Finch. Tuning of PI Speed Controller in DTC of Induction Motor Based on Genetic Algorithms and Fuzzy Logic Schemes

6 Pages·0.393 MB·English

by  Shady M. Gadoue, D. Giaouris, J.W.

Tuning of PI Speed Controller in DTC of
Induction Motor Based on Genetic Algorithms
and Fuzzy Logic Schemes

Shady M. Gadoue, D. Giaouris and J. W. Finch
University of Newcastle upon Tyne
Power Electronics, Drives and Machines Group,
School of Electrical, Electronic and Computer Engineering
Merz Court
NE1 7RU Newcastle upon Tyne, UK
{Shady.Gadoue, Damian.Giaouris, J.W.Finch}@ncl.ac.uk

Abstract- PID controllers are very common
Flux hysteresis
in industrial systems applications. The tuning of Flux controller
command
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The first method applies off-line genetic |λ s |
algorithm (GA) strategies and the other one
makes use of an online Fuzzy Logic (FL) tuning Fig.1 Block diagram of DTC with speed control loop
scheme. DTC is then tested with the two schemes
for two cases, with normal operating conditions and they can offer a satisfactory performance
and with a sudden change in load torque applied over a wide range of operation.
to the motor. Results obtained show that the
The main problem of that simple
fuzzy logic on-line tuning technique can provide
controller is the correct choice of the PID gains
better speed control performance when system
and the fact that by using fixed gains, the
parameter variations occur. On the other hand
controller may not provide the required control
for nominal operation the genetic algorithms
scheme is preferred. performance, when there are variations in the
plant parameters and operating conditions.
Therefore, a tuning process must be performed
Index Terms – Speed control, induction
motor, direct torque control, Fuzzy logic, Genetic to insure that the controller can deal with the
algorithms. variations in the plant.
To tune the PI controller (usually in drives
applications the derivative part of the
controller is not used) a lot of strategies have
I. INTRODUCTION been proposed. The most famous, which is
frequently used in industrial applications, is
Recently there has been a fast growth in
the Ziegler-Nichols method which does not
industrial applications of the DTC technique.
require a system model and control parameters
This is due to its quick torque response,
are designed from the plant step response.
simplicity and robustness against rotor
Tuning using this method is characterised by a
parameters variation. Compared with a vector
good disturbance rejection but on the other
control scheme, DTC provides similar
hand, the step response has a large percentage
dynamic performance with simpler controller
overshoot in addition to a high control signal
architecture [6]. The basic block diagram
that is required for the adequate performance
representation of the direct torque control of
of the system. Another technique uses
three-phase induction motors with a speed
frequency response methods to design and tune
control loop is shown in Fig.1.
PI controller gains based on specified phase
The most common choice for the speed
and gain margins as well as crossover
controller shown in Fig. 1 is the so called PID
frequency. Furthermore, root locus and pole
compensator since they have a simple structure
assignment design techniques are also
proposed in addition to transient response three switching functions s , s , s and the DC
1 2 3
specifications. All these methods are link voltage (V)as:

