Estimation, Identification AC MOTORS

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Kouhei OhnishiNobuyuki Matsui

Yoichi Hori

h pter 9

Estimation, Identification,and Sensorless Controlin AC Drives

1 INTRODUCTION

Since the early years of the twentieth century, electric motors for variable speeddrives have been widely applied in large-capacity applications such as the steelindustry and the automobile industry. In the early stage, DC motors were widelyused for adjustable speed control. Since the late 1960s, however, AC motors havebeen replacing DC motors in a wide area of industry applications. Since AC drives

required more complicated controllers in the beginning stage, they were not soeconomically feasible and did not meet with wide acceptance. However, allied toadvances both in digital control technology and power semiconductor devices, ACdrives became more and more economical and popular. In almost all areas, DCdrives are now replaceable with AC drives.

However, there still exist some areas which are not suitable for AC drive applications. One of these is the area of applications, which requires precise torque control. For instance, injection machines need accurate torque control at a very lowspeed or in a standstill state. AC motors sometimes generate torque error or torquepulsation due to some parameter variations. To overcome such problems, more

sophisticated techniques are necessary in the controller. These techniques employthe recent developments in digital control, including high-speed digital signal processors (DSPs) and parallel processing and are based on estimation or identificationof motor parameters. A description of the recent advances in such areas with a focuson estimation and system identification is given in this chapter. The results are not

Power Electronics and Variable Frequency Drives: Technology and ApplicationsEdited by Bimal K. Bose. © 1997 The Institute of Electrical and Electronics Engineers Inc.

Published 1997 by The Institute of Electrical and Electronics Engineers Inc.



9.2. Parameter Estimation in AC Drives 455

only reflected in control design itself but also directly used to dispense with mechanical sensors. The chapter first introduces the electrical aspects of AC motor drives,emphasizing par am eter estim ation, flux identification, an d speed estima tion based onvarious methods, including self-tuning regulators, model reference adaptive systems,and so on. Important applications are the drives of induction motor and brushlessmotor without speed sensor. Theoretical analyses based on the physical viewpointare presented, and the associated experimental results are shown. The chapter alsodescribes the design of robust motion controllers which take mechanical aspects intoaccou nt. By integrating these two aspects (electrical and mec hanical), versatile applications will be possible. At the end of the chapter, a summary of the state of the art isgiven.

9.2. PARAMETER ESTIMATION IN AC DRIVES

9.2.1. Parameter Identification in Brushless Motors

Parameters of Brushless Motors. The contro l scheme of brushless m otor swith trapezoidal flux distributions (BLDM, brushless DC motor) is relatively simple.Usually it does not need parameter identification. Generally identification of theparameters is necessary for precise control of brushless motors with sinusoidal fluxdistribution (PMSM, permanent magnet synchronous motor), as less torque pulsation is required. Particularly such a method is employed for fine torque control.

From the control viewpoint, the brushless motor has three electric parameters.The first is armature resistance, the second is armature inductance, and the thirdis E M F coefficient. They are significant pa ram ete rs to be identified.

Two effective appr oach es are presented here. One is self-tuning regulator (STR ),which has a tuning ability to make output-error zero inside the controller; the otheris model reference adaptive system (MRAS), which has a referred model in thecontroller. It is important to note that direct applications of STR and MRAS toparameter identification do not always lead to successful results, because of thelimitation of the processing time of the controller CPU. Since identification shouldbe performed in parallel with current and speed control, it is essential to reduce the

processing time for identification by a simple algorithm.

STR-Based Parameter Identifier. At steady-state, the PM SM has the simpleequivalent circuit just like a DC motor. Terminal voltage, line current, and armatureresistance are measured to identify the circuit parameters. Figure 9-1 shows anexperimental evaluation of the influence of such parameter variations in armaturecurrent error at steady state. A current-regulated voltage source inverter suppliesalmost sinusoidal current. In the figure, the ordinate is the current control error dueto the parameter variation and the parameter variation coefficient is defined as

motor parameterK = — i- (9.1)controller parameter






/'*Input

I Ke

\Current control

algorithm

\ ',

V

Identificationalgorithm

, 1

Brushlessmotor Output

Identification starts

Figure 9-2. STR-based parameter identifier with experimental results. L is estimated armatureinductance, Ke is estimated EMF constant.

ference is decomposed into two elements, from which the armature inductance andthe EM F coefficient are identified. The identification algo rithm is as follows.Rearranging the d-q axis voltage equation of the brushless motor, the referencemodel is given by the following equation.

i ( « - l ) = TL{n - 2)

+ wr(n-2)T

v(n - 2) - Ri(n - 2)]

-iq(n - 2)id(n - 2) - Ke(n - 2)/L(n ~ 2)

+ /(« - 2) (9.4)

The current difference between the model and the actual motor is



9. Estimation, Identification, and Sensorless Control in AC Drives

10

0

-102000 (rpm)

o/'J = 13 0 A

• /J=2.6A

10

0

-101000 2000 rpm)

Figure 9-3. Estimation errors for various load and speed conditions.

