Speed Anti-Windup PI strategies review for Field Oriented Control of Permanent Magnet Synchronous Machines

7/27/2019 Speed Anti-Windup PI strategies review for Field Oriented Control of Permanent Magnet Synchronous Machines

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Speed Anti-Windup PI strategies review for FieldOriented Control of Permanent Magnet Synchronous

MachinesJordi Espina, Toni Arias, Josep Balcells and Carlos Ortega

TIEG, Dep. dEnginyeria Electrnica. Universitat Politcnica de Catalunya. C. Colom 1. 08222 Terrassa.Catalunya. Spain. [email protected]

-Abstract - This paper presents a review and a comparison

between different Anti-Windup PI strategies used in speed motioncontrol for electrical drives. Usually, when facing PI tuning of real

systems the plant is modeled as a linear system and thereforesimplified disregarding its physical limitations such as maximumcurrent and voltage values. Consequently, the PI output mayincrease indefinitely its value. This phenomenon is know as Wind-up is characterized by system saturation. The end result is a clear

performance degradation which may even result in instability.Firstly, this paper models and tunes the current and speed PI

controllers with the root locus method for Field Oriented Controlof a Permanent Magnet Synchronous Machines. Secondly, it is

shown the mentioned unwanted Windup phenomenon in the speedloop. Finally, the Anti-Windup strategies are simulated and theirbehavior are compared when driving a Permanent MagnetSynchronous Machine with Field Oriented Control.

I. INTRODUCTION

Recently fully integrated adjustable speed drive applicationshave attracted more attention for a wide range of industrialapplications such as hybrid electrical drives, more electrical

aircrafts actuators, robots and machine tool drives. [1] [2]With the improvements in the rare magnet materials such as

(NdFeB), Permanent Magnet Synchronous Machines (PMSM)are gaining market when compared to other AC Machines dueto its higher efficiency, lower inertia, weight reduction andvolume[3].

In order to get a fast PMSM performance in terms of speedand torque, the Field Oriented Control (FOC) is one of the bestvector control strategies [1]. Figure 1, shows the FOC scheme,where three PI controls are used, one for the outer speedcontrol loop and two for the inner current loops. However,linear PI controllers do not have output magnitude limiters, andtherefore, the output can take values relatively large and as a

consequence, the real system can be damaged by the largecontrol action [4] [5]. For instance, in the FOC PMSM drive,an excessive current and voltage might end up damaging thePMSM itself and the power electronics converter. In order toprotect PMSM, these commanded values are limited andconsequently the outer speed PI accumulates error, producing abig overshoot on the speed response which, in the worst case,

could even unstabilize the system; phenomenon known asWindup [4].

In order to avoid the unwanted Windup phenomenon, amaximum integrator output value will be kept within limits;strategy which is known as Anti-Windup (AW). Anothersolution might be to continuously tune the PI parameters tokeep the response undamped at all times [6].

This paper reviews different AW strategies, providing ageneral classification, which is firstly divided between themethods which do depend on the Saturation and the ones whichdo not. The latter are normally named as PI limited or PIdead zone which has the advantage of being easy to

implement whereas its drawback is the tuning difficultness [7].Methods depending on the Saturation might be divided intotwo different subgroups, the digital and analog ones. There aremainly two different digital approaches, the one which resetsthe Integral action of the PI when the Saturation is reached andthe second one which holds the integral value when theSaturation is also reached [8]. The analog approaches areconsidered to be a bit more accurate since its AW methoddepends not only in the fact that the system is saturating butalso considers the amount of this Saturation to proportionallycompensate the integral action. Among them, the PI trackingor Back calculation is based on removing from the input, ofjust the integral part, either the difference between the non

*

PMSMVSISVM

dq

PI

PIPI

id*+

-

+

-

Vd

Vq

V

V+

-

dq

abc

ib

ic

i

i

id

iq

P

re

e

e

dtd

r

iq**

PMSMVSISVM

dq

PI

PIPI

id*+

-

+

-

Vd

Vq

V

V+

-

dq

abc

ib

ic

i

i

id

iq

P

re

e

e

dtd

r

iq*

PMSMVSISVM

dq

PI

PIPI

id*+

-

+

-

Vd

Vq

V

V+

-

dq

abc

ib

ic

i

i

id

iq

P

re

e

e

dtd

r

iq*

Fig. 1. Field Oriented Control of Permanent Magnet Synchronous Machines scheme with speed AW PI.


