a fuzzy variable structure controller for statcom

A fuzzy variable structure controller for STATCOM

Stella Morris *, P.K. Dash, K.P. Basu

Multimedia University, Selangor, Malaysia

Received 24 January 2002; received in revised form 26 September 2002; accepted 9 October 2002

Abstract

Two new variable structure fuzzy control algorithms are presented in this paper for controlling the reactive component of the

STATCOM current in a power system. The control signal is obtained from a combination of generator speed deviation and

STATCOM bus voltage deviation fed to the variable structure fuzzy controller. The parameters of these fuzzy controllers can be

varied widely by a suitable choice of membership functions and parameters in the rule base. Simulation results for typical single-

machine and multimachine power systems subject to a wide range of operating condition changes confirm the efficiency of the new

controllers.

# 2002 Elsevier Science B.V. All rights reserved.

Keywords: Multimachine; Power systems; Generator; STATCOM; Fuzzy controller

1. Introduction

In recent years, various types of FACTS devices

(UPFC, STATCOM, TCSC, SVC, etc.) have been

studied for their use in the existing power systems with

a view to improve the flexibility, controllability and to

enhance system stability. Reactive power compensation

is an important issue in electrical power systems [1�/5]

and STATCOM plays an important role in controlling

the reactive power flow to the power network and hence

the system voltage fluctuations and angle stability. One

of the most important advantage of the STATCOM is

its behavior during the voltage collapse at the bus where

it is located as it supplies almost a constant reactive

power without being affected by voltage variation across

it.

Normally the STATCOM comprises a voltage source

shunt converter connected through a transformer and

filter across a load bus where the voltage is to be

regulated. The shunt converter is usually modeled as a

controllable voltage source generated by the inverting

action of the converter with a DC voltage applied

through a charged capacitor. The converter controls

the current injected to the power system and as the

energy exchanges by the STATCOM is limited by the

capacitor stored energy, only reactive power can be

exchanged in steady state.

In essence, the desired reactive power exchange is

achieved by a reactive current component Is to maintain

DC capacitor voltage constant. However, certain

amount of real power flows into the STATCOM and

the real component of the STATCOM current provides

the losses in the resistive elements of the converter and

maintains the capacitor voltage. The STATCOM, there-

fore, is modeled as a controllable active and reactive

current source; the active part It is obtained from the

DC link voltage error through a PI controller and the

reactive part through a time delay unit.

The control of active and reactive components of

STATCOM current are normally achieved through a PI

controller. However, these controllers suffer from in-

adequacies of providing a robust control and transient

stability enhancement over a wide range of power

system operating conditions. Hence other state feedback

control methods have been considered in reference [4],

which provide superior performance in comparison to

the PI controller. Both the pole placement technique and

linear quadratic regulator are based on a small signal

linearized model of the power system including STAT-

COM and hence are suboptimal in nature. Thus, there is

the need of a nonlinear controller to stabilize the* Corresponding author.

E-mail address: [email protected] (S. Morris).

Electric Power Systems Research 65 (2003) 23�/34

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0378-7796/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved.

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inherently nonlinear power system under dynamic

operating conditions. The fuzzy logic approach [7,8]

on the other hand, provides a model free approach for

STATCOM control and can be effective over the entirerange of power system operation. Furthermore, the

fuzzy logic approach allows the knowledge from experi-

ences to be incorporated to the control scheme as a set

of linguistic rules and membership functions. Also

multimachine simulation studies under fault conditions

have been included in this paper to highlight the

effectiveness of this new controller.

In this paper, a new fuzzy variable structure controlalgorithm is used, in which there is a fuzzy controller

derived from a sliding surface and a supervisory control

which is designed to satisfy the sliding conditions. This

new controller is able to compensate the effects of

uncertainties, disturbances and unmodeled system dy-

namics. This is verified by performing simulation studies

on a single-machine infinite-bus power system subjected

to wide range of operating conditions like faults andmechanical torque changes, etc.

2. System model

In order to illustrate the performance of the power

system with a current controlled STATCOM detailed

models of exciter, turbine control loops are omitted and

the transient emf in the quadrature axis, e ?q, and

mechanical power input, Pm, remain constants. The

single-machine infinite-bus power system shown in Fig.