L Ke

Currentcontrolalgorithm

\

VReference

model

\

Brushlessmotor

Identificationalgorithm

i

•

l

' +

F

Identificationstarts

(a)

Figure 9-4. MRAS-based parameteridentifier with experimental results.




Ai[n — 1) = ojr{n - 2)T

1+ T

0Ke/L-Ke(n-2)/L(n-2).

1 [v(n - 2) - Ri{n - 2)]L(n -2) L

From the ¿/-axis component of current, the d-axis current difference is

Aid(n-l) = T[vd(n-2)-Rid(n-2)} l l

L(n - 2) ¿

(9.5)

(9.6)

The current difference of the q-axis component is given under the assumption thatthe armature inductance could be identified as L = L(n — 1) by using equation 9.5.

Aiq(n-\)=jè [Ke-Ke(n-2)}.

Using these two equations, the identification algorithm is summarized as

L(n-\)= A p s g n [Λ [η — Δ )\η ι\η — i ; -t- Λ /

(9.7)

£(«- )«-1

where

= Kpsgn[A(n - 2)]Ai{n -l) + K¡^2 s 8 n [ ^ (k - 1)]^«W (9.8)k=\

T{vd(n-2)-Rid(n-2)}A(k) 0

0θ (η - 2)

(9.9)

and KP and K¡ are the gain matrices, respectively. Figure 9-5 shows the experimentalestimation error under the various load and speed conditions. In this case, theestimation error of the EMF coefficient is larger compared to that of the armatureinductance, particularly in low-speed range.

20

Cf 10

' 5 0

-10

-20

20

10

0

Figure 9-5. Experimental estimationerror under various load and speedconditions.

- 1 0 -

-20

1000

1000

2000 (rpm)

• / q= 13.0 A

2000 (rpm)



9. Estimation, Identification, and Sensorless Control in AC Drives

Application of Param eter Identification to Torque Con trol. An interestingapplication example for the parameter identification of the brushless motor is a"torque sensorless" torque control. In Figure 9-6a, the conventional current-basedtorque control system is shown. The torque reference is divided by a torque constant

With identifier

Figure 9-6. Torque sensorless torque control system and control characteristics.




(= EMF coefficient in SI unit) to generate a current reference. In Figu re 9 .6b, theabscissa is the operating time of motor with load which corresponds to temperaturerise. With temperature rise, the torque constant decreases due to negative tem perature coefficient of the perma nent ma gnet. Since the arm atur e cu rrent is controlled tobe constant due to the current m inor loop, the generated torque also decreases inproportion to torque constant as shown in the figure. H owever in Figure 9.6c, theidentified torque constant is used to modify the current reference to compensate fordecrease of the torque co nstan t of the m otor . As a result, the torque is maintainedconstant with an accuracy of less than 1% aga inst tem pera ture rise. T o improveaccuracy, the voltage calculation should be more precise by taking into account theturn-on and turn-off time of the switching devices and cu rren t dep enden cy of theturn-off time, and so on.

9.2 .2. Parameter Identification in Induction Motors

Parameters of Induction Motors. Basically indu ction moto r in steady state isrepresented by the equivalent circuit in Figure 9-7. The classical no-load test, lockedrotor test, and electrical quantity measurement test give identified parameters inFigure 9-7.

Recent computer technology makes it possible to carry out these tests on-lineand in a real-time manner. In the process, as it is requisite to use fundam entalcomponents of voltage and current for the identification process, Fourier seriesexpansion is usually u sed. Also some special meth ods have been proposed to measure electric quantities. For instance, to measure the stator resistance, the inverter isoperated as a chopper m ode. A sample of flowchart is shown in Figure 9-8 [4].

A direct application of this steady-state a ppro ach is an autom atic boostingfunction a t low-speed in V/f inverter-supplied induction m otor drive. Figure 9-9shows experimental results where the effectiveness of the boosting function in alow-speed range is observed [4]. The dead-time com pensation of the inverter alsoprevents torque in the low-speed range from decreasing, since the dead time gives theeffect in fundamental com ponent.

Parameter Identification in Vector-Controlled Induction Motors. Vector-

controlled induction motor is one of the promising driving actuators. There are twotypes of vector control in indu ction m oto rs, and they can be specified as follows:

1. Field orientation control type2. Slip frequency control type.

Lis " s * * " fo —rjipi—j\M| 1 ιΤ Π Ρ VW 1

Figure 9-7. Equivalent circuit of cagedinduction motor without iron loss.



462 9. Estimation, Identification, and Sensorless Control in AC Drives

C Start }

During theno-load andsingle-phase

testsOn-line sampling ofcurrent and voltage

(samples are saved infile memory)

I

Number of sampled points

= 167 points0*60 per period

Compute Fourierseries coefficient

of voltage:a vi and bvj

3

Compute Fourierseries coefficient

of current:a-ff an d b,i

w^

"

cos<j>

'1

Compute equivalentcircuit parameters

h ΎThis is repeated 120

times in order to getaverage values

Figure 9-8. Flow chart of autonomous identification of induction m otorparameters.

