This paper describes the early states of work to implement a fuzzy logic controller to optimize the efficiency of AC induction motor/adjustable speed drive (ASD) systems running at less than optimal speed and torque conditions. In this paper, the process by which the membership functions of the controller were tuned is discussed and a controller which operates on frequency as well as voltage is proposed. The membership functions for this dual-variable controller are sketched. Additional topics include an approach for fuzzy logic to motor current control which can be used with vector-controlled drives. Incorporation of a fuzzy controller as an application-specific integrated circuit (ASIC) microchip is planned

Chappell, Jeff

Jani, Yashvant

Sousa, Gilberto

Spiegel, Ron

Turner, Wayne

English

NASA Technical Reports Server

FUZZY
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EFFICIENCY OPTIMIZATION OF AC INDUCTION MOTORS
5/_ G "_
t
Yashvant Jani
Togai InfraLogic, Inc.
Houston, Tx
Gilberto Sousa
University of Tennessee
Knoxville, Tn
Wayne Turner
Research Triangle Institute
Research Triangle Park, N.C.
Ron Spiegel and Jeff Chappell
U.S. Environmental Protection Agency
Research Triangle Park, N.C.
This paper describes the early states of work to implement a fuzzy logic controller to
optimize the efficiency of AC induction motor/adjustable speed drive (ASD) systems
running at less than optimal speed and torque conditions. In this paper, the process by
which the membership functions of the controller were tuned is discussed and a controller
which operates on frequency as well as voltage is proposed. The membership functions
for this dual-variable controller are sketched. Additional topics include an approach for
fuzzy logic to motor current control which can be used with vector-controlled drives.
Incorporation of a fuzzy controller as an application-specific integrated circuit (ASIC)
microchip is planned.
76
https://ntrs.nasa.gov/search.jsp?R=19930013174 2020-03-17T06:15:25+00:00Z
FUZZY LOGIC CONTROL OF AC INDUCTION MOTORS
In research funded by the U.S. Environmental Protection Agency (EPA), the authors have
been pursuing the development of energy optimizer algorithms for ac induction motors
driven by adjustable speed drives (ASDs). Our goals are:
1) increase the efficiency of ASD/motor combinations, especially when operating off
of rated torque/speed conditions. ASDs using V/Hz control, which is the current
predominant industry standard, still do not gain maximum efficiency from motors
operating at less than rated loads and speeds;
2) develop a generic energy efficiency optimizing controller (EEOC) which can be
applied to a wide range of ac induction motors, regardless of their size and
corresponding equivalent circuit values;
3) develop an energy efficiency optimizing controller (EEOC) which can eliminate the
requirement for tachometer or encoder feedback, and still maintain the stability of
closed-loop control; and
4) develop an energy efficiency optimizing controller (EEOC) which is self-tuning, thus
eliminating the need for extensive operator/manufacturer involvement in the
installation of the energy optimizer into ASDs.
Fuzzy logic approaches to these goals are attractive for two reasons:
1) the use of fuzzy logic promises to simplify the energy efficiency optimizing
controler (EEOC) control problem, which is highly nonlinear;
2) fuzzy logic offers a way to develop an energy efficiency optimizing controller
(EEOC) controller which will offer the stability of closed loop control without the
need for speed feedback, thus eliminating the cost of tachometers and encoders.
Fuzzy Efficiency Optimization for Steady State Motor Operation
Our main interest has been to solve the problems above for large horsepower motors
(>10 hp) running at steady state conditions in industrial applications (e.g. pump and fan
motors).
An induction motor simulator has been developed based on the equivalent circuit
representation of a motor. As a starting point, the simulation values which are produced
correspond to those which would be produced by a V/Hz controller. The simulator
computes the values of the motor state variables (currents, voltages, power, frequency,
etc.) in response to changes in the value of the stator voltage, V s. The values of V s are
77
provided to the simulator by a fuzzy energy optimizer. (This energy optimizer was
discussed in a previous paper delivered at FUZZ-IEEE '92 in San Diego in March.) This
energy optimizer, referred to as the Single Variable Fuzzy Logic Motor Controller, and
illustrated in the accompanying block diagram, alters the value of stator voltage (Vs) and