1 comprises a synchronous generator connected to the

infinite-bus through a double-circuit transmission line.The STATCOM is located at a bus between the

generator and the infinite-bus.

An equivalent circuit is shown in Fig. 2, where both

active and reactive components of the STATCOM

current are shown.

The differential and algebraic equations of the power

system are given by

v�v0�pd (1)

where, p�/d/dt (differential operator)

pv�pf

H(Pm�Pe) (2)

pIs�1

ts

(Is0�Is)�ks

ts

u (3)

pIt�1

t1

(It0�It)�k1

t1

(Vdc0�Vdc) (4)

pVdc�vC

Vdc

fjVmjjItj�(I2t �I2

s )Rsg�vCVdc

Rdc

(5)

where, It and Is are active and reactive components of

the STATCOM current, respectively and Vdc is the DC

capacitor voltage.

In the above equations ks, and k1 are gains and ts and

t1 are time constants of the STATCOM current control

loop; Rdc and C are resistance and capacitance of theDC link capacitor; Rs is the shunt converter transformer

resistance. The electrical power output Pe of the

generator is given by:

Pe�E?qVm

x?d � x1

sinu�V 2

m

2

�x?d � xq

(x?d � x1)(xq � x1)

�(6)

and STATCOM bus voltage Vm and angle um are

Vm�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(V 2

md�V 2mq)

q(7)

where

Vmd�(x1 � xq)Vbsind� x2(Issinum � Itcosum)(x1 � xq)

x1 � x2 � xq

(8)

Vmq�(x1 � x?d)Vbcosd� e?qx2 � x2(Iscosu� Itsinu)(x1 � x?d)

x1 � x2 � x?d(9)

The symbols used above have the usual meaning as in

the single-machine infinite-bus power system andFig. 1. Single-machine infinite-bus power system.

Fig. 2. Equivalent circuit with real and reactive components of the

STATCOM currents.

S. Morris et al. / Electric Power Systems Research 65 (2003) 23�/3424

u� tan�1

�Vmd

Vmq

�(10)

3. Derivation of variable structure fuzzy controller

Recently, combinations of fuzzy control and variable

structure controller (VSC) approaches have achieved

superior performance [9�/15]. Briefly, for instance,

Hwang and Lin [13] developed a non-adaptive fuzzy

controller, and Wu and Liu [14] used the switching

manifold as a reference, where sliding modes are used todetermine the optimal values of parameters in fuzzy

control rules. Othani and Yoshimura [15] also presented

a fuzzy control law using the concept of sliding mode,

where fuzzy rules are tuned by learning.

For designing a linear sliding mode current controller

for STATCOM, a linearized model of the system

equations is developed in the form

e

e

DI s

24

35�

0 1 0

a1 0 a2

0 0 a3

24

35 e

e

DIs

24

35�

0

0

b

24

35u (11)

where a1, a2, a3, b depend on power system operating

condition and machine and line parameters.

A time varying sliding surface is defined to track thespeed error (Dv�/v�/v0) of the generator. However, if

the speed is not available at the STATCOM bus due to

its location away from the generator, the bus angle um is

used. In either case, the sliding surface s is defined as

s� e�l1e (12)

where error, e�/d�/d0, or e�/v�/v0, or e�/um�/um ref,l1�/0.

Another definition of s also could be

s�l2e�l1e�(Is0�Is); l2�0 (13)

The parameters l1 and l2 are obtained from the

principles of sliding mode control design using pole

placement technique as follows:Eq. (13) is rewritten as

s�l2e�l1e�DIs (14)

For the existence of sliding mode,

s�0; and ssB0 (15)

Thus with s�/0, DIs is eliminated from Eq. (13) and

substituted in Eq. (11) to yield

e

e

� ��

0 1

a1�a3l1 a2�a3l2

� �e

e

� �(16)

which is of the form

X �AX (17)

The characteristic equation of the A matrix is

designed to have two eigenvalues p1 and p2, which are

found as

p1�p2�a3l2�a2

p1p2�a3l1�a1

g (18)

By suitably choosing the values of p1 and p2, the

constants l1 and l2 are found as

l1�p1p2 � d1

d3

l2�p1 � p2 � d2

d3

g (19)

where d1, d2, and d3 depend on power system operating

condition and machine and line parameters.

After evaluating l1 and l2, s is rewritten from Eq.

