Control

A SEMI-CLOSD LOOP TORQUE CONTROL OF A BURIED PERMANENT MAGNET MOTOR BASED ON A NEW FLUX WEAKENING APPROACH Akita Kumamoto and Yoshihisa Hirane Faculty of Engineering, Kansai University Yamatecho 3-3-35, Suita City, Osaka 5 6 4 JAPAN

ABSTRACT - The paper deals with a semi-closed loop torque control of a Buried Permanent Magnet Motor, based on a new flux weakening approach. Following the modeling of the motor, power capability of the machine is briefly summarized. The available motor's power in a steady state, assuming a constraint to both the terminal voltage and line currents of a motor, widely varies according to motor parameters. A buried permanent magnet motor, with additional reaction toque due to a large Q axis reactance, exhibits a high- power operation over a wide speed range. Although a good selection of machine parameters theoretically results in a broader operation range, it is only after a certain control method is implemented to stably d i e the high-power steady state condition in a flux weakening region that this particular set of parameters is meaningful. Conventional representative methods to attain flux weakening, when available DC voltage source is limited, are discussed from the viewpoint of feasibility of implementation to a control system. After discussions on this point, a new flux weakening method is presented, in which the controller generates current commands so that the operating point of a motor satisfactory shifts from a normal mode to a voltage limited state and vise versus. This flux weakening approach is then extended into a torque control system, which enables an almost open loop torque control of a motor , although a hundred percent open loop control is unrealizable. The presented system utilizes an estimator, or more precisely, its alternative, for a shaft generated torque. The system thus realizes a semi-closed loop torque control. Some simulation results are given to verify the effectiveness of the presented control method. It is shown that the shaft torque follows its torque command with a certain time delay when the reference varies rapidly. In the steady state, however, the average shaft toque is well regulated to coincide with its command in spite of inadequate feedback. Effects of deviation of motor parameters adopted in the controller from their actual values is also investigated and some other factors to affect the system performances are discussed.

1. Introduction A buried permanent magnet synchronous motor has recently been in progressive practical use resulting from the improvement of magnet materials. This type of a motor, in comparison with its counterpart of a surface-mountedpermanent magnet motor, finds its advantage in that it can be operated in a comparatively high speed range because of the reduced speed limit imposed on the motor. In case of a surface type, the magnet material is fixed around the rotor's peripheral and eventually brings a lower mechanical speed limit. On the contrary, a buried type,or an interior permanent magnet motor, as it is frequently called, is somehow free from this mechanical speed limitation because all the magnet material is totally buried into the rotor as the name indicates. Despite the above mentioned advantage, little has been so far studied as to the nature of a buried permanent magnet motor in variable-speed drives, partly because the machine exhibits a strongly salient characteristics. The field orientation technique is one of the most commonly adopted variable-speed drive methods and its resulting quick torque response has widely broadened the application area of a permanent magnet motor into various practical fields including robotics. However in such an application where the fast torque is not necessarily the major concern, it is reasonable to put an emphasis on how to attain the maximum power-handling capability in the steady state, rather than to be inclined to adoption of a sophisticated control strategy in the transient, occasionally falling into a complicated and costly system. It has been well known that a buried motor, with its additional