The re are some direct orientation feedback loops in the former m ethod , which issometimes called direct vector control. A Hall device was used for the purpose in thefirst stage. On the contrary, the magnetic flux vector is not explicitly oriented in thelatter method. The phase and the magnitude of magnetic flux are regulated throughslip frequency control, and the latter is sometimes classified into indirect control.Since slip frequency control type is an inherently open loop control, the variation ofelectric parameters, particularly rotor resistance, gives significant effect to the performance. There have been many papers on the estimation of rotor resistance orrotor time constant for vector-controlled induction motors with shaft encoders.Most of the papers have been based on the LMS (least mean square) or similarapp roac h. As shown in an early pap er [15], PR BS (pse udo-r ando m binary sequence)added to ¿/-axis current reference is effective for the well convergence of the estimatedrotor time constant. It will be shown later that such kind of persistently excited (PE)condition of ¿-axis current is indispensable for sensorless drive since rotor speed androtor resistance cannot be estimated simultaneously.

Not only the secondary resistance but other parameters are also estimated.Holtz and coworkers proposed and realized a self-commissioning scheme for vector-controlled induction motor drive, where 80196 microcontrollers with ASIC areemployed to identify the parameters, such as stator resistance, stator transient timeconstant, rotor time constant, rotor magnetizing current, and mechanical time con

stant [5]. Following his approach, several commercially available inverters have beensuppled with such functions.




121110987654321

» » » « « » » » — g » » » g

ι · · 5 O O 0 0 Ο θ Ο °

.. y X x

X X X

_L _L l _L0 20 400 600 800 1000 1200 1400 1600 1800

o(rpm)

Figure 9-9. Experimental torque controlcharacteristics (2.2 kW, four-pole induction motor).

Reference torque

° Before dead-time compensation

• After dead-time compensation

x Without voltage autoboost

k ° ° ; ; x x; ; s s x » « »

l _L J_ J_0 200 400 600 800 1000 1200 1400 1600 1800

co rpm)

Flux Estimation in Vector-Controlled Induction Motors. From th e fieldorientation control view, many papers have been proposed to estimate the rotorflux. In general, the caged induction m oto r represented in Figure 9-7 has a dynamicalsystem equation a s

(9.10)

=

s

~ n A n ~

An A 22 .

10]

is +Bi

_ 0

where

}\i

(jJL/^JLit- I *-^rI u rJ




L m K r

σ Ζ ,,

LsLr

1 0

iJ, J =

0|_1

- Γ

oSince this equation is observable, it is possible to construct an observer to estimatethe rotor flux. The minimum order observer is derived from the well-knownGopinath's method.

Ψ , = A2iis + Α 22 Ψ + G[Í , - {Anis + A uVr + B^)} (9.11)

Th e first two terms on the right-ha nd side shows the "sim ulat ion " of flux circuit,and the last on the right-hand side is a "correction" term. Figure 9-10 shows arealization.

Flux estimation error denoted by e is

¿ = (A22-G An)e

= -He (9.12)

Eigenvalues of H determine the error dynamics. The parameter variation of theinduction m otor gives transient e rror in flux obse rvation. It is proven th at sensitivityto the rotor resistance variation is minimized if H is skew symmetrical as

H = a I ßJ (9.13)

Here — a ± jß are the allocated poles of flux observer, a and ß are

aRr

^i +w * £>-β = -ω , (914)

Figure 9-10. Flux observer realization.



9.3. Sensorless Drives of AC M otors 465

W is a weighting coefficient to be determined by taking maximum variation ratio ofrotor resistance ε , as

W < 1 + - 1 (9.15)

For instance, for ε = 0.3, the recommended value of W is less than 3 or 4. Figure9-11 is also effective in minimizing other parameter variations. When the estimatedflux is fed back, this approach is a kind of an extension of original vector controlby Blaschke [14]. Figure 9-11 is an example of a realization. The flux observer hasa function similar to a flux detector.

9.3. SENSORLESS DRIVES OF AC MOTORS

Basically, the vector-controlled AC motors require speed or position sensors.However, these sensors bring several disadvantages from the standpoint of drivecost, reliability, machine size, and noise immunity. For these reasons, it is necessaryto achieve the precise control of torque and speed without using position and speedsensors, that is, so-called sensorless drives of AC motors. In this chapter, first sensorless drive of brushless motors is described, then the induction motor is considered.

9.3.1. Sensorless Drives of Brushless Motors

As stated, there are two kinds of brushless motors: the motor with a trapezoidalflux distribution and that with a sinusoidal flux distribution. The approaches tosensorless drive of the brushless motor vary, depending on the rotor flux distribution. The brushless motor with a trapezoidal rotor flux distribution provides anattractive candidate, because two of the three stator windings are excited at atime. As a result, the unexcited winding can be used as a sensor [10, 11]; that is,

-—»-o—+ | -

^ >rA

> —

ω ,

PIJ M

-TV*.+ >

PI

1 ,

T> Γ^+ 1

ΙΨ Γ Ι

.->-

PIV«,

1 ^

PI'

J L

CO S Ö

sine

IM

¡f

Vectorrotator

1

"

>—

'

Vas / ^ Τ " "

sin/cosgenerator

Vectorrotator

vbs

J Vbr

I

Flux

,as

bs1

Î

cA a^ O s

,

Figure 9-11. Flux observer-based field orientation.




the speed EMF induced in the unexcited winding is used to determine the rotorposition and speed.