(13) as

s�l1e�l2e�DI s

�l1e�l2e�a3DI s�bu (20)

The reachability condition for the sliding mode

control is used to obtain u ; since

s��h sgn s; ssB0; and h�0 (21)

The control u is obtained as

u�1

bf�h sgn s�l2e�l1e�a3DIsg (22)

Due to sgn(s) term in the control law there is the

possibility of undesirable chattering and hence fuzzy

control is used.

In designing fuzzy sliding mode control scheme, the

fuzzy controller employs two inputs: the sliding signal s

and the rate of change of the sliding signal s: This fuzzy

controller has only one control output u . The value of s

is not obtained easily due to system uncertainties andhence an approximation is used as

s�s(k) � s(k � 1)

h(23)

where h is a small positive constant (h�/0.01).

Another alternative is to use a first order filter given

in Fig. 3 to obtain s:

s1�s� s1

Tf

(24)

/s1 replaces s in the calculations(Tf is a small positive

constant, Tf�/0.1).

Based on the chosen membership functions, the fuzzy

control rules are written as

Fig. 3. Representation of first order filter.

S. Morris et al. / Electric Power Systems Research 65 (2003) 23�/34 25

R1 : If s is P and is P then u is NB:

R2 : If s is P and is N then u is NS:

R3 : If s is N and is P then u is PS:

R4 : If s is N and is N then u is PB:

In the above rule base K is a scaling factor to be

suitably chosen to limit s and Ks values to lie within �/

L and �/L . the membership functions for positive andnegative sets are given by

mP(s)�

0 sB�Ls� L

2L�L0s0L

1 s�L

8>><>>:

mN(s)�

1 sB�L�s� L

2L�L0s0L

0 s�L

8>><>>:

(25)

where P and N stand for positive and negative sets; PB,NB, PS, NS stand for positive big, negative big, positive

small, and negative small fuzzy sets, respectively. The

value of K is 1/50.

Similar positive and negative sets are used for the

fuzzification of the input Ks: Fig. 4(a) shows the

membership functions of s and/Ks: For the control

output u , the membership functions are shown in Fig.

4(b).The maximum values of the output sets PB, PS, NB,

NS are u1, u2, u3, and u4, respectivelywhere

u1��L; u2��L

10; u3�

L

10; u4�L (26)

From the fuzzy rule base it can be understood for

rule-1, the system states are above the sliding surface

and are moving away from the sliding surface. Hence

the control action needs to be negative and big enough

to turn the system states downwards. In a similar way

rules 2, 3, and 4 can be interpreted in terms of the sliding

mode control strategy.Using Zadeh’s rules for antece-dent part of the rule base (mA and mB�/mA�/mB) and

general defuzzification formula, the output u is obtained

as

u�

X4

j�1

(mj)guj

P(mj)

g�W TU (27)

where U � [u1 u2 u3 u4] is the consequent vector, in

which uj is the output of the jth rule, mj is the

membership value of the j th rule, and W �[w1 w2 w3 w4] with

wj �(mj)*

gP(mj)*g

; j�1; 2; 3; 4: (28)

In the above formulation, if g�/1, we get the centroid

defuzzifier. The fuzzy controller, if properly tuned willresult in minimizing the error terms e and e in Eq. (13)

when u is replaced by uf. However, the uncertainty in the

bus voltage variation Vm or due to unmodeled dynamics

of E?q might introduce an error in the STATCOM

current reference Is ref and hence ss will not become

zero to guarantee the sliding of the states of the power

system to the origin. Hence the total current control of

the STATCOM will comprise of a fuzzy control uf and asupervisory control term us in the form as

u�uf �us

The supervisory control is chosen by following the

power rate reaching law and boundary layer approach

as

us�Ks

�½s½

e�si

�bsgn (s); b�0 (29)

Due to the power rate reaching law, this control

ensures the higher reaching speed when states are faraway from the switching manifold and reduces the rate

when the states are near the manifold. The result is a fast

reaching and low chattering reaching mode [9]. The

boundary layer is automatically constructed from the s

values between sets Big and Small.

The above expression is motivated by boundary layer

approach in reducing chattering. The value of di is

chosen using a fuzzy rule base as follows:

Fig. 4. (a,b) Membership function.