reaction torque due to a large Q-axis reactance, exhibits a high power operation over a comparatively wide speed range [ 1,4,5,71.This high power capability is deeply related to an effective flux weakening in the high speed. In practice, however, the actual operation speed range tends to be limited within two times the base speed mainly because the failure of current control in high speed will result in an increased terminal voltage, eventually causing inverter's destruction. In order that the machine be safely operated over a wide speed range, a satisfactory stator current programming strategy is essential. It is only recently that a couple of effective flux weakening methods appeared in the references [ 1,2,4,5] and yet it seems that some more studies are required to appropriately implement a both practical and simple flux weakening scheme [71. Presented in the paper is a new type of flux weakening method in which stator current commands are generated in the controller so that the operating point of a motor satisfactory shifts from a normal mode to a voltage limited mode requiring flux weakening and vise versus. Since this presented method originates from the pioneering work by Jahns [4], a brief summary of his work is given with some additional discussions from the viewpoint of feasibility of implementation into a control system. The fundamental concept of a new flux weakening in programming stator current command is that the controller utilizes the information of intermediate current commands to moderately adjust the original current commands. This is done by introducing an torque estimator, or more precisely, its alternative, for a shaft generated toque. This estimator plays an important role in the presented system not only in the new flux weakening but also in the next stage of flux weakening to extend the method to a semi-closed loop toque control. Since it is without doubt impossible to attain a perfect open loop torque control, even a semi-closed loop control may be beneficial when a simple torque control is required. Inherent to the new method is the study of an effect of variation of motor speed, because the builtin controller generates current commands calculated assuming an electrically steady state at a given speed. Furthermore, deviation of some motor's parameters used in the controller may affect system performances when they are mismatched. A computer simulation following the Jahns' 3 hp model machine is carried out considering these points and the effectiveness of the proposed method is described in the followings. 2. Power cambilitv of a mnnanent mamet motor 2.1 Motor model Although there are some discussions as to whether a permanent magnet motor ca be successfully modeled with a conventional D-Q theory or not [2], it is still certainly one of the most convenient candidates to describe the machine. Considered in this paper is a lossless (or resistances-neglected) motor shown in Fig. 1 where a current regulated PWM inveter supplies sinusoidal currents. In proportion to the progress of motor's capacity of a few kilowatts up to almost a hundred kilowatts, neglecting stator resistances is becoming a good approximation and actually previous works deal with such a model [ 1,3,4,5,61. In terms of a rotor referred reference frame, the D-Q model assuming a lossless machine is given by

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capability of the motor. While the speed is low, the stator current components are calculated so as to yield in a Maximum Torque / Minimum Current condition for a given current amplitude. This is done by choosing an optimal current angle y* given by a simple algebra. Figure 2 shows how this maximum torque varies according to the stator current amplitude. It is clearly shown from the figure that, given an allowable current limit Ilim, the operation with this Is'Ilim yields in the maximum power at a given speed.

Rotor position feedback

T

I

1

/Feedback *1.6 .

O

-

l

d

Fig. I A current regulated PWM inverter drive system of a permanent magnet motor using a standard nomenclature. Phase quantities are related to D-Q quantities by the conversion of

where 8 is the angle of qr axis measured from the stator a-phase axis. Given the current angle y and current angle 6, both measured from qr axis, we obtain

- h~,siny

h~,cosy

,

ids

vqs = h v s c o s 6

,

Vds= - f i V @ l S

iqs

=

=

IS

Fig. 2 Variation of maximum available power unuder the Maximum Torque with Minimum current condition

(3)

With an increase of speed N, the machine can no longer operate at y* and Ilim ,since motor terminal voltage increases rapidly. Because of a limitation by the DC source voltage, the current angle y should be appropriately advanced. This advancing current eventually causes a decrease of generated power in the motor with normal design parameters. However it is first shown by Schiferl [ I ] that appropriately selected motor parameters will brake this power decrease and, ideally speaking, the high power operating range will be extended to some multiples,of the base speed. Figure 3 shows some examples of power capability curves with a constant stator current amplitude for different machine designs. As is shown in the figure, a particular machine, say #3 in this case, guarantees a nondecreasing power capability at high speed.

where Is and Vs are rms phase values of the stator. Introducing the upper case letters as Iqs

= Iscosy

vqs =vscoss

- 1,siny

,

Ids

,

Vds=-VSsin6

=

(4)

The steady state equations result in

Max. Per Unit Output Power 1.0-

-

Machine parameters are normalized here using a base speed Oe,BASE as

xds = ae,BASE Lds%ASE

0.8-

-

We,BASELqs'%ASE E0 = w e,BASE%m'fi

(6)

0.6-

-

'BASE

0.4-

to yield in the normalized equation of

vqs= N(EO V

=

ds

+

-

xdslds)

- NXqJqs

0.2-

x -x

-

(7)

P = NT, = N[EnIscosy + 1isin2yl where both voltages and currents are normalized values of quantities defined by Eq. (4) although using a same notation. 2.2 Power caDabilitv 111 Let us consider the maximum power available from the motor at a given speed and stator current. The envelope in a P(power)N(speed) plane of this maximum power is the resulting power

1

2 3 Per Unit Speed

4

5

Fig. 3 Examples of power capability curves for differrent motor parameter designs, both stator voltage and line current at 1.OPU. (Ref. Ill)

