Application of Fuzzy Control Technique to Thyristor DC Drive
Krzysztof Zawirski
Institute of Industrial Electrical Engineering
Poznañ University of Technology
Poznañ, Poland
Konrad Urbanski
Institute of Industrial Electrical Engineering
Poznan University of Technology
Poznan, Poland
Abstract. In the paper a study of fuzzy logic controller (FLC)
application for solution of some control problems of thyristor
DC drive is presented. The control problems, which are taken
into account during FLC synthesis, consist in variable
structure of the current control plant and variation of moment
of inertia in the speed control loop. Comparison between
fuzzy control system and traditional digital cascade control,
carried out by simulation method, proved that FLC as a
robust control gives better performance in the range where
non-linearity and parameter variation is observed.
continuous and discontinuous converter current, and
variation of moment of inertia in speed control loop.
I. INTRODUCTION
Fuzzy logic controllers (FLC) based on fuzzy logic
principle and expert knowledge, converted into automatic
control systems, still increase their industrial application. In
recent years this new technique has been successfully
implemented in control system of power electronic
converters and converter-fed drives [1,2,3]. Most of these
systems are strongly non-linear with variable parameters
and structure, what makes them a difficult plant for
traditional control technique. Application of fuzzy logic
controllers in these conditions provides an efficient tool to
design robust control systems [4,5].
In the paper a study of FLC application for solution of
some control problems of thyristor DC drive is presented.
Improvement of DC drives performance is still an
important task because of their application in many
industrial branches. Most of the control problems of these
drives were solved on the base of traditional control
technique. Interesting research tasks is to investigate how
the new fuzzy technique can deal with some difficult
control problems of DC drives, consisting in non-linear
characteristics and parameter variation. Implementation of
FLC system to a solution of problems solved yet in
traditional way, should provide to better control
performance or similar performance but achieved on the
more simple way of realisation [4,5,6].
In the presented work a comparison of two control
systems for DC drive was provided. One investigated
system is a digital control system with connected in
cascade controllers of current and speed. Second one is a
FLC system designed with similar general structure,
decomposed into speed and current controllers connected
in cascade, but realised in fuzzy technique. This
decomposition gives a chance to apply in synthesis of FLC
some expert knowledge, collected during analysis and
synthesis of traditional control system. General structure of
this FLC system is presented in fig.1.
The control problems, which should be taken into
account during FLC synthesis, consist in variable structure
of the plant in current control loop, being a result of
Fig.1 Structure of FLC system for DC drive
II. CURRENT CONTROL LOOP
A. Control problems in current loop
It is well known that as a result of two possible mode of
converter operation, with continuous and discontinuous
current, the current control plant has variable structure.
This is a reason that in many application adaptive current
controller - with variable structure PI/I is applied [7].
Proposed in some papers more sophisticated control
algorithms require time consuming complex calculations
and are more sensitive on error of system parameters
identification [7,8].
In the paper such a structure of current FLC was
assumed, which can be comparative with traditional
adaptive PI/I current controller. Among many known
solutions of digital current controller that one was chosen,
which concept bases on calculation of current average
value only once per converter period [6,7]. This simple
solution has structural limit of its dynamic behaviour but it
is not important for comparative character of provided
analysis. Each structure of adaptive current controller is
optimised individually at its range of operation: PI in the
range of continuous current and I in the range of
discontinuous current mode [7]. Exemplary simulation
results for investigated controllers during separate
operation of each structure (PI/I) are shown in fig. 2.
Investigations were provided with exemplary system
consisting of DC motor 15kW/220V/8A/1450rpm supplied
from proper 3-phase thyristor rectifier. The problem of
adaptive control consists in proper changing over PI and I
structures during the changes of converter mode. The
simple changing over, at the point of boundary between
both ranges of converter operation, provides sometimes to
unexpected oscillations or an overshoot in the step
response.
adaptive current controller concept of PI/I structure
changes.
First of proposed structures (FLC-I) is the most complex
and represents three-input fuzzy controller. In normal
realisation these controllers are two (PI) and one (I)
dimensional fuzzy processes but in proposed control
system the third input signal is applied for proper
realisation of adaptation mechanism [9]. As third signal the
armature current is introduced. Its value well determines a
boundary between rectifier operation modes. Obtained the
three-inputs FLC structure is presented in fig.4.
