 / j . mechatronics . 2017 . 02 . 003. URL: http : / / www .

sciencedirect.com/science/article/pii/S0957415817300168.

Feng, Gang (2000). “Position control of a PM stepper motor using neural networks”. In: Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187). Vol. 2, 1766–1769 vol.2.DOI:10.1109/CDC.2000.912117.

Fitzgerald, A. E. (Arthur Eugene) (2003). Electric machinery. eng. 6th ed.. Hill series in electrical engineering. Power and energy. Boston, Mass.: McGraw-Hill.ISBN: 0-07-366009-4.

“Friction” (2011). In: Tribology of Ceramics and Composites. Wiley-Blackwell. Chap. 5, pp. 49–59.ISBN: 9781118021668.DOI:10.1002/9781118021668.ch5. eprint:https:

//onlinelibrary.wiley.com/doi/pdf/10.1002/9781118021668.ch5. URL:

https://onlinelibrary.wiley.com/doi/abs/10.1002/9781118021668.ch5. He, Yanzhao, Shiqiang Zheng, and Jiancheng Fang (2017). “Start-up current

adap-tive control for sensorless high-speed brushless DC motors based on inverse system method and internal mode controller”. In: Chinese Journal of Aeronautics 30.1, pp. 358 –367. ISSN: 1000-9361. DOI: https://doi.org/10.1016/j.cja.

2016.12.006. URL: http://www.sciencedirect.com/science/article/pii/

S1000936116302254.

Karlsson, Lina (2016). Sensorless Control of a Hybrid Stepper Motor. eng. Linköpings universitet, Institutionen för systemteknik, Fordonssystem.

Kim, W., C. Yang, and C. C. Chung (2011). “Design and Implementation of Sim-ple Field-Oriented Control for Permanent Magnet Stepper Motors Without DQ Transformation”. In: IEEE Transactions on Magnetics 47.10, pp. 4231–4234. ISSN: 0018-9464.DOI:10.1109/TMAG.2011.2157956.

High Precision and Low-cost Stepper Motor Control for Industrial Implementation

High Precision and Low-cost

Stepper Motor Control for

Industrial Implementation

CHUYAO ZHOU

KTH R

OYAL

I

NSTITUTE OF

T

ECHNOLOGY

M

T

High Precision and Low-cost Stepper

Motor Control for Industrial

Implementation

Abstract

Sammanfattning

Acknowledgements

Contents

List of Abbreviations

List of Symbols

Chapter 1

Introduction

1.1

Purpose

1.2

Challenge and Scope

1.3

Background

1.4

Previous Work

1.5

Thesis Contribution

1.6

Thesis Outline

Chapter 2

System Modeling and Control

Strategy

2.1

Hybrid Stepper Motor

2.2

Open-loop Control and Microstepping

2.3

Close-loop and Vector Control

2.4

Different Controller Structures

2.5

Reverse Challenge and Friction Compensation

Chapter 3

Extended Kalman Filter

3.1

EKF Algorithm

3.2

Implementation of EKF

3.3

Experimental Results

3.4

Conclusion

Chapter 4

Other Signal Processing Solutions

4.1

Linear Regression and Harmonics Compensation(LRHC)

4.2

Neural Network

∑

4.3

Conclusion

Chapter 5

Experimental Test Result

5.1

Test Rig Setup

5.2

Controller Design Test

5.3

Friction Compensation Test

5.4

Linear Regression Compensation Test

5.5

Test Summary