651

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The motor's output power P becomes zero when y reaches d2 as the current angle changes. In this final state,

Therefore, given the maximum allowable voltage of Vlim, the power becomes zero at a maximum speed Nmax of 'Iim Nm,

=

I

X A

I

\

(9)

//

01

6s

if operated with a constant Is . The machine #3 in Fig. 2 is an example of such parameters as to satisfy Nmar-. The effect of demagnetization [8] is neglected in the above discussion and in practice there arises both the limit of operating speed and a decrease of power capability especially in high motor speed range. Furthermore, Fig. 2 is the power capability with only a fixed stator current Is. That is, the actual power capability in its real sense is the overall envelope of each curve obtained with stator current changed. In any case, this steady state calculation suggests nothing more than the fact that a burried permanent magnet motor basically has a potential ability to be operated over quite a wide range if and only if a proper flux weakening strategy is figured out to safely guarantee a stable steady state operation. 3. Drive svstem consideration 3. I Feasibilitv requirement for a drive svstem We are concerned with how to realize an effective flux weakening of a motor. Before going into details, let us first discuss a feasibility of any control strategy for a computer-based variable-speed drive stem. The remarkable recent features of a drive system using a computer are: a) A sophisticated control strategy, utilizing an intelligent function of a microprocessor, b) An even faster control using a DSP (Digital Signal Processor) if necessary. The advent of a microprocessor has brought the above features into power electronic control scheme. There are some arguments still going on , however, that even a DSP based system is not fast enough to fully control the fast-switching power electronic devices. From a viewpoint of feasibility of implementation, the allowable calculation incorporated in the controller should be, at present, within the scope of either a table look up (if a nonlinear calculation is required) or a sequence of simple mathematics. In calculating stator current commands in flux weakening, therefore, the system should not require a complex mathematics. Assuming that each motor parameter is precisely identified and that the motor speed variation is very slow, we can compute required currents in flux weakening by solving a set of multidimensional nonlinear equations. This will result in an almost open-loop torque control but this method is for the moment beyond a reasonable approach of a controller design due to the discussion given above.

Vg. limited ellipse I Ids Fig. 4 Current loci in the D-Q current plane His method of flux weakening is to use this excursion. Figure 5 is a block diagram of Jahns' flux weakening. Blocks f1 and f2 are current programming tables to produce a minimum current condition for a given torque reference Ts. The deviation of D-axis current is sensed and fed to a PI controller, which finally adjusts the maximum Q-axis current command. Thus the controller generates a new current command, point C for example, instead of point B in Fig. 4, guaranteeing a shift of the operating point from point A to upwards along the voltage limited ellipse. Figure 6 is his experimental results for a prototype of a 3-hp and 4-pole ferrite magnet motor, intentionally driven with a low DC voltage of 100 volts.

Aid'

Yector Rotator

E

P- I

Regulator

2

Limiter

Fig. 5 A Hod( diagram of flux wakening method by Jahns (Ref [41)

7T

3.2 Conventional flux weakeninnl4.51 The behavior of D-Q axis stator currents of a buried type motor is examined in Jahns' pioneering work [4]. He treated a system in which a feedfonvard torque control is incorporated. Given a torque command, D-Q current components are so determined to give Maximum Torque 1 Minimum Current condition. This is done by chasing the current loci of OAB shown in Fig. 4. Each current component is supplied to a vector rotator, which produces phase current commands to a current regulated PWM inverter. The system thus attains a drive including a basic feedforward torque control. This scheme is assuming a good current regulating ability of an inverter. Jahns has shown in his paper that an increasing torque command, let's say, point B in the Minimum Current Trace in Fig. 4, brings the system far beyond its voltage limited ellipse in the same figure. As the current commands move from the origin toward point B with the increase of torque reference, passing point A, it was shown that actual D-Q currents move downwards to point D, for example, instead of point B.