considered as model based strategies and then
u (s,s ,s )=u + ju
the efficiency of the tuning law depends on the s 1 2 3 sd sq
accuracy of the proposed model as well as the
2 ⎡ ⎛ j2π⎞ ⎛ j4π⎞⎤ (1)
assumed conditions with respect to actual = V⎢s +s exp⎜ ⎟+s exp⎜ ⎟⎥
operating conditions. 3 ⎣ 1 2 ⎝ 3 ⎠ 3 ⎝ 3 ⎠⎦
Artificial Intelligence (AI) techniques Where u and u are the d-axis and q-axis
sd sq
such as neural networks, fuzzy logic and stator voltage components.
genetic algorithms are gaining increased
In direct torque control schemes the
interest nowadays.
magnitude of the stator flux linkage vector is
A lot of techniques have been proposed to
controlled which can further be decomposed to
tune the gains of PI controller based on AI
its orthogonal components expressed at a
techniques: Self tuning FL and neural network
stationary reference frame as:
techniques are some of these methods
proposed for the online adaptive tuning of PI
ψ =∫(u −Ri )dt (2)
controller. In such application, the controller sd sd ssd
gains are tuned with the variation of system ψ =∫(u −Ri )dt (3)
conditions. Moreover, GA is proposed for sq sq ssq
both online and offline tuning procedure [4]
where ψ and ψ are the d-axis and q-axis
sd sq
even though this may require high processing
stator flux linkage components.
power. The advantage of tuning with GA is the
ability of choosing controller gains which The stator flux position (θs) is determined by
optimize drive performance based on multi dividing the d-q plane into six 60˚ regions and
objective criterion without tripping in a local three sign detectors are used to determine the
minima solution. Furthermore, combinations sector over which that vector passes.
of AI techniques are also introduced such as
The basic DTC strategy is that the status
Neuro-Fuzzy and Genetic-Fuzzy techniques
of the errors of stator flux magnitude | ψ | and
s
[8]. The advantage of these techniques is that
electromechanical torque (T ) can be detected
em
they are model free strategies because they use
and digitalized by two- and three-level
the human experience for the generation of the
hysteresis comparators. The optimum
tuning law.
switching table is then used to calculate the
This paper provides a comparison between
status of three switches s , s , s that will
1 2 3
two strategies used for tuning the PI speed
determine the location of the voltage space
controller in the direct torque controlled
vector u which depends on the stator flux
s
induction motor. The first one is based on
angle (θ).
s
Genetic Algorithms (GA), while the second
one is based on Fuzzy Logic (FL). In the first If the drive contains a speed control loop,
method, GA searches for the optimal gains of then the reference speed input is compared
the PI speed controller based on a fitness with the actual motor speed and the speed error
function and the search procedure is such that is fed to a speed controller. The output of the
a performance index is minimized. In the other speed controller is the reference
method, FL is used for tuning the PI controller electromagnetic toque.
online based on a group of IF-THEN control
In an induction motor, the mechanical
rules which mimic the human logic and are
balance equation can be written as:
generally derived from experts’ knowledge.
J • B (4)
II. DTC STRATEGY T −T = ω+ ω
em L P r P r
In principle, DTC is a direct hysteresis
And the electromagnetic torque is given by:
stator flux and electromagnetic torque control
scheme, which triggers one of the eight T = 3 P ψ i sinα (5)
available discrete voltage vectors generated by em 2 s s
a Voltage Source Inverter (VSI) to keep the
Where T is the load torque, J is the combined
stator flux and torque within the limits of two L
motor and load inertia, B is the friction
predefined bands. The correct application of
coefficient, P is the number of motor pole
this principle allows a decoupled control of
pairs, ω is the rotor electrical speed, ψ is the
flux and torque [6]. r s
stator flux linkage space vector, i is the stator
The primary space voltage vector of the s
current space vector both expressed in the
PWM inverter u can be expressed in terms of
s
stationary reference frame and α is the angle applications [4], multi population techniques
between the stator flux linkage and stator and others.
current space vector. In the case of using a GA method to tune
the PI gains in the previously mentioned speed
III. PI CONTROLLER TUNING, USING GA
control loop, the fitness function used to
GA is a stochastic global search evaluate the individuals of each generation can
optimisation technique based on the be chosen to be the integral time of absolute
mechanisms of natural selection. Recently, error (ITAE):
GA has been recognised as an effective
technique to solve optimisation problems and ITAE=∫e(t)tdt (6)
compared with other optimisation techniques;
GA is superior in avoiding local minima which During the search process, the GA looks
is a common aspect in nonlinear systems. for the optimal setting of the PI speed
GA starts with an initial population controller gains which minimizes the fitness
containing a number of chromosomes where function (ITAE). This function is considered
each one represents a solution of the problem as the evolution criteria for the GA. The
which performance is evaluated by a fitness choice of this fitness function has the
function. Generally, GA consists of three main advantage of avoiding cancellation of positive
stages: Selection, Crossover and Mutation. and negative errors. Each chromosome
The application of these three basic operations represents a solution of the problem and hence
allows the creation of new individuals which it consists of two genes: the first one is the Kp
may be better than their parents. This value and the other one is the Ki value:
algorithm is repeated for many generations and Chromosome vector = [Kp Ki]. It must be
finally stops when reaching individuals that are noted here that the range of each gain must be
the optimum solution to the problem [3, 7]. specified. The genetic algorithm parameters
The GA architecture is shown in Fig.2. chosen for the tuning purpose are shown in
Table I. Here the GA starts by generating an
Start
initial population containing 8 chromosomes
then the fitness value of each chromosome in
Create Initial
the initial population is calculated.
Population

