IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 4, NO.

4, JULY 1996 431

A New Control Scheme for Improving Disturbanc:e Rejection in

Speed Control of Permanent Magnet Synchronous Motors
B. Srinivasan, N. J. Rao, U. R. Prasad, and A. Pittet

Abstract- The major hurdle encountered in achieving high In the present context, the issue of improving disturbance
performance in servo speed control is the occurrence of large rejection further than what can be achieved by the best
relative errors at low speeds due to torque variations. In this feedback controller, is addressed. Traditionally, feedforward
paper, it is shown that this problem can be tackled in the case of
synchronous motors, by keeping the stator current and the rotor action is used to augment the feedback loop for the rejection of
flux nonorthogonal and including an inner position control loop disturbances [ 11, but is applicable only when the disturbances
to improve the transient behavior of the system. Such a scheme are available for measurement. A popular method to generate
substantially improves disturbance rejection at the cost of accen- feedforward action is to use the inverse of the plant [2]. As the
tuating the nonlinearities of the system and increasing the copper parameters of the plant may vary, however, the inverse should
losses. In view of the pronounced nonlinearities encountered here,
adaptive control using neural networks is resorted to. constantly keep track of the plant variations using on-line
identification techniques [2]1. Such a policy cannot be adopted
here as most of the disturbances are either not available for
I. INTRODUCTION measurement or expensive to measure [3]. Very little work

H IGH-performance state-of-the-art industrial servos are

commonly designed using the field-oriented control tech-
nique, which consists of decoupling of the slow and fast
appears to have been done for such problems. In this paper,
we propose an alternative control structure for the servo speed
control problem, which improves rejection of disturbances
dynamics followed by design of classical feedback controllers. without actually having to measure them. As a result, this
This normally gives good time response to a step change in scheme achieves rejection of all the disturbances that arise
speed and reasonable rejection of torque disturbances. The and at all the speeds. The price paid in the scheme is having
change in speed caused by a torque disturbance is absolute, to contend with the nonlinearities of the motor, requiring the
however, in the sense that the error is independent of the speed adoption of adaptive control using neural networks and the
at which the motor is running. This means that if the operating increased power dissipation. Even so, the scheme has merit
speed range is very wide, relative errors at low speeds can since it is one of the very few methods to handle disturbance
be quite large. For example, with a demanded speed range rejection effectively.
of 1 : 3000 (e.g., 1-3000 rpm), if the error due to a change Control of electrical machines can be broadly classified into
in load torque is 0.01% of the maximum speed, then the 1) closed-loop field oriented control, where the two physical
corresponding error at the minimum speed can be as high quantities generating the torque (viz., the flux and the current)
as 30%. If the closed-loop system is fast enough and if the are kept orthogonal; and 2) open-loop control without field
amplitude of disturbance is small, field-oriented control might orientation where the two are not forced to be orthogonal [4].
be sufficient to meet the desired performance limits even with a V/f control of ac machines falls under the second category. In
wide speed range. In many cases, however, the system is either the field-oriented control of synchronous machines, the stator
sluggish (due to the presence of large inertias, low sampling current and rotor flux are kept orthogonal. As can be seen
period, etc.) and/or the torque disturbances are large, rendering later, field orientation gives good dynamic performance but
the disturbance rejection provided by a feedback controller suffers from poor disturbance rejection at low speeds. This
insufficient. In short, achieving disturbance rejection becomes can be attributed to the fact that with a feedback structure,
the bottleneck in realizing high performance, especially in the change in output due to a disturbance does not depend on
applications which are characterized as above. A solution to the present output value. In the servo control problem, this
such a problem is proposed in this paper. implies that the error in speed caused by a torque disturbance
is independent of the speed at which the motor is running.
Manuscript received October 2, 1994; revised July 20, 1995. Recommended
by Associate Editor, B. Lohmann. On the other hand, we will show in the next section, that in
B. Srinivasan was with the Department of Computer Science and Automa- an open-loop control structure such as the V/f control, field
tion, Indian Institute of Science, Bangalore-560012, India. He is now with the deorientation causes a “spring type action” internal to the
Institut d’Automatique, Ecole Polytechnique FCdCrale de Lausanne, CH-1015
Lausanne, Switzerland. motor, due to which the disturbance rejection at low speeds
N. J. Rao is with the Department of Computer Science and Automation, would be better (i.e.>smaller peak deviation from set speed).
Indian Institute of Science, Bangalore-560012, India, and the Center for Elec- The transient response is, however, in general oscillatory and
tronics Design Technology, Indian Institute of Science, Bangalore-560012,
India. inferior to the field-oriented case.
U. R. Prasad is with the Department of Computer Science and Automation, Since the disturbance rejection provided by the feedback
Indian Institute of Science, Bangalore-560012, India. controller is insufficient, it becomes necessary to enhance the
A. Pittet is with the Center for Electronics Design Technology, Indian
Institute of Science, Bangalore-56001 2, India. open-loop characteristics of the system so as to meet the
Publisher Item Identifier S 1063-6536(96)04918-4. performance requirements. So, in this paper, we propose a
1063-6536/96$05.00 0 1996 IEEE
438 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 4, NO. 4, JULY 1996