P o i n t Key Weakening Inactive Active

It 0w -

0

2000

4000

Rotor Speed o r (r/min> Fig. 6 Experimental resuts of f l u weakening by Jahns (Ref 141) 658

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Another approach has been recently presented by Bose who uses different control configurations for a constant torque and a constant power operation [51. The basic principle of flux weakening is to switch from a constant torque mode to sin6 adjusting mode in the constant power operation by forcing the system construction to change. After the switching into flux weakened mode, the inverter supplies a square wave to the motor, while Jahns’ method still keeps a sinusoidal excitation.

race

3.3 Discussion of conventional methods We have seen the two representative flux weakening methods thus far developed. Among them Jahns’ method is an excellent idea in the sense that it keeps the basic feedforward torque control framework both in voltage saturated and non-saturated modes. It must be noticed, however, that his method no longer guarantees that the shaft torque be controlled to coincide with its command. In his experiments, the actual torque Te begins to deviate from a reference at some point where the latter increases beyond 2.7 Nm when a linearly time varying torque command is applied to the system at or=3200rpm. As can be understood from Fig. 5 , the D-axis current is fundamentally decided by the function block of fl whose input is a command torque. In other words, if one wishes to adjust the shaft torque at will, an additional torque feedback is necessary and the resulting system will look something like the one shown in Fig. 7.

fl

Vg. limited ellipse

Ids Fig. 8 Principle of generating a currennt component command point B. using an intemediate current iqs in the D-Q current plane

Flux

T’

Current

PI

This is done in our case by using an intermediate current command iqsin the previous stage of control. Basically this iqs is the delayed quantity which is the output of a first order delay with an input of current command. We first compute a point C which is the cross point of a hyperbola of an equal torque curve T=T2 and a straight line of Iqs=iqs. This computation requires nothing more than a simple algebra and is easily implemented into a controller. The next step is to find point B which yields the same D-axis current on a voltage limited ellipse as the point C. The corresponding torque at point C is slightly different to have a value of T=Ti, but this difference between T I and T2 is normally small. To find the point B again is a simple calculation which can be done by adopting a table look up. The whole procedure thus remains within the scope of the feasibility discussed previously. In this way, the controller generates a new current command point B, corresponding to a slightly different torque command. The flux weakening strategy in the preceding section is easily extended to an almost open loop or a semi-closed loop torque control system given in Fig. 9. In order to control a shaft torque in any sense, at least some information related to the shaft toque must be fed back. In the figure, this is fulfilled by a Torque Computing Block, which calculates Te* based on current commands to the PWM inverter. Precisely speaking, this block computes a shaft torque’s alternative value Te* using outputs of the first order delay blocks whose inputs are current commands to the inverter. This delay may be considered to model the current regulating function of the inverter, but it has a more positive meaning to produce the previously mentioned intermediate current commands required in flux weakening.

Weakening

Program

i Te or Te

0

\b

Enc

U

Fig. 7 Extension of Jahns’ flux weakening to a closed loop torque control system Either the average shaft torque of Te or its estimate Te is calculated by some means and the error between the command T* and Te (or Te) is fed to a PI controller. The output of the PI controller determines initial current commands using functions fl and f2. These outputs are introduced to Jahns’ flux weakening to modify Q-axis current command. A torque control system based on Jahns’ method therefore will have the following characteristics: a) Multiple PI controllers are required, b) Either shaft torque or its estimate is to be detected, c) The flux weakening block of Fig. 7 itself is rather complicated and requires tuning. From the control system design point of view, a more simplified control scheme with a fewer tuning parameters will be required. This standpoint leads us to a nextly presented new flux weakening approach.

PI

4. New flux weakeninn method

Current Program

4.1 Flux weakeninn stratem

In such an application that does not necessarily require a quick torque response, the motor speed varies rather slowly so that current commands can be calculated assuming an electrical steady state at a constant speed. This standpoint is basically the same as Jahns’ work although he does not use a speed information in his controller design. Given the motor speed N and its corresponding voltage limited ellipse as in Fig. 8, current command point B is calculated in the following manner. Suppose some additional information of intermediate current commands can be used. While current commands, calculated in the same manner as in the case of Jahns using functions f l and f2, remain within the portion of OA of the Min. Curr. Trace, they are directly supplied to the inverter. As the torque reference increases, for example when T=T2, beyond the cross point A of the Min. Curr. Trace and the ellipse, the actual current commands must be modified.

b

I

s

N, 0

orque

Fig. 9 A schematic block diagram of a semiclosed loop torque control based on a new flux weakening 659