On the contrary, the brushless motor with a sinusoidal flux distribution excitesthree windings at a time and the sensorless control algorithm becomes complicated.Figure 9-12 shows an analytical model of a brushless motor where the d-q axiscorresponds to an actual rotor position and the η -δ axis is a fictitious rotor position.Since the actual rotor position is not known without a position sensor, the aim is tomake the angular difference Δ Θ between the fictitious and actual roto r positionsconverge to zero.

Two approaches have been proposed. Both are the estimation of the angulardifference by using the detected state variables and the estimated state variableswhich are obtained from a motor model in the controller. The approaches differaccording to the motor model, that is,

• Voltag e mo del-based drive [12]• Cu rren t mo del-based drive [13]

These two are basically the model-based control and generally require on-lineidentification of the motor parameters if higher performance is required. However, itis interesting to note that the second method has robust control characteristicsagainst the motor parameter variation.

In the voltage model-based sensorless drive, the voltage equation is given asfollows, where P is the differential operato r.

R + PL -L9C

R + PL+ ΚΕΘ

— sinAffcos ¿10

(9.16)

On the other hand, the voltage equation under the ideal condition that the fictitiousand actual axes are coincident is

V6M.

R + PL ~L9Lé R + PL ls\

κ θ (9.17)

Figure 9-12.less motor.

Analytical model of brush-



9.3. Sensorless Drives of AC Motors 467

Taking a difference between 7-axis voltage assuming Δ Θ is small, the followingrelation is obtained.

Δ νΊ = v7 νη Μ = -ΚΕθ ή η Δ Θ ~ -ΚΕΘ Δ θ (9.18)

Since the voltage difference can be calculated by the actual applied voltage in equation 9.16 and the model voltage calculated from equation 9.17, the angular differencecan be made to converge to zero by the following rule:

if Avr > 0, then 6C decreases

ii Avr < 0, then 6C increases

(for clockwise rotation)

The current model is given in equation 9.20.

7 "7 RLèr

-L6CR

Κκθ - sin Δ Θcos ¿do

Similarly, the current difference is calculated and the result is as

AL llM KETL

0 sin ¿10-0cos¿l0 + 0M

Κ κ Τ Θ Δ Θ-Δ θ

(9.19)

(9.20)

(9.21)

where T is a sampling period and ΘΜ is the mo tor speed of the mode l. Equ ation 9.21means that the current errors of each component of current correspond to positionand speed errors, respectively. Therefore, the following algorithm is obtained.

Θ ,= / ( *> M + KeAL)dt

(9.22)

(9.23)

Figure 9-13 shows torque-speed characteristics under a current model-basedalgorithm. The motor rating is 1.2 (kW), 6-poles, 1200 (rpm), 98 (kgf cm). Themaximum speed is 1500 (rpm), the minimum speed is 60 (rpm), and a steady-statemaximum speed error is within 0.4%.

9.3 .2. Se n so rl es s Drives of Vector ControlledInduction Motors

There have been many reports on the speed sensorless drive of the vector-controlled induction m otor s [6]. Various ap proac hes have been propose d where thebasic idea is estimation of speed by using applied voltage, line current, and frequency.

Slip frequency control approach is relatively simple, as shown in Figure 9-14.Here, the inverter frequency is controlled so that the vector control conditions are

satisfied by estimating a slip frequency from the stator current transformed to thesynchronously rotating coordinates {d-q axis) system. The slip frequency is given by




1000Φ -

τ *Q.<z>

J L J I L50

Load Torque (kg cm)

Reference speedo1500(rpm)

——o 1400 (rpm)

-o 1200 (rpm)

-o 1000 (rpm)

-o 800(φ m)

-o 600 (rpm)

-o 400 (φ m)

-o 200 (φ η ι)^ 100 (rpm)^ 60 (φ m)

J L100

Figure 9-13. Torque-speed characteristics of sensorless brushless motorunder current model-based control.

'Slip 1

vector control

Estimation ofslip frequency

*—

Hdq

d-q/a-ß ~Γ Motor j — * ~

Figure 9-14. Basic schematic diagram ofslip frequency-based sensorless controlof induction motor.

Rr lsq (9.24)

and the motor speed is indirectly estimated by the inverter frequency and the estimated slip frequency as

ώΓ = ω — ûs (9-25)

In this approach, as the estimated slip frequency is directly fed back to the vector-controlled algorithm, the vector control and the speed estimation are coupled, andthey should run simultaneously.