scheme applicable to synchronous motors, which allows the

;
stator current and the rotor flux to be nonorthogonal, so that
the internal “spring effect” can be used for improving the
disturbance rejection at low speeds. To achieve the desired s (Js+B)
transient response, a nonlinear position controller based on
neural networks is used. The position control loop is placed
inside the speed control loop to provide a more accurate
“point-to-point” control of speed. Here we have analyzed
and applied this control scheme to a two phase permanent
Fig. 1. Inherent loop.
magnet synchronous motor (PMSM), because of its simplicity,
versatility, and growing importance in the servo systems
market [5]. the speed back to its original value without any external
In the next section, we describe the new scheme for im- control action and hence contributes to the improvement of
proving disturbance rejection. We also perform an approximate disturbance rejection.
analysis to show that the relative error at low speeds can be To characterize this loop, consider a situation where the
improved with this scheme. Section I11 is devoted to the details stator position ps is held constant and a torque AT, is applied.
of implementation of this scheme using neural networks. Last, Then, the change in rotor position, p T , is given by
conclusions are drawn in Section IV.
AT(s) - AT, (s)
= s ( J s + B) (4)
11. A NEW CONTROL SCHEME FOR
IMPROVING DISTURBANCE REJECTION By differentiating (2),we see that the increase in the generated
torque due to a change in rotor position is given, to a first-order
A. Characterization of the Inherent Feedback Loop approximation, by
Consider a two-phase permanent-magnet synchronous mo- AT E K T I , COS @)A6
tor with i, and i b being the stator phase currents. The stator
flux position ps and the effective stator current I, are given by
= -KTI, cos (&)ap,. (5)
Equations (4) and (5) are two elements of the internal loop as
shown in the Fig. 1.
The closed-loop transfer function of the internal feedback
I, = 42: + 2;. (1) loop of the motor is

Let us assume that the current controllers are fast, and the 1
stator flux can be positioned at its desired position. Then the b ( S ) = (-1) +
s ( J s B)
torque is given by ATL(S) 1 + KTIs cos (6) s ( J s1+ B)
T = K T I , sin ( p s - p r ) -1
-
-
= KTI, sin (6) (2) Js2 + + Bs KTI,* cos (6).
(6)

where KT is the torque constant and 6 = ( p , - p,) the lag It can be seen that the torque generated with (5) is equivalent to
angle. It may be noted that KT may vary due to saturation having a “spring” with a spring constant K = K T I , cos (6).
effects. Let us assume a mechanical load with J being the Examining the transfer function (6), certain remarks are in
inertia and B the friction. With w, being the rotor speed and order:
w,,f the reference speed, TLthe lode torque, the rotor position, Remark I : The dc gain of the small signal system is a
p,, can be obtained as measure of the steady-state error in the absence of any speed
controller. In the case of field oriented control for which
(3) S = (7r/2), K = 0, and dc gain = 00, the rotor angle may lag
without bound. Though the system is only marginally stable
To understand how different schemes differ in disturbance (one of the characteristic root is at the origin), the other root
rejection characteristics, let us first study the effect of load is well damped.
disturbances on a motor. When the load torque increases, the Remark 2: In the case of deorientation, the dc gain is finite,
speed decreases thereby decreasing pr and increasing 6. In the as K # 0, indicating that the position lag is finite. This
field oriented scheme, where the controller tries to maintain implies that the speed will eventually return back to the set
6 = (7r/2), any increase in 6, consequent to an increase in speed without any external action. Since the characteristic
load torque, will first take it into the second quadrant, thereby roots are now complex in general, however, the response is
reducing the generated torque, T . On the other hand, when the not acceptable.
fluxes are not orthogonal i.e., S < (?r/Z), 6 continues to be in Remark 3: For large K , i.e., when the damping ratio
the first quadrant even after the load disturbance and increases B / ( Z m ) M 0, the change in speed will be a sinusoid
the generated torque. This is an internal feedback which puts with amplitude ATL/2/JK and natural frequency m.
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 4, NO. 4, JULY 1996 439