1

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Enc

In Fig. 9, the error between T* (command torque) and Te* is fed to a PI controller whose output Ts becomes an input to a current programming block. This block normally generates current commands according to the Min. Curr. condition. With the increase of Ts , going beyond voltage saturation, this current programming block modifies current commands according to the discussion described in section 4.1. It is shown in the figure that the output of a current programming block is the voltage V,* and a voltage angle 6* , but this is a rather conceptual presentation to demonstrate that an appropriate voltage limitation by the controller is successfully attained. The output of a current programming block can of course be utilized as input commands to the inverter. This system thus follows the principle illustrated in Fig. 8, when interpreted replacing T in Fig. 8 with Ts in Fig. 10. The resulting system contains only a single PI controller and its tuning is not so difficult. Furthermore, the necessary procedure within a controller is also a simple mathematics easy to be implemented into a microprocessor. It must be noticed here that this approach loses its meaning if Ts exceeds the maximum available torque at a given speed. In such a situation the cross point between curves of a constant torque hyperbola and a voltage limited ellipse can never be found. The point D in Fig. 8 is such a point where torque is in its maximum. The output TS o f a PI controller in Fig. 9 therefore must remain a little bit apart from such maximum point at a given speed. In other words, the maximum torque point D in Fig. 9 is an unstable equilibrium. This resembles the fact that the load angle must be less than TO in a normal non-salient synchronous motor to resume controllability.

1

0 J’ 0

5

10

15

Time T (mS) Fig. 10

Torque response of the presented drive system at N= I . OPU. :torque reference. Te:shaff torque, Te’:intermediate torque)

(I

1 j 1

4.3 Simulation results of a torque resuonse The performance of the presented flux weakening and a semiclosed loop torque control is simulated using a simulation language. The model motor is the same 3-hp Jahns’ unloaded motor [4]. A hysterisis type current regulator is assumed in the inveter. Since we are concerned with a high speed operation, examples of base values are as follows. Wr,BASE = 3200 rpm TBASE = 6.6786 Nm IBASE = 7.46 A These values indicate that a point which lies far beyond the constant power locus of P= 1650W in Fig. 6 is selected as a reference point. Figure 10 is one of the examples of a torque response for a stepwise torque command at a constant speed of N=l.OPU. The motor is initially free-running at N= 1.OPU without stator currents supplied. The shaft torque Te gradually increases from zero to the reference value of T*=0.3PU. After about 2.5 mS, the average value of torque Te is well regulated to stay near the reference. This steady state point is within the region requiring no flux weakening as can be seen from Jahns’ experiment of Fig. 6. At time T=5mS, the torque reference is increased up to l.OPU, which inevitably requires flux weakening. Here, again, it is observed that the torque control is successfully attained even in the high power operation. The output o f a torque computing block of Fig. 9 is also plotted in the simulation result. It is interesting to notice that Te*, as a matter of course, differs from actually generated shaft torque Te, and yet, Te satisfactory follows Te* after a certain time delay mainly due to large inductances of the stator. Since Te* is the signally processed output using continuous current commands, no fluctuation is seen in Te*, while the actual Te fluctuates because of switching of the inverter. The control system illustrated in Fig. 9 is therefore considered to be utilizing a filtered value of Te in the steady state. Figure 11 shows the motor‘s actual current trace in the D-Q current plane for the same condition as in the case of Fig. 10. It is seen that the current loci stays for a while on the Min. Curr. Trace and then moves toward point A on the voltage limited ellipse at N = l .OPU. The point B corresponds to the maximum torque point and it can be seen that the operation generating a torque close to the maximum is stably realized.

1

/

i

-3

F@. 1 1

Bahavior of the motor current trace in the transient in the D-Q current plane overlapped on a voltage limited ellipse and the Minimum Current Trace.