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saturated output and the saturated one multiplied by a gainfactor from 0 to 1 [7] [9] [10] or just the input of the Saturationblock [11]. Another approach is the analog compensation ofnot only the integral action but in both the proportional andintegral [8].

Other more complex techniques are based on internal plantmodels [12], it is continuously comparing its output to the

actual plant. In [13] and H-infinite feedback controller is incharge of getting rid of the overshooting troubles.This paper reviews all non model dependent AW strategies

introducing a comparison of its performance when driving aPMSM with a FOC.

II. FOC OF PMSM

Fig. 1 illustrates the speed and control loops when driving aPMSM with well known FOC scheme [1].

In motion control, the abc to transformation is widelyused, known as a Clarke and to dq transformation or Park.These transformations allow to simplify the 3 phase system to a

2 phase one, where daxis current components controls directlythe flux-linkage and q controls torque. Moreover, SISO linearcontrollers might be easily applied [5].

The electrical part of PMSM is modeled in the dq framecoordinate [1] by the following set of equations.

iqL

Li

L

R

L

Vi

dt

de

d

q

d

dd

dd +=

(1)

q

eme

q

dq

qq

q

qL

idL

Li

L

R

L

Vi

dt

d

=

(2)

Finally, a third equation (3) which models the electro-mechanical PMSM torque is needed to complete the model.

( )[ ]qdqdqme iiLLiPT += 2

3

(3)

PMSM in standard operation do not require to create the fluxsince the permanent magnet (m) already provide it and the daxis is aligned with it. Therefore, q current component controlsproportionally the motors torque as shown in (3) ifdcurrent iskept to zero.

FOC is composed of two inner current loops and an outerspeed control loop. The inner loops are controlled by twoidentical PI. The speed control loop will be connected incascade with torque, i.e. q current, control loop as shown inFig. 1. It must be pointed out that the current loops dynamicsare faster than the speed loop and therefore, can be tunedindependently.

From (1) and (2), it can be deduced than the plant dynamicsjust depends on the electrical pole; therefore, these twoequations can be simplified, just for tuning reasons, to (4),which clearly shows a first order system.

TABLE IMOTORPMSMYASKAWA

Output power 200 W Lq 8.6 mHRated current 2 A Magnet flux 0.046 WbVoltage 100 V Rated torque 0.64 NmPole pairs 4 Rated speed 3000 r.p.mStator resistance 2.5 Friction 0.05 NmsLd 8.3 mH Inertia 0.810-3 kgm2

( ) qdR

L

R

qd vs

siqd

/

1

/)1( /

+= (4)

In Fig. 2, the electrical pole (R/Ld/q) is placed in the rootlocus plane and Matlab computer software is used to tune thePI parameters. The conditions used to determine the PIparameters are Damping factor 707.0= and SettlingTime R

LT 5= . Fig. 3 shows the closed electrical loop with thePI controller.

-2500 -2000 -1500 -1000 -500 0-1500

-1000

-500

0

500

1000

1500

Root Locus Editor (C)

Real Axis

-40

-20

0

20

40

60

G.M.: Inf

Freq: NaN

Stable loop

Open-Loop Bode Editor (C)

101

102

103

104

105

-180

-135

-90

P.M.: 67 deg

Freq: 2.19e+003 rad/sec

Frequency (rad/sec) Fig. 2. Root locus current PI tuning.

The resultant PI(s) is as (5) shows:

( )( )

2020006.16

0081.0120200

==

+=

ip KKs

ssPI

(5)

PI+

-

*

/ qdI qdV / qdI /

+1

1

/s

R

LR

qd

Fig. 3. PMSM Current control loop.

Similarly, the mechanical PMSM model can be modeled as afirst order system as shown in (6).

( )T

ss

DJ

D

r +

=1

)(1

(6)

From Table I the mechanical parameters have beenconsidered to adjust the speed control with the same root locustechnique. The PI obtained is given in (7)


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( )( )

123393.0

0032.01123

==

+=

ip KK

s

ssPI

(7)

+1

1

sK

K

i

p

)1(

1

+sDJ

D

Fig. 4. PMSM Speed control loop with the pre-filter.

The speed loop will be the main control used to apply thedifferent AW. Firstly, the speed PI together with themechanical plant will be reduced to a pure second order systemas shown in (8).