Hence, the maximum change in speed due to a change in load function is given by
torque is given by

(7)

For having the best possible rejection of disturbances i.e., low

( A w ~ it ) can ~ ,from (7) that K and hence 1, should
~ ~be~seen
be as high as possible. Hence, we set I , to I,,, the rated 1
current, in the rest of the discussion. c
(
2 1 ’ (9)
s2+-s+T
Tpm Tpm
B. The Inner Position Control Loop
For a critically damped response with two poles at - 1 / ~ ~ ~ ,
The remarks of the previous section set the stage for the the desired closed loop transfer function is proportional to
new scheme which has two main features: 1) allowing the ~ / ( T + ~ 1)’.
~ s By equating the actual closed-loop transfer
stator current and the rotor flux to be nonorthogonal so as to function and the desired one, the controller gains can be
utilize the inherent feedback loop for providing disturbance obtained as
rejection and 2) using a suitable external position controller
to improve the poor transient behavior caused by the inherent
feedback loop.
We set Is = I,,,,, to make the best use of the internal
feedback loop. Having thus given away one of the two degrees
of freedom, we plan to improve the transient response by uti-
lizing the other degree of freedom available in a synchronous It can be seen that the dc gain and the maximum speed error
machine i.e., the lag angle S. The control is achieved by due to a step change in load can be minimized by choosing
adjusting the stator flux position ps in accordance with the a low rpm.Such a “linear” scheme cannot be used directly,
variation in the rotor flux position pT. In other words, a however, as the gains become extremely large when 6 is close
position controller is designed to meet the transient response to (7r/2), [S --+ (7r/2) + M + 0 + K p , Kd --+ CO], causing
requirements. The rotor flux position, p r , can be obtained from instability.
the physical position of the rotor in synchronous machines
using a position encoder. Note that the position or phase C. The Outer Speed Controller Loop
loop discussed here is not the normal position loop used The above problem can be tackled by choosing a proper
in an accurate position servo. The loop under discussion is nonlinear controller for G,, instead of a ‘‘linear’’ one. When
inside the speed loop for a more accurate control of speed. the set speed is changed, however, the motor can only ap-
Let us now define the synchronous rotor flux position to be proach the new set speed with a lag due to inertia and finiteness
/SI.
p T s(s) = [R,,, (s) This is the position where the rotor flux of the torque. The controller described in (8) demands the
should, in principle, be. So the position controller, G,, can reference and actual positions to be equal, which also means
then be written as that the integrals of the set and actual speeds should match. In
a bid to achieve this, the motor speed exhibits overshoots re-
sulting in undesirable oscillatory transients. This is a standard
situation when an integral type controller is used along with
output saturation [ 2 ] . But, it may be realized that matching
Note that we devised the scheme, in many respects, to be of the positions is really not required in the speed control
intermediate to the V/f and field-oriented control schemes and problem and the degradation of the transient performance is
having the features of both, so that the latter may indeed be rather due to the control structure used. From the definition of
considered as special cases of the new scheme. In the present the synchronous rotor position we see the difference
framework, G , is a proportional controller of unity gain, for 1
the Vtf control scheme, i.e., pb = prs and the output of G , Pr.s(S) - Pr(.) = ;[fL,,(S) - Rr(s)l. (11)
is independent of the error fed to it, for field-oriented control.
In one sense, the Vlf scheme solely depends upon the internal So prs can be viewed as an integrator which integrates the
feedback loop of the motor for disturbance rejection while the speed error [U,,, - (4.1relative to the present rotor position,
field-oriented control scheme completely disregards this loop. which causes the above mentioned problem. To solve this,
The present scheme, on the other hand, utilizes the inherent the pTs integrator should not be allowed to integrate under
feedback mechanism of the motor for disturbance rejection certain conditions to avoid the oscillations arising due to
and supplements it with an external one. nonlinearities. For this we choose
Since we need to improve the damping, we first look
into a PD (proportional derivative) type “linear” controller,
G c p ( s )= Kzl+ K d s . With this setup, the closed-loop transfer
440 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 4, NO. 4, JULY 1996