then measures the input power Pin to see if it has changed.
DeltaP in
DellaV old
> DeltaV new
Figure 1. Block Diagram of the Fuzzy Logic Energy Optimizer
Dependent on the magnitude and direction of the change in Pin, a set of fuzzy rules,
represented here by the section labeled 'Perturber' in the block diagram and using API,
and the last change in Vs, AVs_oU, as inputs, computes an incremental change in the
stator voltage AVs_..now which is then applied to the simulator. A new set of state variables
is computed and the process is repeated until either a minimum input power is obtained,
characterized by the return of a value of 0 for AV s from the fuzzy controller, or, if
tolerance limits on the output torque or the shaft speed of the motor have been exceeded.
After some testing, the max-dot inference method and centroid defuzzification were
employed.
This technique is essentially a search scheme for the minimum input power point, which
occurs in a motor driven by a pulse-width-modulation (PWM) ASD when the copper
losses and core losses of the motor are equivalent, as shown in the following figure.
78
Torque (To= TL)
Speed (Wr)
Time
Total Loss
Copper Loss.
Converter Loss
Loss
"lime
Efficiency Optimized
Operating Point
Figure 2. Efficiency Optimization Control based on Real-time Search.
79
Note that the prediction in the search scheme is that the stator voltage will decrease and
the stator current will increase. This prediction has been borne out by the simulator
results. The simulator also predicts efficiency improvements by the energy efficiency
optimizing controller (EEOC) over standard V/Hz control, as shown in Figure 3.
After the controller rules were refined from simulation of motors of various sizes, a set of
13 fuzzy rules were developed, shown in Table 1.
RULES
1. IF APIn IS N AND AVs__old IS N, THEN AVs_ne w -- N.
2. IF APIn IS N AND AVs..o w IS P, THEN AVs..n _ = P.
3. IF APin IS N AND AVso_d IS NM, THEN AVsn,, w = NM.
4. IF APIn IS N AND AVs_ol d IS PM, THEN AVs_n_ = PM.
5. IF A-P_n IS NM AND (AVso u IS NM OR AVs._ou IS N), THEN AVs_no w = NM.
6. IF &Pan IS NM AND (AVs_oSd IS PM OR AVs._o_dIS P), THEN AVs_n, w = PM.
7. IF z_Pin IS PM AND (AV,_oU IS NM OR AVs_old IS N), THEN AVs__now= PM.
8. IF '*'Pin IS PM AND (AVs._old IS PM OR AVs._o_dIS P), THEN AVs__r_ew = NM.
9. IF APin IS P AND AVs_ol d IS NM, THEN AVs_no . = PM.
10. IF APin IS P AND AVs_.old IS PM, THEN AVs_no w = NM.
11.
12.
13.
IF Aeln IS P AND AVs_.old IS N, THEN AVs_n, w
IF APIn IS P AND AVs_.okJ IS P, THEN AVs_ew
IF APin IS Z AND AVs._old IS ANY, THEN AVs_n. w =
=P.
=N.
Z.
Table 1. Single Variable Controller Rules
8o
100.00 - !
95.00
20.00
1111 Till
--- --
| I I I l ! ! I I I I I I ; ! I I ! '! ! ! '1 I !
30.00 t.O.O0 $0.00 60.00 70.00 80.00 90.00 100.00
I P_RCI[MTACE RATED SHAFT SPEED J
Figure 3. Energy Efficiency Optimizing Control (EEOC) versus V/Hz Control
for a 100 HP Motor with Torque o_ Speed 2.
81
The variable values, N, NM, P, PM, and Z stand respectively for negative, negative
medium, positive, positive medium, and zero. Data gathered from the motor simulator
led tO development of limits for membership functions for the fuzzy variables voltage and
power. Figure 4 illustrates this for the linguistic variable APh_.
•
15 _ N
A
I 1
1 1 I ]
p
-400 0 400
-]
-0.5
WAILS
Figure 4. Final Membership Functions for the Fuzzy Variable APin.
It was found from the simulator that the Pin can vary by as much as +400W. Surfaces
were constructed from curves relating the various changes in AVno w to changes in APin
and AVok j. An example of such a surface, generated from data collected with the
simulator, is shown in Figure 5.
82
QJ
Q
\
83
r,-
o_
a.
t-im
l-
.c
0
r-
CZ
°_
OF)
t-
C_
°m
.t-p
Q_
C_
r_
im
O
C_
E
om
E
O
Im
am
r-
im
0_
U.
These surfaces can be used to optimize the membership functions by examining the
surfaces for abrupt or discontinuous changes in the output variable AV s at various values
of the input variables AP,n and AV s o_- Based on the magnitude of the discontinuity either
the input membership functions' ovedaps could be changed or the width of the output
membership functions could be changed.
As this initial controller was used to simulate, from equivalent circuit data, several different
motors, several features of the controller became clear as this data was analyzed. For
example, any change in stator voltage produced a drop in the output shaft speed 0_r,
which is generally undesirable. Also, for a given set of equivalent circuit values,
maximum efficiency is closely related to total circuit impedance, _n, regardless of the
torque/speed condition.