In the field orientation control approach, not only the speed but also the rotor

flux are simultaneously estimated for the sensorless drive in a wide speed range.Schau der attacke d this problem with MR A S [7]. His appro ach was based on the



9.3. Sensorless Drives of AC Motors 469

so-called voltage reference model where the speed terms are not explicitly included.The stator equation is used for correction of adjustable current reference model. Thespeed is estimated by a kind of error of flux components which is derived fromPopov's stability criteria.

One modified imple me ntation of this appro ach is shown in Figure 9-15, which isfor application in the the low-speed range as well as mid- or high-speed ranges. Therotor flux observer based on the motor voltage model estimates the rotor flux byusing the stator current transformed to the stationary coordinates (a-ß axis) system,and the vector control is carried out on the basis of the estimated rotor flux while themotor speed is directly estimated through MRAS by using the flux and the statorcurrent. Therefore, unlike the slip frequency-based approach, the estimated speed isused to adjust the motor model. The vector control can be decoupled with the speedestimation and be self-controlled. The speed is estimated according to the followingrelations.

= KP || e¡ x ΨΓ II +K, j II e¡ x Ψ , dt (9.26)

^i 's 's

It should be noted here that x in equa tion 9.26 mea ns the outer pro duc t.Since the speed estimation is based on the motor model, the parameter variation,especially the rotor resistance, has some effect on the speed estimation. With reference to this problem, Shin-naka clarified the impossibility of simultaneous estimation of both the speed and the rotor resistance theoretically [8].

From the voltage equation based on the stationary coordinates system, therelation

d_Jt

Vr \\2=2V?[-R r i r + uj rJV r

— — 2 / vr x r lr

is obtained. Rearranging equations 9.27 and 9.28, equation 9.29 holds.

Rr-irJ*r)-l± *r

(9.27)

(9.28)

(9.29)

Field orientation-basedvector control

Figure 9-15. Basic schematic diagram ofvector-controlled sensorless control ofinduction motor.

2 α β

φ2 ο β . Ί α β

/Motor model

observer

à m (

MRAS

9-1-Tφ2 α β . Ία β

e




It is noted here that the following relation is obtained from basic equations ofthe vector-controlled induction motor.

det [-i , 7ΨΓ] = -ΨΓΓ/Γ (9.30)

By substituting equation 9.30 into equation 9.27, the following relation isderived.

^ | | Vr | |2 = 2 i ?r d e t [ - /r /ΨΓ] (9.31)

Equation 9 31 and equation 9.29 mean tha t a simultaneous identification of the rotorresistance and the motor speed is possible only when the rotor flux is persistentlytime variant (PE condition). Under the vector control, the rotor flux is kept constantin principle for the orthogonality of rotor flux and rotor current. Then the simultaneous identification is theoretically impossible in the vector-controlled inductionmotor. This problem is overcome by adding small AC component to the d-axiscurrent. The convergence is improved if such an AC component has a rich frequencyspectrum like PRBS [15, 9].

Figure 9-16 shows an example of the sensorless control characteristics of 2.2(kW), 4-poles induction motor. The maximum speed is 2400 (rpm) under the field-weakening control and the minimum speed is 5 (rpm). It is noted here that the speedcontrol accuracy is 0.4% under the tuned condition; however, it is 1.4% under thedetuned condition. Like the conventional vector control with sensors, the identification of the rotor resistance is important and difficult.

9.4. ROBUST MOTION CONTROL BY ESTIMATIONOF MECHANICAL PARAMETERS

9.4.1. Estimation of Disturbance Torque

In general, the outputs of the motion system are position or force. There is acertain relational function between them as equation 9.32.

f = g(x) (9-32)

In this equation, / is force applied to the mechanical system, and x is deviationby / . The control stiffness is defined as in equation 9.33.

control stiffness = — (9.33)ox

Ideal force control has zero stiffness, and ideal position control has infinitestiffness. Any compliant or hybrid motion occupies the midway place between position and force control.

The robust controller should be both insensitive to external disturbances andparameter variations. In the motion system, the former characteristics correspond toa very high rejection capability against disturbance effects. As the external disturbance is the load, a robust m otion controller should have an infinite control stiffness.



9.4. Robust Motion Control by Estimation of Mechanical Parameters

2500 1

2000 '

1500'

1000

Έ&3

500 =

400

300 '

200

100 .

601

40 j

20,

- co*r= 2400 rpm

- ω *=2200 rpm

- ω = 2000 rpm

- ω *= 1800 rpm

~ o>*= 1500 rpm

- ω * = 1200 rpm

- <o* = 900rpm

- ω * = 600 rpm

- ω * = 450 rpm

ω * = 300 rpm

- o>í=150rpm

(o* = 60 rpm

r '" co* = 30rpmΓ 9r (oJ= 15 rpjn

i l l

9

99

I

•0

, . Φ

After motor warmBefore motor

9

Q

up

warm-up

a_

Constant power operation

g_

. . . . . . . a_

o

0

9

I I

9

$

0

0

0

1 1 I

9

MB

\a

9

9

9

9

9

9

0

0

8l i

9

9

9

V v 9

9

9

9

a

9

9

9

0

O

1 10 5 10

Tj. (N.m)

Figure 9-16. Example of control characteristics of stator flux-controlledsensorless vector control of induction motor.