Fig.2. Step responses of digital current controller:
A) I controller in discontinuous current range,
B) PI controller in continuous current range.
Fig.4. Structure of 3-inputs fuzzy current controller (FLC-I)
This is a result of ambiguous control characteristic of
converter, which requires different input signal (control
voltage) in discontinuous and continuous mode of
operation for the same value of output voltage. Fast
controller integration, during discontinuous current mode,
provides to much higher value of the control voltage than it
is necessary in the continuous range. In result some
overshoot takes place, like it is shown in fig.3. This
undesired effect can be avoided if correction of the
controller settings is provided, but unfortunately it must
reduce dynamics of control operation.
The provided adaptation mechanism acts in this way that
in area near boundary between two modes of converter
operation an mixed control effect of both PI and I
controller, as a result of proposed fuzzy rules, is achieved.
This proposed commutation mechanism between both
controller structures is a new farther development of fuzzy
switch concept described in [7] and could be named "soft
commutation".
The linguistic fuzzy control rules for both controllers are
presented in table I and II [9].
TABLE I
FUZZY CONTROL RULES FOR PI CURRENT CONTROLLER
Change of error ( DE )
NB NM NS NZ PZ PS
E NB NM NM NM NM NM NS
r NM NM NS NS NS NS NZ
r
NS NM NS NS NZ NZ PZ
o
NZ NM NS NZ NZ NZ PZ
r
PZ NS NS NZ PZ PZ PZ
PS NS NZ NZ PZ PZ PS
(E) PM NZ PZ PZ PS PS PS
PB PZ PS PS PM PM PM
Fig.3.Step response of digital current controller with simple switching
over adaptive mechanism; transient process in both ranges of converter
operation
B. Structures of current FLC
Introduction of the FLC gives a chance to obtain robust
adaptive current controller due to implementation of fuzzy
adaptive mechanism. For this purpose three different
versions of FLC structure were analysed. General idea of
all these versions is similar and bases on well known
PM
NS
NZ
PZ
PS
PS
PS
PS
PM
PB
NZ
PZ
PS
PS
PM
PM
PM
PM
TABLE II
FUZZY CONTROL RULES FOR I CURRENT CONTROLLER
Change of error ( DE )
NB NM NS NZ PZ PS PM
E NB NB NB NB NB NB NB NB
r NM NB NB NB NB NB NB NB
r
NS NB NB NB NB NB NB NB
o
NZ NM NM NM NM NM NM NM
r
PZ PM PM PM PM PM PM PM
PS PB PB PB PB PB PB PB
(E) PM PB PB PB PB PB PB PB
PB PB PB PB PB PB PB PB
PB
NB
NB
NB
NM
PM
PB
PB
PB
The adaptation mechanism operates according the
membership function of third (current) signal, presented in
fig.5. There are only three linguistic values of current
signal distinguished. Values PB an NB mean that the
current value is enough high to be in continuous current
mode and linguistic value ZE (zero) means that the
operation point is in the range of discontinuous current
mode.
digital PI controller. The structure FLC-III is shown in
fig.7.
TABLE III
FUZZY CONTROL RULES FOR ADAPTATION MECHANISM
kd
ke
Current ( Id )
E
r
r
o
r
(e)
NB
ZE
PB
NB
PB
PB
PB
ZE
ZE
ZE
ZE
Current ( Id )
PB
PB
PB
PB
E
r
r
o
r
(e)
NB
ZE
PB
NB
ZE
PS
ZE
ZE
PS
PB
PS
PB
ZE
PS
ZE
The controller is equipped with fuzzy adaptation
mechanism operating in the same way like in FLC-II. The
same fuzzy rules like presented in table III are used but
Fig.5. Diagram of membership functions for current signal
The structure FLC-I, the most general and interesting
from theoretical point of view, creates some difficulties in
practical realisation. This was a reason that for analysis two
other versions of structure with more simple realisation,
were proposed. Structure FLC-II contains a two-inputs
FLC equipped with fuzzy adaptation mechanism. This
structure is shown in fig.6.
Fig.7. Structure of current controller with adaptive mechanism (FLC-III)
instead of normalisation factor coefficients of proportional
kp and integral ki controller operation are determined.