where T~ is the sampling time, and 0 is some nonlinear effective gain will be
function. If 0 = 0, there will be no integration of the error
and if 0 = T ~ ( W , , ~- wT), the error will be integrated always.
Four possibilities exist: 1) keep 0 at one of its extremes; 2)
choose a fixed value of 0 somewhere in between; 3) switch
between the two extremes depending on certain switching
conditions; and 4) allow 0 to be some nonlinear function
of the speed error. The technique of antireset wind up [2]
Equation (15) implies that Gceff is an increasing function of
used with integral controllers falls under option 3), where the
I,,,. When K p = Gceif,and Kd is chosen appropriately, then
integration is paused whenever the output saturates. In general,
the synchronous rotor position prs can be obtained as some
nonlinear combination of reference and actual speeds and the
lag angle as mentioned in option 4)
1
oc- (16)
Imax

as 1) K x I,,, and 2) Gceffincreases with I,,. If the motor

is fed from a constant voltage supply of magnitude V, then
where G,, is the speed controller. Then, the position controller the maximum current it can be made to draw is given by
is given by the equation
V -K~w,
Imax
= Jm
V
M-
Now we have some sort of a cascade controller with an WrL
1
inner position loop and an outer speed loop. As noted earlier, K-
the scheme appears contrary to the normal convention, with
the inner loop designed basically for a more accurate control
of the speed. One may designate the inner loop a phase loop
so as to conform to the normal convention, but calling it a
position loop seems more appropriate.
The issues that have to be noted here are: 1) in this
formulation, the problem is heavily nonlinear right from the So, with this scheme, we have approximately achieved our
inner loop and 2) the speed controller now faces a totally objective of making the relative error in speed proportional to
different nonlinear plant (in fact even the order of the plant is an absolute change in torque. Hence, the relative error over
not preserved) and its task is quite different. Hence, linear the desired speed range can be improved.
techniques fail and one has to resort to nonlinear control Remark4: Given the same load torque, the demanded
techniques for the design of the controllers G,, and G,,. In +
torque (TL B w ) is less at lower speeds. Hence, in the field
the next section, neural networks are used to this end. oriented control, the current passed through the windings at
In the proposed scheme, maximum current is drawn at all low speeds is normally less than that at higher speeds. On the
time instants. This will increase the copper losses inside the contrary, in the present scheme, the current drawn at lower
motor. In some situations it may be necessary to decrease speeds is much higher than that at higher speeds. This is
the dissipation and improve the efficiency. Under such a deliberately intended for the sake of improving disturbance
situation, one can switch between the proposed scheme and rejection. Yet only the required torque is generated by de-
the traditional field oriented control to get the better of both orienting the field. The extra current, or the component of the
worlds. Fuzzy logic can also be used to progressively transit current that does not produce a torque, gives a “reserve torque”
from de-orientation with maximum “spring effect” to a field- which is called upon in the event of a disturbance.
oriented scheme. Remark5: At low speeds, the resistance of the windings
dominates the inductance. Hence the current cannot increase
with decrease in speed as given in (17). Even if a higher current
D. Approximate Analysis of the Speed Error is drawn, the flux produced is not increased to the desired
Our objective in developing this scheme was to improve extent due to the saturation of the core. So a relationship such
the relative speed error caused by a change in load torque at as that given in (18) is quite difficult to achieve. Also, in
low speeds. We now perform an approximate analysis of the this scheme we increase the stator copper-losses (12Rlosses),
controller to find if the relative error has indeed been reduced. and the heat generated has to be properly dissipated. In short,
Let G,,,, be the maximum gain in the position loop which still the winding resistance, the magnetic saturation and the thermal
keeps the lag angle S within its saturation limits &(7r/2). Even considerations are the deciding factors which finally determine
if a higher gain is incorporated in the controller, the effective the operational limits and the level of performance at low
gain, Gceif,will be lower due to saturation. The value of the speeds under this scheme.
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 4, NO. 4, JULY 1996 441

I n I
Speed Position
Controlle Motor
Controller
P,
fi

Fig. 2. Proposed scheme for servo control. Fig. 3 . Approximate model of Ihe overall system.