To realize a versatile motion system whose control stiffness changes widely, the totalmotion system should have the double cascade structure of the acceleration referencegenerator to regulate total stiffness and the acceleration controller as shown in

Figure 9-17.To clarify th e robust mo tion controller, a t first, simple one-degree-of-freedom

motion is analyzed. T he dynam ical equation is

(9.34)




Input

û C m d

f cmd

Accelerationreference

Accelerationreferencegenerator

;,

/ ,

Po

Robustmotion

controller

Mechanicalsystem

. 1

Acceleration

sition (speed), force

Output

M

Figure 9-17. General structure of motion system based on robust control.

J = inertia about motor shaft (kgm2)T¡ = load torque (Nm)

Tm = motor torque (Nm)The load torque is the sum of inertial torque Tm, external torq ue Tnl, and

friction torque T{ic. They are functions of position and/or time. The motor torqueis the product of the generalized torque coefficient K¡ corresponding with the magnetic flux by the generalized to rque curr ent Ia. Since the generalized to rqu e current isassumed to be regulated by the high-gain current controller and the output currentwill completely coincide with its reference, the following equation holds.

Tm = K,Ia = Ktlf (9.35)

Combining equation 9.35 with equation 9.34, the following equation is obtained.ά ω

-*=« *ref

(T int + Text + Tfrc) (9.36)

In equation 9.36, the parameter variations denoted by A are shown in equation 9.37,

(9.37)= J n + AJK, = Km + AK,

Using equation 9.37, the parameter variation and the load are treated in the torquedimension. The sum of both gives the disturbance torque.

Tdis = T¡ + AJsiú — AK tI aref

— Tint + Tex, + T{frc (9.38)

+ (J-J„ )sLJ+(Km-Kt)Iiref

The basic dynamic equation 9.34 is transformed into equation 9.39 by equations 9.37and 9.38.

-* dis ~ -tn'a ·*·duTt

(9.39)

The left side of the equation is the sum of unkno wn factors, that is, the unpre dictableload and the unknown parameter variation; however, the right side of the equation is



9.4. Robust Motion Control by Estimation of Mechanical Parameters 473

Figure 9-18. Calculation of disturbance torque based on acceleration.

known or detectable. Thus the disturbance torque can be calculated as shown inFigure 9-18.

As Figure 9-18 has a pure differentiation process, it is modified to be realizableas shown in Figure 9-19, where one low-pass filter (LPF) is inserted. Although anyLPF is applicable, a simple first-order LPF is chosen here. In this case, the disturbance is estimated as

Tdis — 's + g

Zdis (9.40)

where g is a cutoff angular frequency of a first-order LPF. If g is large enough, theestimated disturbance torque is almost similar to the real one. Figure 9-19 is called adisturbance observer.

By direct feedback of the estimated disturbance torque shown in Figure 9-20,the modified diagram shown in Figure 9-21 is obtained. Figure 9-21 means that thedisturbance has little effect on the motion system, since the feedback loop of disturb anc e is just the same as the feedforward effect of disturban ce to cancel it. Byattaching an auxiliary gain element Jn/Ktn in front of the cur ren t con troller , it is clearthat the physical meaning of the input of Figure 9-21 is acceleration. It is possible toextend such a robu st motio n contro l from one-degree-of-freedom systems to multi-degrees-of-freedom systems [17].

Figure 9-19. Calculation of disturbancetorque by disturbance observer.

i r í

* a

Γ

1

K,

Kin

-¿O*-

-¿ r>£-V'9

s+g

1Js

QJn

ω

-*—

\-tJ ' QJn

1s

.

θ




r ref

¿ o

'cmp

Kin

¿ 6

s+g

+ "

05-' d i s

±Js

QJn

η

Figure 9-20. Feedback of estimated disturbance torque.

¿ref

Gs(s)

1^

s+g

JnKm

rref

1'Kin

1

μ & Figure 9-21. Acceleration controller bymodifying Figure 9-20.

9.4.2 . Estimation of Instantaneous Speedand Varied inertia

For more accurate motion control, the instantaneous speed accuracy is very important. The incremental position encoder with a very short sampling time will loseresolution of the speed due to a small number of incremental pulses in a samplingperiod. On the contrary, in case of longer sampling time, resolution will be higher.However, the total motion system tends to be unstable. The instantaneous speedobserver which is an ex pansion of the disturban ce observer solves this antinom y; thatis , accuracy is kept higher even in the case of a very short sampling time. Figure 9-22shows a timing chart in such a case.