If ½s½ is Big; di is Big

If ½s½ is Small; di is Small

The membership function of the fuzzy sets Big and

Small are

mBig(½s½)�1�e�½as½

mSmall(½s½)�e�½as½ (30)

Fig. 5 shows the membership grades for the sets Big

and Small. The constants a , b , and Ks are chosen as a�/

2, b�/0.2, Ks�/0.05.

The control block diagram for both reactive and

active current controller are shown in Fig. 6(a) and (b),

respectively.

A simple condition for stability can be established forthis control law by using the sliding mode relation

ss�0/

Thus

ss�sfl1e�l2e�a3(Is0�Is)�b(uf �us)gB0 (31)

Knowing the bounds of e; e; the maximum value of uf

can be estimated. Further since uf is obtained from

s and s; the fuzzy control will tend to make both s 0 0;and s 0 0 and hence stability will be achieved. This isverified from actual nonlinear simulations of a power

system.

4. Takagi sugeno fuzzy controller

In comparison to the conventional Mamdani type

fuzzy controller presented in Section 3, a Takagi Sugeno

(TS) fuzzy control scheme [6,7] is presented in this

section to provide a wide range of variation of thenonlinear gain of the current controller for STATCOM.

The simplified TS rules are shown to parameterize the

characteristics of the gain variation and consequently an

infinitely large number of gain variation characteristics

can be produced. The inputs to the TS fuzzy controller

are the sliding surface s and its derivative s: The

membership values mP(s) and mN(s ) or mP(/s) and mN(/s)

are obtained using similar membership functions givenin Eq. (25). The following fuzzy rule base is used:

R1 : If s is P

and Ks is P then u1�K1(s�lKs)

R2 : If s is P and Ks is N then u2�K2u1

R3 : If s is P and Ks is P then u3�K3u1

R4 : If s is P and Ks is N then u4�K4u1

In the above rule base, the computation of the

strength of the antecedent part of the rule with an

AND operator is performed by multiplication of

membership values m (s )�/m (/s); respectively for each

rule.

The effective control u is obtained using a centroiddefuzzifier

u�

X4

i�1

miui

m1 � m2 � m3 � m4

(32)

which when simplified yields

u�(s�lKs)Keff (33)

and

Keff �K1(m1 � K2m2 � K3m3 � K4m4)

m1 � m2 � m3 � m4

(34)

The value of l , K , K1, K2, K3, and K4 are chosen as l�/

0.2, K�/1/50, K1�/1, K2�/0, K3�/0, and K4�/0.5,

respectively for this study.

5. Simulation results

5.1. A. single-machine infinite-bus power system with

STATCOM

The single machine infinite-bus system shown in Fig.1 is considered for simulation studies. The various

transient disturbances due to faults and mechanical

power changes are created to study the performance of

the variable structure fuzzy controller (VSFC), VSFC

with supervisory control, and VSC with Takagi Sugeno

(TS) fuzzy control for STATCOM placed at bus no.3 of

the power system. The power system data is given in the

Appendix A. The conventional PI controller is used forcomparison. The control output from the PI controller

is obtained as

u��

Kp�Ki

S

�f(Vm ref �Vm)�KwDvg (35)

where the PI gains are optimized using ITAE criterionas Kp�/0.1, Ki�/0.1, and Kw�/10.The values of K , L ,

l1, b , and h are chosen as 1/50, 50, 0.2, 0.2, and 0.01,

respectively.Fig. 5. Membership grades for the sets Big and Small.


5.1.1. Case 1

The operating power level of the generating system is

P�/0.8, Q�/0.6 and a 3-phase fault of 0.1 s duration is

simulated on bus no.3. In this condition, the voltage

across the STATCOM bus suddenly goes to zero and

hence there is a significant rise in swing angle d from

nearly 808 to 1358. The transient response of the PI

controller, VSFC with a supervisory control, and VSC

with TS fuzzy control are shown in Fig. 7. From the

figure it is observed that the VSFC with a supervisory

control and VSC with TS fuzzy produce significant

improvement in damping of the electromechanical

oscillations of the generator in comparison to the

conventional PI controller. In comparison to the con-

ventional Mamdani type fuzzy controller with a super-

visory control, the TS fuzzy controller provides

significant damping and reduces the overshoot in nearly

1.5 s. The terminal voltage of the generator and the DC

voltage across the STATCOM capacitor are also

damped fast with these two fuzzy controllers.