C. Analysis of adaptive current controller operation
Fig.6. Structure of current FLC with adaptive mechanism (FLC-II)
The controller has one fixed table of fuzzy control rules
but variable normalisation factors due to the adaptation
mechanism. Changes of the factors provides to realisation
of two different control characteristics PI/I. The adaptation
mechanism bases on current signal and on the
"soft commutation"
process
of
switching
over
characteristics, similar like in structure FLC-I. Additional
adaptation mechanism is used for variation of the error
normalised factor. This mechanism requires as an input
signal a control error. Tables III show fuzzy rules of
adaptation mechanism for normalisation factors of control
error ke and change of error kd. On the base of the rules
using simplified reasoning method values of factors ke and
kd are calculated in each step of controller operation. Table
of fuzzy rules for FLC-II is identical with table I.
Membership functions of current signal are similar to
presented in fig. 5. The structure FLC-III is similar to the
structure FLC-II but contains instead of FLC a traditional
Investigations carried out by simulation method showed
that structure FLC-I is very difficult for proper adjusting by
trial error method. Lack of separated adaptation mechanism
makes the adjusting process more complex so in result the
performance of the FLC-I is not as good as for other two
described structures. The properties of the structures FLCII and FLC-III, which are based on the same adaptation
mechanism are comparable. Exemplary simulation result
for FLC-III, presented in fig.8, was obtained in the same
conditions like transients in fig.3. The presented wave
forms proved that effect of robust control was achieved. In
the range where each controller PI or I operates
individually FLC gave the same control properties like
traditional control system. Operation of FLC-II provides to
similar wave forms like FLC-III.
Fuzzy evaluation of boundary between continuous and
discontinuous operation mode (membership functions in
fig.5) gives a chance to avoid problem with incorrect
estimation of converter parameters. In case of traditional
controller with simple (binary) switch over of the
structures, accuracy of boundary evaluation plays
important role.
Fig.8. Step response of the current controller with fuzzy adaptation
mechanism (FLC-III). Transient process in both ranges of converter
operation
Fig.9.A illustrates transient process in the case when
controller switching over with wrong evaluation of
boundary takes place. Introduction of fuzzy switching
mechanism to this controller (FLC-III) provides to better
(without oscillations) transient process (fig.9.B).
exist in the case of other types of servo drives, DC or AC
[2,5,10].
In the paper two fuzzy speed controllers were taken
under consideration:
• a PI fuzzy controller (FPI),
• a sliding-mode fuzzy controller (FSM).
These two versions were compared with traditional digital
PI controller. In realisation of all investigated speed
controllers the same sampling time, equal one period of
converter operation, and the same digital current controller,
operating with identical sampling time were assumed .
Fuzzy control rules for FPI are presented in table IV.
Membership functions of input and output signals were
modified during tests to achieve controller robustness.
Final version of membership functions is shown in fig. 10.
Operation of traditional PI and FPI controllers was
compared on the base of simulated transient process with
different value of moment of inertia. Both controllers were
tuned in such a way that for the same big value of moment
of inertia, equal triple value of motor moment of inertia,
similar transients of control process were obtained.
TABLE IV
FUZZY CONTROL RULES FOR PI SPEED CONTROLLER (FPI)
NB
E NB NB
r NM NB
r
NS NB
o
NZ NB
r
PZ NB
PS NM
(E) PM NS
PB PZ
Change of error ( DE )
NM NS NZ PZ PS PM
NB NB NB NB NM NS
NB NM NM NM NS NZ
NM NS NS NS NZ PS
NM NS NZ PZ PS PM
NM NS NZ PZ PS PM
NS PZ PS PS PS PM
PZ PS PM PM PM PB
PS PM PB PB PB PB
PB
NZ
PS
PM
PB
PB
PB
PB
PB
Fig.9. Step response of adaptive current controller with incorrect
evaluation of boundary between continuous and discontinuous mode.
Controller with :
A) - traditional adaptation, B) - fuzzy adaptation mechanism.
Simulation analysis proved that general properties of
fuzzy controllers FLC-II and FLC-III are equivalent. The
FLC-III is a little more sensitive on non linearity of
converter control characteristics but this problem can be
avoided by characteristic linearisation using an cos-1
functional block. Investigation results provide to general
conclusion that the most simple structure FLC-III should be
recommended for future application.