At the shorter sampling points of T2 (represented by k = 0 ,1,2, . . . , K), the totalacceleration torque T me<A [m k} (1 < k < K) is given by the sum of the motor torqueand the estimated disturbance torque as

^mechKfe] = K,„ i[m,k] + fdis[m\ (9.41)

By integrating equation 9.41, the instantaneous speed at T2 points can be estimatedby



9.4. Robust Motion Control by Estimation of Mechanical Parameters 475

Figure 9-22. Timing chart of the instantaneous speed observer (position inputtype).

m-1 m

fc=0

m+1K

Readout period Control period of DSP

of position

Position from encoder

9(m+1)

û [m,k] =w[m,k- 1] + ^2 (fmech[m,k) + T mech [m,k- 1](9.42)

The position is calculated by integrating equation 9.42 and the position error Δ Θ canbe obtained at the next point, k = K, when reading out the counter.

Δ Θ = ê [m,k] - θ [π ι (9.43)

It is im porta nt to evaluate Δ Θ in the observer design. Suppose that 7 ¿10 (0 < ηχ < 1)is caused by Δ ω0 (the error in the initial value of the estimated speed) and72Δ Θ (0 < 72 < 1) by dT dis0 (the error in the estimated disturb ance in the section),namely

Ύ \Δ Θ — Τ \Δ ω

T2

1ιΔ Θ = ^ΓΔ Τ ζ

(9.44)

(9.45)

Based on equations 9.44 and 9.45, the values in the next section of [m + 1,/c] aremodified as follows before starting the speed estimation.

(9.46)d\s[m+\} = fdis[m\ - Δ Τ ^

Tû [m + 1,0] = û j[m,k] --j-Δ Τ ά ί5 - Δ ω (9.47)

The observer poles can be designed by 7, and 72 introduced in equations 9.44and 9.45 [22]. The m ain ad vanta ge of the speed observer is the improv eme nt ofsystem stability by the equivalently reduced sampling period. By adding adaptivealgorithm to instantaneous speed observer, the varied inertia is identified and theself-tuning regulator (STR) is realized.

At the rath sampling point of Tx to read the encoder, the mechanical system'sbehavior is approximately given by

andJú [m] = Kmi[m] + T dis [m] (9.48)

Jù >[m - 1] = Ktni[m - 1] + T dis [m - 1] (9.49)




Since the variation in the torque coefficient K, is included in the disturbance torqueT&%, a parameter K,„ is used in these equation s. By subtracting equ ation 9.49 fromequation 9.48, the following is obtained.

JAw[m\ = KtnAi[m] + ATdis[m\ (9.50)

Equation 9.50 is the basic equation for inertia moment identification. It is importantthat ATá is[m ] can be assumed random Gaussian, if the disturbance torque is assumedto be constant in the neighboring sections of Tx. By summing up the equation errorbetween the left and right terms of equation 9.50, the objective function to be minimized takes the form of

M

Σm=l

/ ( / ) = Y^(JAú [m} - K,„ Ai [m]f -> min (9.51)

By taking the partial differentiation of / ( / ) by J, the estimation equation of theinertia moment is obtained by

J M

Σ ¿lcj[m]¿lí[w]~~MK<» m=l E m = l ( ^ M )

(9.52)

The actual calculation is performed by equation 9.53 replacing the oldest data withthe newest data which comes into the rectangular window of equation 9.51.

/fM= Σ AÚ [j]Ai[ j]

j=m-M+\ 12j=m-M+l ( ¿M.(9.53)

The identified inertia moment is applied to the speed controller in a STR manner asis shown in Figure 9-23.

Speed controller Current controller

1 + t„ ,s

/IsLKm

1 +t;S

- i t -Speed

observer— i

Adaptive identificationof the inertia moment

Figure 9-23. STR based on inertia identification.



9.5. Conclusion 477

Figure 9-24 shows the identification performance when the inertia momentvaries from nominal value to three times of it. The varying inertia moment is estimated exactly with enough response time.

The systems described here led to improvement both in the robustness andpreciseness in the motion systems. It is interesting that robust control is used forvery fast imp rovem ent of control characteristics like disturban ce rejection, and ad aptive identification helps the robust control to increase the stability in a relatively slowmode [24].

9.5. CONCLUSION

A description of motion system is given in this chapter with an emphasis on bothestimation and identification of parameters and control variables of AC motor-driven motion systems. In modern electrical drive systems, it is required to takenot only the electrical aspect but also the mechanical ones into total system design.

Improvement in the electrical aspect needs various information pertaining toelectrical machines and power electronic circuits of AC variable speed drives.Important techniques of identification or estimation of parameters and control variables in AC drives are explained. Such information includes machine parameters,flux, and so on. There is some theoretical limit of perfo rma nce in the identification orestimation process. For the mechanical phase, the estimation of the disturbancetorque, instantaneous speed, and varied inertia are described.

It is shown that the total robustness is attained by integrating the electricalimprovement and the mechanical improvement. There are a wide variety of controllers based on combinations of these two aspects depending on applications. Furtherresearch is expected for total performance impro vem ent.

Figure 9-24. Identification performanceof inertia moment. (T2 = 100μ /, Τχ

= 5ms,' pole: z =0.6, M = 50.) The

inertia moment changes between J„ and3Λ .