The power level of the generating system is then

increased to P�/1.0 and Q�/0.4 and the reactance is

decreased from 0.7 to 0.5 pu. A 3-phase fault of 0.1 s.

duration is simulated at bus no.2 (near the infinite-bus).

The performance of PI controller, VSC, and VSFC with

supervisory control are shown in Fig. 8. Here, since the

power level is high the load angle swings to nearly 1408and to maintain the stability the reactance of the line

was decreased. From Fig. 8 it can be observed that the

VSFC performs well in reducing the system oscillations.

The conventional PI controller, on the other hand,

shows large oscillations and takes more time to damp

out the system oscillations. Thus an uncertain reactance

change condition is handled very well by the fuzzy

controller.

Another loading condition which produces severity in

transient oscillations by changing the operating power

levels to P�/0.8, Q�/�/0.2 and reducing the line

reactance from 0.7 to 0.6 is shown in Fig. 9. A 3-phase

fault of 0.1 s duration is simulated at bus no.2 (near the

infinite bus). The VSFC with supervisory control per-

forms very well in producing significant damping to the

electromechanical oscillations of the system. The per-

formance of the PI regulator is very oscillatory.

Fig. 6. (a) Control block diagram for reactive current controller. (b) Control block diagram for active current controller.

Fig. 7. Transient response with P�/0.8, Q�/0.6.


5.1.2. Case 2

A 3-phase fault of 0.1 s duration is simulated on line

no.2 at bus no.3 of the power system. The operating

power level is taken P�/0.8, Q�/0.2. The performance

of the PI controller, VSC, and VSC with TS fuzzy

control are shown in Fig. 10. The performance of both

the VSC and the VSC with TS fuzzy control are found

to provide significant damping to the system oscilla-

Fig. 8. STATCOM performance with P�/1.0, Q�/0.4

Fig. 9. Transient performance with negative reactive power (P�/0.8, Q�/-0.2).


tions. However, the VSC exhibits larger overshoot in the

first swing and takes a little more time than TS fuzzy

control scheme for the STATCOM.

Now the transmission line with reactance x21(x21�/

0.3) is removed from the power system for a duration of

1 s and its transient response is depicted in Fig. 11. It is

seen from the response that the effect of uncertainty is

very well controlled by the proposed controller.

5.1.3. Case 3

The mechanical torque input to the generator is

increased by 30% for 0.5 s and then brought to normal

and after 4 s, the torque input is reduced by 30% for 0.5

s. The operating power level is taken as P�/0.8, Q�/0.6.

The transient performance of the VSFC with super-

visory control, and VSC with TS fuzzy control shown in

Fig. 12 are found to be quite satisfactory in reducing

Fig. 10. STATCOM performance with P�/0.8, Q�/0.2.



transient excursions in the states of the power system

line load angle, terminal voltage and DC voltage for the

STATCOM. The performance of the PI controller is

very oscillatory.

5.1.4. Case 4

To take care of the unmodeled dynamics of the

generator voltage E ?q behind the transient reactance,

the value of E ?q is increased by 50% and the system

oscillations are depicted in Fig. 13. The proposed

controller is practically immune to the increase in the

value of E ?q and damping is achieved very fast.

5.2. B. Multimachine power system operating with

STATCOM

To verify the performance of the proposed variable

structure fuzzy supervisory controller, a two-area four-

generator power system of Fig. 14 is considered. This

system has been specially designed for fundamentalstudies of inter-area oscillations due to power flow

from one area to the other area. Each generator of the

multimachine system is equipped with an ordinary

voltage regulator and a power system stabilizer (PSS)

for damping local mode oscillations during transient

conditions due to faults. The PSS alone cannot provide

sufficient damping to the inter-area oscillations and

hence the STATCOM is used at the bus 8 to provideextra damping during system oscillations. In this study a

third order synchronous machine model is used and the

system equations are given in the Appendix A. The

system data is given in Ref. [16]. The STATCOM is

modeled as before providing real and reactive current

injections at the STATCOM bus. The sliding surface s

used in this case takes the form

s�c1Du78�c2Du78�DIs (36)

Here u78 (u7�/u8�/phase angle difference between the

bus 7 and bus 8) is obtained in the following way.