( )22

2

2 nn

n

sssT

++=

(8)

The closed loop transfer function from the mechanical loopwith the tuned PI gives not only the desired pure second order

system, but also an unwantedzero, which worsens the transientresponse.

( )

J

K

J

K

J

Dss

sK

K

J

K

GH

GsT

ip

i

pi

+

++

+

=+

=2

1

1

(9)

The solution to have a pure second order system is to insert apre-filter (F(s)) to get rid of the unwantedzero (10).

( )

+

=

1

1

sKK

sF

i

p

(10)

Fig. 4 shows the closed loop with the pre-filter, and then thesystems behavior is equal to the desired second order like in(8).

III. REAL SYSTEM WITH THE WINDUP PHENOMENA.

Every real system presents some physic limitations or hassome control constraints to safeguard systems integrity. Theideal control, which has been introduced above, is completelyvalid, although it fails when the input reference or load aredeeply changed. Under these conditions, because of theWindup phenomena, the systems performance worsens andeventually it may become unstable.

This section shows the two types of possible unstableresponses. The first one arises when the current referencecommand is limited to protect the system as Fig. 5 shows, andthe second appears when the Voltage Source Inverter (VSI)DC-bus is restricted as Fig. 6 illustrates.

These two limitations, implies not only an instabilityproblem as shown in Fig. 5 and 6, but also brings the Windupproblem in the integral part of the PI control.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4-50

0

50

100

150

200

t (s)

w*(rad/s),wr(rad/s),iq*(A)

wr

iq*

w*

Fig. 5. Effect of current limitation.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4-800

-600

-400

-200

0

200

400

600

t (s)

w*(rad/s),wr(rad/s),vq

(V)

wr

vq

w*

Fig. 6. Effect of D.C voltage limitation.

Next points summarize how this Windup phenomenaemerge: Difference between input reference and the feedback

generate a large error. PI acts in consequence applying an output value accordingwith PIs gains. The integral action starts accumulatingerror, increasing its value.

Eventually, the PI output value, mainly due to the integralaccumulated magnitude, can be larger than the Saturationlimit level. Under this condition the Saturation block actsproviding the maximum tolerable value to the plant.

Once the actual output reaches its reference, the error isagain zero, but the integral accumulated value still remainsat a value which can be much higher than the Saturationlimit bringing the responses previously shown in Figs 5 and6.

IV. BASIC ANTI-WINDUP

The main goal of AW scheme is to avoid the over value inthe Integrator, therefore the Integration output will be keptwithin a limited range.

Fig. 7 shows the basic AW PI compensator, where anintegrator limiter has been added which do not depend on theSaturation.


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s

1

Fig. 7. AW PI-limited.

Fig. 8 shows the speed responses with and without the AW.Notice how the AW slows down the speed response whencompared to the ideal one without any type of saturation. Onthe other hand, the overshoot has been reduced.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

20

40

60

80

100

120

t (s)

w

(rad/s)

w*

wr ideal responsewr PI anti-windup

Fig. 8. Ideal and AW speed responses.

V. DIFFERENT ANTI-WINDUPS STRATEGIES

In this section the structure and performance of different AWstrategies are introduced. An important highlight is that theAW inserted in the speed PI loop, makes the PI and the wholespeed loop non lineal. However, non-lineal PI can always bedivided in three different parts, each of them being linear itself.

A. AW PI with dead zone.In this case the limit is controlled by a dead zone element as

Fig. 9 shows. Whenever the integral value does not achieve thedead zone limit, the integral value remains linear and therefore,unchanged. On the contrary, when the integral output is largerthan the dead zone limit, the total integral value is reduced dueto the self subtraction action [7].

s

1

Fig. 9. AW PI with dead zone.

( ) ( ) ( )( )( ) ( )( )( )

( ){ satetout

sateouteK

deadeeeKtrefeKrefeKKtout

deadeedttrefeKtrefeKKtout

sateouteK

t

iipt

ipt

t

_

__

_int_int___

_int___

__

=

+=


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D. AW PI tracking with gainThe generic case of the AW PI tracking includes a gain (G),

whose margins are within 0 1 (14) as Fig. 12 illustrates, tovary the non linear feedback action. This gain also controls theovershoot response, increasing the gain (G) get decrease theovershoot.

s

1

Fig. 12. PI tracking with gain.

( ) ( ){ ( )

( ) ( ) ( ) ( )( )( )

10

_

_

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Speed Anti-Windup PI strategies review for Field Oriented Control of Permanent Magnet Synchronous Machines