0.00588 (kgm2/div), ω - 50.0 (rpm/div)fdis - 2.0 (N m/div), time - 250 (ms/div)



478 9. Estim ation, Identification, and Sensorless Control in AC Drives

A c k n o w l e d g m e n t

The authors would like t o express their thanks to B. K. Bose a nd A. Denker fortheir helpful suggestions in preparing this chapter.

R e f e r e n c e s

[1] Bose, B. K., guest editor, "Power electronics an d motion control—specialissue," Proc. IEEE, Vol. 82, no . 8, 1994.

[2] Wang, C , D. W. Novotony, and T. Lipo, An autom ated rotor time constantmeasurement system for indirect field-oriented drives," IEEE Trans. Ind. Appl.,Vol. 24, no . 1, 1988.

[3] Depenbrok, M., and N . R. Klaes, "Determ ination of induction machine parameters and their dependencies on saturation," Conf. Rec. 1989 IEEE Ind. Appl.Soc, Part 1, 1989.

[4] Gastli, A., M. Iwasaki, and N. Matsui, An auto m ated equivalent circuitparameter measurements of an induction motor using a V/F PWM inverter,"Proc. IEEJ (Institute of Electrical Engineers of Japan), IPEC-Tokyo, 1990.

[5] Khambadkone, A. M., and J. Holtz, "Vector-controlled induction motor drivewith a self-commissioning scheme," IEEE Trans. Ind. Elec, Vol. 38, no . 5, p p.322-327, 1991.

[6] Nandam, P. K., G. F. Cumm ings, and W. G. Dunford, "Experimental study ofan observer-based shaft sensorless variable speed drive," Proc. 1991 IAS AnnualMeeting, Part 1, 1991.

[7] Schauder, C , "Adaptive speed identification for vector control of inductionmotors without rotational transducers," Conf. Rec. 1989 IEEE Ind. Appl.Soc, Part 1, 1989.

[8] Shin-naka, S., A unified analysis on simultaneous identification of velocity androtor resistance of induction m otor," Trans. IEEJ, Vol. 113-D, no. 12, 1993.

[9] Kubota, H., and K. Matsuse, "Simultaneous estimation of speed and rotorresistance of field oriented induction motor without rotational transducer,"Trans. IEEJ, Vol. 112-D, no . 9, 1992.

[10] lizuka, K. , "Microcomputer control for sensorless brushless motor," IEEETrans. Ind. Appl., Vol. IA-21, 1985.

[11] Erdman, M. D., H. B. Harms, and J. L. Oldenkamp, "Electronically commu-tated DC motor for the appliance indu stry," Conf. Rec. IEEE-IAS, 1984.

[12] Matsui, N . , and M. Shigyo, "B rushless D C mo tor control without position andspeed sensors," Conf. Rec. IEEE-IAS, 1990.

[13] Matsui, N., T. Takeshita, and K. Yasuda, A new sensorless drive of brushlessDC motor," Conf. Rec. IEEE IECON 92, 1992.

[14] Blaschke, F., Das Prinzip der Feldorientierung, die Grundlage fü r derTransvektor-Regulung von Drehfeldmaschinen," Siemens-Z, pp. 757-760,1971.

[15] Leonhard, W., Control of Electrical Drives, Chap. 12, Springer-Verlag, Berlin,Germany, 1985.



References 479

[16] Ohishi, K ., et al., "Torque-speed regulation of DC m otor based on load torqueestimation," Int. Power Electr. Conf. IPEC-Tokyo, Vol. 2, pp . 1209-1216, 1983.

[17] Nakao, M., et al., A robust decentralized joint control based on interferenceestimation," Proc. IEEE Int. Conf. Robotics and A utomation, Vol. 1, pp. 32 6-331, 1987.

[18] Murakami, T., et al., "Torque sensorless control in multidegrees-of-freedommanipulator," IEEE Trans. Ind. Electr., Vol. 40, pp. 259-265, 1993.

[19] Ohnishi, K., et al., Recent Advances in Motion Control, Nikkan KogyoShimbun, Tokyo, 1990.

[20] Ohishi, K., et al., "M icroprocessor-controlled DC motor for load-insensitiveposition servo system," IEEE Trans. Ind. Electr., Vol. 34, pp . 44-49, 1987.

[21] Umeno, T ., et al., "Tw o degrees of freedom controllers for robust servomechan-ism—Their application to robot man ipulators without speed sensors," IEEE 1stInt. Workshop Advanced Motion Control, Yokohama, pp. 179-188, 1990.

[22] Hori, Y., et al., An instantaneous speed observer for high performance controlof DC servomotor using DSP and low precision shaft enc ode r," 4th EuropeanConf. Power Electronics (EPE 91), Vol. 3, pp. 647-652, 1991.

[23] Awaya, I., et al., "New motion control with inertia identification function usingdisturbance observer," Proc. IEEE IEC ON '92, Vol. 1, pp . 77-80, 1992.

[24] Hori, Y. , "Robust and adaptive control of a servomotor using low precisionshaft encoder," IEEE IECON '93, Hawaii, 1993.

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Estimation, Identification AC MOTORS