TABLE I
Gen=er 0at ion GENETIC ALGORITHM PARAMETERS
Number of generations 20
Evaluate Fitness No of chromosome in
Value each generation 8
For each
No of variables in
Chromosome 2
each chromosome
Chromosome length 40 bit
Perform
Selection, Selection method Stochastic
Crossover and Universal Selection (SUS)
Mutation
Process Crossover method Double point
Crossover probability 0.7
Mutation rate 0.05
Gen > max
Gen = Gen+1 No generation
Or min The three main parts of GA: Selection,
performance
index reached Crossover and Mutation take place and then a
new generation is produced. This procedure
continues for some generations and then a
Yes
convergence to the optimal solution
Stop represented by a given chromosome is reached.
Fig.2 Genetic Algorithm Architecture
A lot of techniques have been proposed to IV. FUZZY SELF TUNING PI CONTROLLER
increase the convergence speed of GA such as
Fuzzy Logic Control (FLC) has been
Parallel Genetic Algorithm based on the Allied
found to be excellent in dealing with systems
Strategy (PGAAS) which is suitable for online
that are imprecise, non-linear, or time-varying.
FLC is relatively easy to implement, since it this case, the weights represent the output
does not need any mathematical model of the scaling factors of FLC. Mokrani et al. [5]
controlled system. This is achieved by proposed a fuzzy adaptation scheme for the
converting the linguistic control strategy of purpose of tuning the scaling factors of FLC.
human experience and knowledge into an Each input of the FLC has 5 triangular
automatic control strategy. membership functions with equal width and
FLC has become very popular in the field overlap. The first output (∆Kp) has 3
of industrial control applications. triangular membership functions, while as the
On-line tuning of controllers becomes of second output (∆Ki) has 5 membership
interest since it is very difficult for off-line functions. The inference rules base has 25
tuning algorithms to deal with the continuous rules. Membership functions can be tuned by
variations in the induction motor parameters trial error techniques or using any other tuning
and the nonlinearities present in inverter, strategies such as GA. The Fuzzy inference
motor and/or controller. The stator and rotor rules used for on-line tuning of PI controller
resistances of induction motor may change gains are shown in table II and table III [1].
with the temperature variation up to 50%, The flow chart of the Fuzzy self tuning PI
motor magnetizing inductance varies with the speed controller is shown in Fig.4.
magnetic operating point and becomes
nonlinear near the saturation level. TABLE II
Furthermore, the load torque and inertia FUZZY INFERENCE RULES FOR UPDATING THE
may change due to mechanical disturbances. PROPORTIONAL GAIN (∆Kp)
e NB NS ZE PS PB
Nonlinearity also arises in the drive system ∆eω
ω
due to voltage and current limits of the power NB PB PB PB
converter and the load torque nature. NS PB PS ZE
When FL is used for the on-line tuning of ZE PB ZE PB
the PI speed controller of induction motor PS ZE PS PB
DTC drive, it receives the scaled values of the PB PB PB PB
speed error and the change in speed error. Its
output is the updating in PI controller gains TABLE III
(∆Kp and ∆Ki) based on a set of rules to FUZZY INFERENCE RULES FOR UPDATING THE INTEGRAL
maintain excellent control performance even in GAIN (∆KI)
e NB NS ZE PS PB
the presence of parameter variation and drive ω
∆e
nonlinearity [1]. ω
NB ZE NS NB NS ZE
The most important parameters of Fuzzy
NS PS ZE NS ZE PS
Logic are the scaling factors. The input
ZE PB PS ZE PS PB
scaling factors affect the FLC sensitivity while
PS PS ZE NS ZE PS
the output scaling factors affect the system
PB ZE NS NB NS ZE
stability [7]. The block diagram of the control
system is shown in Fig.3. Start

k= 0
Ψ
s
Receive
ωr* eωr Te* e ω(k) and ∆eω(k)
Calculate
∆Kp(k )and
∆KI(k)
⎡∆K ⎤ From FLC
P
⎢ ⎥
⎣∆KI⎦
∆e Set
ωr ∆Kp(k ) No eω(k) < 2%
and ∆KI(k)
from FLC
Fig.3 Fuzzy self tuning PI speed controller
Yes