Because of the loss of shaft speed, it was clear that even the optimized controller would
never perform adequately working alone. Therefore attention was turned to a controller
which could both compensate for the loss in shaft speed resulting from the voltage
perturbations and still allow a minimum input power point to be reached. It was
recognized that the loss of rotor speed could be corrected by increasing the frequency
of the stator voltages and currents, while the minimum power input point can be obtained
by perturbing the voltage. Furthermore, a correlation of o_r impedance suggested that if
the change in input impedance were known for a particular change in synchronous
frequency coo and voltage V s, then approaching an optimum impedance as rapidly as
possible should achieve both the minimum input power and the correction of the drop in
_r" This led us to develop a preliminary controller concept for a frequency perturber,
shown here in block diagram form in conjunction with the existing voltage perturber.
old/
AVo,, 1
\
Fuzzy Controller - :1
Avow
Motor Model
P in__ew
Figure 6. Dual Variable Fuzzy Logic Controller for AC Induction Motor
84
Thus the set of rules which perturbed the voltage were augmented by another set of rules
which perturbed (eo using the previous value of z_o_e, A_o.ol d, and AZtn. This new fuzzy
rulebase, which has 9 rules, fires simultaneously with the 13 rules of the SVFLC. The
rule-base for inference of the synchronous frequency is shown in the following table.
RULES
1)
2)
3)
4)
5)
6)
7)
8)
9)
IF A(%_oid IS P AND aZin IS N.THEN A(% = P
IF Aee_oi d IS Z AND AZin IS N THEN Aee = P
IF A(Oe_old IS N AND AZin IS N THEN Ao_e
IF ACe_old IS P AND z_Zin iS Z THEN
IF Ae)e _d IS Z AND AZin IS Z THEN
IF A(%_ed IS N AND AZin IS Z THEN
IF A(%_oi d IS P AND AZin IS P THEN
IF A(Oe_old IS Z AND AZin IS P THEN
IF Ao)e_oid IS N AND AZin IS P THEN Aee = P
=N
Ae)e = Z
Ae) e = Z
Ac% = Z
Aee = N
A(J) e = N
Table 2. Added Rules for Control Frequency
The symbols P, N, and Z stand respectively for positive, negative and zero. Limits on the
membership functions were developed as before by analyzing output data from the
simulator and setting the limits. The preliminary output membership functions for Ae_e are
illustrated in the following figure.
85
"I
O
I
O
x
N
"r
O
wp,,.
f,n
c
o
°_
C
U.
°_
t'--
i_
Q)
E
Q)
L_
U.
O
O
O00 _ o
O O O
e"_ uJ..._l_ cLj u.
c5
C)
O
6
O
86
As in the previous work, a control surface was generated and could be used to tune the
membership functions. Note in the control surface graph that there are certainly abrupt
changes in A_ e for certain values of /_71n and A_ e o_d"
DELTA We
DELTA We old
Figure 8. Control Surface for Synchronous Frequency Perturber
Fuzzy Efficiency Optimization using Indirect Vector Control
A parallel effort is taking place to provide fuzzy efficiency optimization for induction motors
which use indirect vector or field-oriented control of induction motors rather than PWM.
Indirect vector control is another approach to the control of ASD/motor combinations
which controls current rather than voltage. This type of energy optimizer emphasizes the
suppression of transient phenomena in the motor, and is focused more on dynamic
process control applications (lathe motors, steel mill rolling, etc) than the steady state
controller. The controller is illustrated in Figure 9.
87
PG
Figure 8. Fuzzy Efficiency Optimization for Indirect Vector Control.
In indirect vector control, the motor is modeled using a change of variables which
represents the state variables of the motor in terms of two magnetically decoupled
equivalent circuits, generally referred to as the d-q representation of a motor. When
vector control is employed the currents ids and iqs control the flux and the torque of the
machine, respectively.
Fuzzy efficiency optimization for indirect vector control utilizes the same type of minimum
input power search scheme outline above, however rather than perturbing the stator
88
voltage, the rotor flux _ is changed by perturbing the current iris. Then Pi, is measured
to see if the input power has changed. In the event that it has, a set of fuzzy rules
computes a new value of/kids, based on AP_, and the previous value of Aids, referred to
as L/kids. Then Pi, is measured again and the process is repeated. A table showing the
preliminary rules relating/kids to Aein and L_ids is shown in the following table.
RULES
1. If LDids is N and APi
2. If LDids is N and/kPi
3. If LDids is N and/kPi
4. If LDids is N and APi
5. If LDids is N and/kPi
6. If LDids is N and/kPi
7. If LDids is N and APi
8. If LDids is P and/kPi
9. If LDids is P and APi
10. If LDids is P and/kPi