5. Sensitivitv simulation The presented control strategy generates current commands based on the calculation in the electrically steady state. This is a reasonable assumption since we are dealing with a rather slowly changing system in terms of speed. However it is interesting to carry out a sensitivity simulation to examine the effect of speed change over system performance. Assuming an inertia, which causes 0.7PU speed change within 0.1s for 0.8PU torque, the effect of speed change is investigated and shown in Fig. 12 for a torque reference of 0.75PU. Although this is a rather small inertia, causing a comparatively fast

660

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speed change, it is seen that the effect of motor speed is not so significant. There are some other parameters incorporated in the controller affecting the system performance. Among all, motor parameters, used in the current programming block, are usually uneasy to identify correctly. This effect of mismatching has not completely been studied so far, but some examples are shown in Fig. 13 where both D and Q inductance values used inside the controller are increased by a factor of 5% compared with the simulated machine’s values. A comparatively large oscillation of shaft torque is observed as the motor speed increases beyond some 0.45PU. The average torque itself, however, still remains within an endurable error range. Illustrated in the small rectangular box with the same scaling is the result for 2.5% increase of inductances. Such amount of mismatching may not be significant to greatly affect the system’s behavior.

2

z 3

B

VI

.* -4

5

b a 1

6. Conclusions

n

I

50

0

!

The paper has dealt with a semi-closed loop torque control based on a new flux weakening. The investigation is still being done to fully explore the actual feasibility of the presented system. At present, the confirmed results are as follows: a) The buried type permanent magnet motor‘s potential ability of high power capability will find its attractive characteristics into many applications. b) This potential ability must be backed up by figuring out an appropriate flux weakening strategy, which has been the major target of this research. c) A practical computer-based control scheme, at present, should incorporate only a sequence of a simple algebra or a table look up and so forth. The flux weakening scheme to be explored is not also free from this bondage. d) Following the work by Jahns, a new flux weakening method is studied which effectively utilizes an intermediate current commands so that the operating point gradually shifts along the voltage limited ellipse. e) A semi-closed loop torque control is presented based on the new flux weakening. Essential to this torque control is the adoption of a torque estimator using the intermediate current commands. This method realizes an almost open loop torque control when the motor speed change is slow. f) The presented control system is robust up to a certain degree as to the speed change and the built-in controller‘s mismatching of motor parameters. Still, a more detailed scanning of sensitivity study will be required to fully explore the nature of the presented scheme.

‘ 0 100

Time T (mS)

Fig. 12

An example of torque response of the presented drive system for a reference torque of 0.75PU when motor speed varies. The inertiais properly asumed to cause0.7PU speed change within 0. lsec for 0.8 shaft torque.

0.7

z U

-

VI

T*

0.6

.-

7. References

5 L

[ 11 Rich Schiferl, ”Design considerations for salient pole permanent magnet synchronous motors in variable speed drive applications”, Ph. D. Thesis, University of Wisconsin, Madison, pp.5 I , 1987 [2] B. Sneyers, D. W. Novotny and T. A. Lipo, ”Field w a k e n i n g in buried permanent magnet AC motor drives”, IEEE Trans. on Ind. A d . , vol. IA-21, MarJApr., pp. 398-407, 1985 [3] T. M. Jahns, G. B. Kliman and T. W. Neumann, ”Interior permanent magnet synchronous motors for adjustable-speed drives”, ,vol. IA-22, JulJAug., pp. 738-747, IEEE Trans. on Ind. ADD~. 1986 [4]T. M. Jahns, ”Flux-weakening regime operation of an interior permanent magnet synchronous motor drive”, IEEWAS Annual Meeting Conf. Rec. ,pp.814-823, 1986 [5] B. K. Bose, ”A high performance inverter-fed drive system of an interior permanent magnet synchronous machine”, IEEWAS Annual Meeting Conf. Rec. ,pp.269-276, 1987 [61 P. Pillay and R. Krishnan, ”Modeling,analysis and simulation of a high performance vector controlled permanent magnet synchronous motor drive”, IEEEYIAS Annual Meeting Conf. Rec. , pp.253-261, 1987 [71 A. Kumamoto and Y. Hirane, ”A flux weakening control of a permanent magnet motor”, IEEJAA Annual Meeting Conf. Rec. ,1989 to appear (in Japanese) [81 Y. Takeda and T. Hirasa, ”Current phase control methods for permanent magnet synchronous motors considering saliency”, PESC Conf. Rec., pp.409-414, 1988

a” 0.5

0.4

0.3

0

100

50

Time T (mS)

Fig. 13

An example of torque response of the presented drive system when the motor parameter values utilized inside the controller are intentionally deviated from actually simulated motor model by a factor of 5% or 2.5%(in a small box). 66 1

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