Set
A lot of researches have proposed tuning ∆Kp(k ) = 0
And ∆KI(k) = 0
methods for the FL scaling factors: Han et al.
[2] proposed a neural network with variable
learning rate. The artificial neural network is
used to represent the output part of the FLC, k = k +1
and then a back propagation algorithm is used
to adjust the weights of the neural network. In Fig.4 Flow chart of Fuzzy self tuning PI speed controller
V. SIMULATION RESULTS AND DISCUSSION again to track the reference value (50 rad/s)
with a total ITAE of 0.1641. The ITAE
To compare the two tuning strategies,
obtained by each tuning technique is shown in
DTC of a 10 hp squirrel cage induction motor
Fig.7. The results are summarised in table V.
with speed control loop shown in Fig.1 is

simulated using Matlab-Simulink software. 51

GA is first applied to the PI speed controller
tilaoundnaddduiint cigttooi.on rqn u temoD. ou tAtrohir ne sg ips e realtodhtea edrd e eftdeus rtneawintnoictgrhe o2fpfl5r u%o5xc0 e osrlfasi n,d rk/asatt ehgidnee Rotor speed (r/sec) 505.05
49.5
magnitude is the input commands to the drive.
The speed response of the motor is
observed and the ITAE is recorded for each 409.12 0.125 0.13 0.135Tim0e . 1(s4ec)0.145 0.15 0.155 0.16
(a)
chromosome in each generation. After 20 70

generations, the optimal solution proposed by 60
GwaniAdth K Wuthni hed=e e cn3rh .r9tthoh8emi.s do lrsoiovamed eisn ycgso tnecsmoins tdiisin tgisoi monf u iKlsa ptae c=dh 1uie5svi1ne.6gd Rotor speed (r/sec) 23450000
the proposed gains, which are set to be
10
constant during the simulation period, with the
00 0.05 0.1 0.15
motor operating with a load torque of 25 % for Time (sec)
(b)
2 s, the ITAE is equal to 0.1269. Fig.5 Transient response (a) GA tuning (b) FL tuning
The Fuzzy self-tuning PI speed controller,
with the parameters listed in Table IV, is 100 % Load
50.4 Torque
simulated with the same conditions and the change
Iw“ToapAst Eiem xupomebct”at eindge adsiin nsic se f o0trh. 1et3 hG1e9A .s psTechchiiesfmi cde icsfoconruednpidtai nothcnyes Rotor speed (r/sec) 45905..082 applied
while the FLC used the “imperfect” human

49.6
knowledge and experience.
49.4 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
TABLE IV Tim(ea )(s ec)
FUZZY LOGIC PARAMETERS 51

Input scaling factors K,K 1.1, 0.1
1 2 1 00 % Load
OuDtpeufut zszcKiaflipicn aigtni ifotanica tmlo resth Ko3d, K4 Centr0e.2 1o,0 f1 g.1ra vity Rotor speed (r/sec) 505.05 cTahoparpqnliugeeed
49.5
Ki initial 12