The active and reactive power flowing in the line 7�/8towards bus 8 are given by:

P78�½V7½½V8½sinu78

x78

(37)




Fig. 14. Multi-machine power system with STATCOM.

Fig. 15. Local and inter-area mode of oscillations.

Fig. 16. DC voltage variation. Fig. 17. STATCOM bus voltage variation.


Q78�½V7½½V8½cosu78

x78

�½V8½

2

x78

(38)

x78�/reactance in the line 7�/8.V7, and V8 are bus 7 and

bus 8 voltages, respectively. u78 is now calculated as

u78�tan�1

�P78=

�Q78�

½V8½2

x78

��(39)

Measurement of P78, Q78 and V8 yields the value of

u78. In Eq. (36) D signifies the small changes in the

values of the variables. The constants c1 and c2 are

chosen as, c1�/2.3, c2�/1.3, for best stability perfor-

mance of the multimachine power system.

5.2.1. Case 1

Taking generator-3 as reference and pre-disturbance

loading conditions in p.u. as P1�/0.44, Q1�/0.20, P2�/

0.66, Q2�/0.26, P3�/1.57, Q3�/0.21, P4�/0.33, Q4�/

0.22, a 3-phase fault is created on the middle of one ofthe transmission line connecting bus-9 and bus-10 and

cleared after 0.1 s. The local mode and inter-area mode

of oscillations are presented in Fig. 15. From the figure

it is clearly found that the system oscillation are damped

much faster using fuzzy supervisory control VSFC in

comparison to conventional PI control. Figs. 16 and 17

show the variation of voltage across the DC capacitor

and the variation of STATCOM bus voltage, V8,respectively. It is seen from the figures that the over-

shoots and the settling time are well controlled by the

proposed controller.

5.2.2. Case 2

The power loadings of the generators are then

changed to P1�/0.55, Q1�/0.20, P2�/0.55, Q2�/0.26,

P3�/1.37, Q3�/0.15, P4�/0.55, Q4�/0.22. A three-

phase fault of 100 ms duration is simulated at the

middle of one of the transmission line connecting Bus-7

and Bus-8. Fig. 18 shows the local mode and inter-area

mode of oscillation. Both the modes of oscillations are

damped very well and overshoots reduced fast with

VSFC with supervisory control.

6. Conclusion

The paper presents new variations of the fuzzy control

scheme for the control of STATCOM current. The

parameters of fuzzy reactive current controller are

adapted by using a sliding surface similar to the sliding

mode control instead of the error and its derivative.

Further, the parameters of the sliding surface can also

be varied by using a pole-placement technique. These

new fuzzy controllers for STATCOM provide a wide

range of gain variations for controlling the electrome-

chanical oscillations of a single-machine infinite-bus and

multimachine power systems. The new controllers are

found to provide significant improvement in damping

electromechanical oscillations of both the single and

multimachine power systems over a wide range of

operating conditions.

Fig. 18. Local and inter-area mode of oscillations.


Appendix A: Parameters of the studied system (in per unit

unless indicated specially)

Single-machine infinite-bus data

Generator x ?d�/0.22, xq�/xd�/1.96 (for nonsali-

ent pole machine case), D�/0, 2H�/

6.7 s

Transformer xT1�/xT2

�/0.1

Transmission

line

x1�/0.2, x2�/0.6/2

STATCOM Is max�/0.5, Is min�/�/0.5, Is0�/0, ts�/

0.02 s, ks�/1.0, k1�/10, t1�/0.02

Multi-machine data. Generator data

Gen. Ke te H t ’d0 xd xq x ’d

1 30 0.05 6.5 8 1.8 1.7 0.3

2 10 0.05 6.5 8 1.8 1.7 0.3

3 10 0.05 6.175 8 1.8 1.7 0.3

4 10 0.05 6.175 8 1.8 1.7 0.3

Power system stabilizer

upss�Kd(stq=(1�stq))((1�st3)=(1�st2))Dv

Kd�0:24; tq�0:4; t3�0:03; t2�0:01

The value of p1 and p2 for best stability performance

of the single-machine infinite-bus power system are

chosen as

VSC p1�/24, p2�/7

VSC with TS fuzzy p1�/2.6, p2�/50

VSC with supervisory control p1�/2.7, p2�/52

References

[1] P.W. Lehn, M.R. Travani, Experimental evaluation of STAT-

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