111. IDENTIFICATION AND ADAPTIVE

CONTROLUSINGNEURALNETWORKS
Now we turn towards implementing the control scheme
1
presented in Section 11. Since, the plant and the controller are
both nonlinear in the present formulation, we opt for nonlinear
I
adaptive control using neural networks for which techniques
have been developed in [6]. In the indirect adaptive control
scheme, the first task is the identification of the plant. As seen Fig. 4. Adjoint of the model.
in Fig. 2, the plant is a mapping between the stator position ps
to the rotor speed w, and rotor position p,. So the identification
scheme has to identify the relation between ps and pT which IBM PC T-800
for user Transputer Carc ADC - DAC
is a nonlinear second-order differential equation. So a neural- Inserted to PC interface
network model used to identify this nonlinearity, with pTpred
being the predicted rotor position, is given by I I A t
Power Phase Work Table and
Drive Currents Motor Magnetic Brake
Sensing
Since the model has no recursion, standard backpropagation
can be used for learning. This system has two controllers in Fig. 5. Experimental setup
cascade. The inner one is the position controller whose inputs
are the rotor position pT and the rotor reference position p r s .
variations are considerably high. The inertia was so chosen
The output is the desired stator position ps
that mechanical time constant of the system was approximately
5 s. Also, a magnetic brake was connected at one end of the
shaft to generate the required torque fluctuations. The torque
was varied from no load to a full load level of 10 Nm. The
power drive was based on bipolar transistors. The position of
rotor was obtained from an incremental rotary optical encoder
The outer speed controller gives out the synchronous rotor po-
sition p r s ( k ) , the inputs to which are the actual and reference connected to the shaft and the speed was obtained from the
position measurement by fitting a cubic and differentiating it
speeds and stator and rotor positions. It is static and can be
at the desired point. The model of the system can be described
modeled using
by three constants, the torque constant K T , the reflected inertia
as seen by the motor J and friction B. The model can then
be written as follows:
J & ( t ) + BPt(t) = K T I ~ (sin
~ [6(t)]
) - T’(t) (22)
The block diagram of the overall system is given in Fig. 3.
For the adaptation of the two controllers, the adjoint of the where pt is the position of the work table, which has a one-
overall model is constructed as in Fig. 4 where the signal flow to-one correspondence with the rotor position p,., except for
is reversed. The nodes are replaced by summing junctions and the backlash. Instead of obtaining an empirical model, an open
vice versa. The error is backpropagated through it for obtaining loop identification of the above system was performed with the
the derivatives necessary for adaptation. The adaptation is data collected, using the nonrecursive least square technique.
carried out using the predictive backpropagation scheme in The identification gave the parameters, KT = 3.34 “/Amp,
a certainty-equivalent manner [6]. J = 0.485 Kg, and B = 0.092 Kg/s.
The proposed scheme was implemented on a Samar- The neural-network algorithms, in this case, were imple-
ium-Cobalt PMSM. The block diagram of the experimental mented on a network of transputers programmed for the same.
setup is shown in Fig. 5. The PMSM was connected to a lead The controller which was a transputer card with four T-800
screw which carried a work table. To illustrate the scenario transputers was connected to the mother board of an IBM PC.
where such a scheme is particularly useful, the parameters One of the transputers handled the communication with the
were so chosen that the system is sluggish and the torque analog-to-digital and digital-to-analog converters and another
442 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 4, NO. 4, JULY 1996

a
E 6.
I
d

5 4 '

01 " " 1 ' " ' I

0 1 2 3 4 5 6 7 8 9 10
Time in Seconds
Fig. 6. Response with a traditional controller. Fig. 8. Response with the new controller after learning.

and could not be detected as it was within the limits of the

measurement noise.

IV. CONCLUSIONS
In this paper, the disturbance rejection problem in the speed
control of PMSM's was considered. The major bottleneck
is the large relative errors caused by torque variations at
low speeds. The stator current and rotor flux are deoriented
to tackle this. The poor transient response resulting from
this arrangement is improved by placing a position control
loop inside the speed control loop. This scheme improves
disturbance rejection at the cost of exposing the nonlinearities
0 1 2 3 4 5 6 7 8 9 10
of the system and increasing the copper losses. Nonlinear
Time in Seconds adaptive control of the modified plant was performed using
Fig. 7. Response with the new controller before learning. neural networks.

handled the communication with the host PC. The control REFERENCES
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a traditional field oriented controller is shown in Fig. 6. The Motors. New York: Pergamon, 1988.
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1985.
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new control scheme are shown in Figs. 7 and 8. Oscillatory Motors. Oxford, U.K.: Oxford Univ. Press, 1985.
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