49
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
To investigate the performance of the Time (sec)
(b)
tuning strategies under system parameter Fig.6 Speed response at time of application of 100% load
variation, the induction motor is subjected to a torque increase at t=1s (a) GA tuning (b) FL tuning
100 % load torque change (from 25% to 50%

of the motor rated torque) at t = 1 s. 0.25
GA
As shown in Figs.5 and 6, the speed 0.2 1i0n0c%re aLsoea adp tpolriqe ude
roevseproshnoseo t uosf in0g.6 %GA w htiulen inthga t hfraosm aF Ls paeuetdo AE (rad) 0.15
tuning has no overshoot and the drive system IT 0.1 Fuzzy
behaves like a critical damped system. At t=1s Logic
0.05
when the load is increased, the speed response
using fixed gains (obtained by GA) drops to 00 0.5 1 1.5 2
Time (sec)
49.94 rad/s with a speed regulation of 0.12 %
Fig.7 ITAE for GA and FL tuning
with a total ITAE (after 2 s) of 0.2132, while
as that obtained by FL self tuning drops
rapidly to 49.6 rad/s before the speed builds up
TABLE V FL auto tuning since it contains the optimal
SUMMARY OF RESULTS controller gains.
GA FL When a change in system parameters takes
Kp = 151.6, Ki = 3.98 Variable Gains place, the results show that self tuning FL is
ITAE 0.1207 0.125 superior in terms of speed reference tracking
(t=0to t=1s) than fixed gains controller obtained from GA
tuning. This is due to the adaptive behaviour
(t=1ITtoA tE= 2s) 0.0925 0.039 of FL when used with an online tuning
strategy.
Total ITAE 0.2132 0.1641 REFERENCES
[1] L. Mokrani and R. Abdessemed, “A Fuzzy self-tuning
Transient 0.6 % speed
response overshoot No overshoot PI controller for speed control of induction motor
drive”, Proceedings of 2003 IEEE Conference on
Initial drop Control Applications, IEEE Part vol.2, 2003, pp.785-
Response to
Speed drop with 0.12 then quickly 90 vol.2. ‘Istanbul, Turkey’.
load torque % speed regulation regain the
application speed [2] Woo-Yong Han, Sang-Min Kim, Sung-Joong Kim and
Chang-Goo Lee, “Sensorless vector control of

induction motor using improved self-tuning Fuzzy
The PI controller gain variations for the PID controller”, SICE 2003 Annual Conference. Soc.
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pp.3112-17 Vol.3. Tokyo, Japan.
Fig.8 (a) and Fig.8 (b). The gains increase
[3] The MATLAB Genetic Algorithm Toolbox v1.2
gradually until the command speed is reached.
User's Guide, Department of Automatic Control and
After that, the gains are kept constant. When
Systems Engineering of The University of Sheffield,
the load torque increase occurs, they rise again UK.
to compensate for the speed decrease and to http://www.shef.ac.uk/acse/research/ecrg/gat.html
return the speed back to the command value. [4] Lin Feng, Zheng Hongtao and Yang Qiwen,
That is, to ensure complete speed tracking. “Sensorless vector control of induction motors based
on online GA tuning PI controllers”, Fifth
40 International Conference on Power Electronics and
35 100 % Load Drive Systems. IEEE Vol.1, 2003, pp.222-5 Vol.1.
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Kp ( 25 scaling factors on the performance of a Fuzzy logic
n
Proportional gai 112050 [6] AciEnon.dn gLutirc.no teMiloelernori h nagbmm,a Vsaoedtodoel ri.n5 o,5n ,Rd Nr.ai voHne. a ” im7,n -dd8iy,Jr 2eoac0unt0rd n4 vaS, elhp captdo.1oyrf8 M8c-o1E.n 9Glte4raco.d tlr oicufoaerl,
5
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n Ki (N. 6 cTahoparpqnliugeeed FTueczhzyn-iNqueeusr”a,l Oxfaonrdd UnGiveenrestiitcy PreAslsg, o1r9it9h9m. Based
Integral gai 4 [8] JPRiIenDsgp -oCnChsuoennsg”tr , SolIhlEeeEnr ,E “ fFoTurrz aznyPs aNlacentiutosrn asl wNoientth w FourUzkzsny df oeSrrd yTasumtenpminesdg,
2
Vol.9, No.2, April 2001.

0
0 0.5 1 1.5 2
Time (sec)
(b)
Fig.8 Fuzzy Self tuning Performance (a) Proportional gain
(b) Integral gain

VI. CONCLUSION
A comparison between two artificial
intelligence based techniques used for the
tuning of the PI speed controller in DTC of
induction motor has been presented. Under
normal operating conditions, an off-line GA
tuning scheme shows better performance than