1 1. If LDids is P and/kPi
12. If LDids is P and/kPi
13. If LDids is P and/kPi
14. If LDids is P and APi
is PB, then LDids is PB.
is PM, then LDids is PM.
is PS, then LDids is PS.
is ZE, then LDids is ZE.
is NS, then LDids is NS.
is NM, then LDids is NM.
is NB, then LDids is NB.
is PB, then LDids is NB.
is PM, then LDids is NM.
is PS, then LDids is NS.
is ZE, then LDids is ZE.
is NS, then LDids is PS.
is NM, then LDids is PM.
is NB, then LDids is PB.
Table 3. Fuzzy Rules for Efficiency Optimization with Indirect Vector Control.
A total of 14 IF-THEN rules are defined for the energy optimizer utilizing indirect vector
control.
Figure 10 illustrates the preliminary membership functions derived from observation of
results obtained from computer simulations.
89
P8
N
J
! /\ ,, '
-L_ 0 L_
-ij -I_ -I]
P
!
| ,_
Lz h_
Z "P5 ?1,A 98
0 h .ie I_
>A(&s
Figure 10. Preliminary membership functions for fuzzy efficiency controller: (a)
change in input power; (b) last change in current ids; (C) new change
in current ids.
9O
The membership functions were developed using variables normalized in the interval [-
1,1], hence the magnitudes of the endpoint variables (+/- PI, +/- L1, +/" I1)acr°ss the
domain of the membership functions is 1. The values of the interior limits on the
membership functions have not at present been arrived at.
The max-min method of inference is being applied to obtain truth values of any particular
rule, hence the design of the fuzzy membership functions for LAids provides a degree of
limitation for the truth value of a rule when LAids iS "negative small" or "positive small",
even though there is no membership function specifically for those fuzzy values. This
avoids using multiple membership functions in a place where fewer will perform the same
job, and thereby reduces the size of the fuzzy rulebase. The overlap between the
positive and negative membership functions assure that division by 0 will not occur in the
height defuzzification method used by UT, since even if LAids is 0, it will have a non-zero
degree of belief in either the 'P' or 'N' region.
Reducing the flux to achieve minimum input power has an effect similar to that of
reducing voltage in the previous controller. The shaft speed will drop. We have found
that this can be compensated for by a change in the torque component of current iqs.
This is a function of the change in ids. After a change in the value of iqs is made (which
is not a fuzzy operation) fuzzy efficiency optimization is not reapplied until the machine
has returned to steady-state condition, which is determined by comparing the sum of the
absolute values of the last three rotor speed errors (z_e_r to a tolerance value of 1)
rad/sec. At that time a new value of Aids is computed by the fuzzy efficiency optimizer
and the cycle repeats. Even after optimum efficiency has been reached, this steady-state
condition is checked for periodically in order to determine that no process disturbance has
taken place which would require the controller to act in order to produce the required
torque output or required speed.
All rules and membership functions are being tuned using computer simulation and by
testing the controller in a laboratory setting. The following diagram shows the overall
scheme of the laboratory setup.
91
* Volta_
* C_m_nt
* P_+et
1 +p_-yLo#c
[ "Da,.Acq.+si_on
* Motor Simulaao_
r_abac_
•Voltage/_'rem
° Frequency
AdjustableSpeed Drive
G
Developed T_que
Momf Load Signal
1
Tmkommtm_
Line Po_T230 VAQ
Dynamometer
Controller
Induction -
Motor Shaft Speed
De Pow_.r
Dynamometer/
DC Brake
Figure 11. Motor Laboratory System
The fuzzy rules are executed in a 486/33 MHz from code compiled with other C routines,
which also monitor system information via a data acquisition board, and communicate
with the ASD to alter the ASD voltage and frequency output. The same code also directs
an analog output on the data acquisition board to vary the strength of the field in the DC
brake via the dynamometer controller, thus simulating various degrees of load on the
motor.
Summary
Computer simulations have shown that a fuzzy controller which optimizes the use of
energy by a motor/ASD combination can be developed. To be truly effective, the
controller should alter both the stator voltage and stator frequency while maintaining the
output power required of the motor/ASD system for the drive at hand. Energy efficiency
optimization can be applied not only to drives which produce sinusoidal PWM output, but
to indirect-vector controlled drives as well.
92


Fuzzy efficiency optimization of AC induction motors

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