III. SPEED CONTROLLER
The FLC is implemented in speed control loop with the
purpose to obtain a robust speed controller in presence of
moment of inertia variation. The same control problems
Fig.10 Diagram of membership functions for FPI speed controller
The exemplary results are presented in fig. 11.A and
11.C. Calculated in these conditions an integral index of
speed control error ( Integral of Absolute Error - IAE) has
similar value for both controllers , equal 35.5. Fig.11.B and
11.D present transient process for reduced three times
moment of inertia (equal only motor moment of inertia). In
this case FPI controller proves to be more robust than
traditional PI. These conclusion is confirmed by values of
IAE calculated during control process. For FPI its value is
equal 26 while for PI it is equal 32.
FUZZY CONTROL RULES FOR SLIDING-MODE SPEED
CONTROLLER (FSM)
Change of error ( DE )
NB NM NS NZ PZ PS PM
E NB NB NB NB NB NB NM NS
r NM NB NB NB NB NM NS ZE
r
NS NB NB NB NM NS ZE PS
o
NZ NB NB NM NS ZE PS PM
r
PZ NB NM NS ZE PS PM PB
PS NM NS ZE PS PM PB PB
(E) PM NS ZE PS PM PB PB PB
PB ZE PS PM PB PB PB PB
PB
ZE
PS
PM
PB
PB
PB
PB
PB
Proposed membership functions for FSM controller are
shown in fig. 12. The effect of FSM controller operation
can be observed in fig. 13, which presents wave forms of
the control process in the same conditions like in fig.11.
Comparision of both figures shows that FSM controller
provides to much better performance. Calculated values of
IAE in this case are equal 35 for big and 21 for small value
of inertia moment.
Fig.11. Step response of speed controllers : A,B) digital PI controllers,
C,D) FPI controller; moment of inertia : A,C) J=3JM, B,D) J=JM
More interesting result was obtained by introducing fuzzy
sliding mode controller - FSM. The simple FSM structure,
easy for realisation, was proposed. The controller has only
partial compensation effect and can be described in the
form:
.
Iref = C ⋅ Id + U fuzzy(e,e)
(1)
where Iref is the output signal of FSM speed controller
(reference signal for current controller), C Id is a
component of partial compensation and Ufuzzy(e,e) is the
output signal of fuzzy term, which realises sliding mode
control with boundary layer [1].
Value of compensation coefficient C was assumed equal
0.85.
Final version of fuzzy rules is given in table V.
TABLE V
Fig.12 Diagram of membership functions for sliding mode fuzzy speed
controller (FSM)
IV. CONCLUSIONS
Some example of fuzzy control technique application to
the control of adjustable speed thyristor DC drives was
elaborated. Fuzzy technique provided a new control tool to
deal with control problems of such non-linear plant.
[5]
[6]
[7]
[8]
[9]
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1
Fig.13 Step response of sliding mode fuzzy speed controller (FSM);
moment of inertia : A) J=3JM, B) J=JM
Comparison between proposed fuzzy control system and
traditional digital cascade control, carried out by
simulation method, proved that FLC as a robust control
gives better performance in the range where non-linearity
and parameter variation are observed. Presented in the
paper FLC structure for adaptive current control and fuzzy
sliding-mode speed controller can be recommended for
practical implementation.
V. REFERENCES
[1] D. Driankov, H. Hellendoorn and M. Reinfrank, An
introduction to Fuzzy Control, Springer-Verlag,
Berlin Heidelberg, 1993.
[2] A. Farjon and M. Tholomier, "Why and how using
the fuzzy logic in the power electronic field",
Proceedings of the European Conference on Power
Electronics EPE’95, Seville 1995, pp.3.127-3.132.
[3] W. Pedrycz, Fuzzy Control and Fuzzy System,
Research Studies Press LTD., Taunton Somerset
England, 1993.
[4] P. Brandstetter and P. Sedlak ,"Fuzzy control of
electrical drive using DSP", Proceedings of the 7th
International Power Electronic and Motion Control
1The work was supported in part by a grant from State Committee for
Science Research (Poland), contract 42-926/T10/96.