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Energy 162 (2018) 910e917
Contents lists available at ScienceDirect
Energy
journal homepage: www.elsevier.com/locate/energy
Hierarchical Takagi-Sugeno fuzzy hyperbolic tangent static model
control for a circulating fluidized bed boiler thermal power unit
Xusheng Zhuo a, *, Chun Lou b, Huaichun Zhou c, Jinxuan Zhuo a, Peifang Fu b
a
Hubei Research Center of Video Image and High Definition Projection Technology, School of Electrical and Information Engineering, Wuhan Institute of
Technology, Wuhan 430205, China
b
State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China
c
Key Laboratory of Condition Monitering and Control for Power Equipment, Minstry of Education of China, School of Energy, Power and Mechanical
Engineering, North China Electric Power University, Beijing 071003, China
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 8 May 2018
Received in revised form
5 July 2018
Accepted 1 August 2018
Available online 4 August 2018
This paper proposed a novel two layer hierarchical Takagi-Sugeno fuzzy hyperbolic tangent static model
control scheme for a circulating fluidized bed (CFB) boiler thermal power unit to cope with the complex
nonlinearity and large inertia performance which make its existing PI type load-fuel control loop not
functioning normally. In the upper layer, a reference governor with Takagi-Sugeno fuzzy hyperbolic
tangent static model control algorithm was developed to yield a compensation for the external load
command of the existing PI type load-fuel control loop in the lower layer. By constructing a new
quadratic integration Lyapunov function, the stability condition of proposed control system was derived.
While implemented in the decentralized control system (DCS) of CFB boiler, the reference governor was
constructed and adopted the cubic variables hyperbolic tangent function algorithm which can oppose
effectively the nonlinearity and large inertia performance. The experimental results shown that the
proposed hierarchical fuzzy hyperbolic tangent static model control scheme can improve the control
performance of the PI type load-fuel control system obviously, weaken the fluctuation in the main steam
pressure and bed temperature apparently and make the controlled system more stable.
© 2018 Elsevier Ltd. All rights reserved.
Keywords:
Circulating fluidized bed boiler
Hierarchical control
Reference governor
T-S fuzzy hyperbolic tangent static model
Quadratic integration Lyapunov function
1. Introduction
Circulating fluidized bed (CFB) combustion technology, with
excellent fuel flexibility and cost-effective emission control, has
been regarded as the best way for burning the fuels such as the low
quality coal, washing coal waste, petcock and other solid combustible wastes [1e3]. Since coal is a major fuel in the thermal power
plants in China and this situation unchanged in the near future, the
CFB coal burning technology has been researched and developed
most actively for half century [4]. Today, over 10% of all coal-fired
generate units in China are the CFB boiler units [5], more than
370 CFB boilers with unit capacity over 410 t/h were in operation
and the total installation capacity was up to 70 GW [4].
However, extreme complexity, such as interactions between the
gas and solid phases, chaotic nature of the heat transferred between the coal particles and water wall, and chemical reactions to
* Corresponding author.
E-mail addresses: Zhuo@wit.edu.cn, zhuoxusheng@sina.com (X. Zhuo).
https://doi.org/10.1016/j.energy.2018.08.010
0360-5442/© 2018 Elsevier Ltd. All rights reserved.
produce release of volatile materials [1e3,6,7], make it difficult for
the researchers and engineers to understand completely the dynamic mechanism of CFB boilers. Therefore, the modeling and
control still remain be one of the most challenging tasks [6e8,17].
Over the past two decades, many efforts have been taken to address
these issues. The intelligence techniques such as fuzzy logic control
and neural network etc had been adopted to deal with the
nonlinearity or complexity of CFB boilers [9e14]. Other advance
control strategies such as linear matrix inequalities (LMI) method
[15] and H∞ robust control [16] had been reported to control
effectively the bed temperature of CFB boilers. A linear parameter
varying (LPV) model based model predictive control (MPC) method
was reported to can yield a better control effect for an industrial CFB
boiler [17]. Even so, for a real CFB boiler thermal power unit, its
control trouble still remain be unsolved well. The main reasons are
that, on the one hand, many advance control algorithms like the
above-mention were unable to be well integrated into the decentralized control system (DCS) of CFB boiler units. On the other hand,
the power plant entrepreneurs are still reluctant to replace their
existing PID-type (proportion and integration and differentiation)
X. Zhuo et al. / Energy 162 (2018) 910e917
controllers because of needing a great deal investment. In the situations, other practical alternative schemes should be selected.
The hierarchical control structures [18e21] and/or reference
governor approaches [22e26] are the available schemes which
both can make the existing traditional control structure unchanged
and improve the control performance. In the power industries, the
hierarchical control structure integrated with the MPC (model
predictive control) technologies can yield the optimal operating
trajectories for the traditional control system of a oil-fired boilerturbine unit [21] or to achieve dynamic optimal control performance and guarantee the system stability [20]. Like the hierarchical
control technologies, the reference governor approaches were also
the frameworks which can integrate with MPC technology [26] or
intelligence scheme [24] to produce the optimal operating reference signals for the control system of the oil-fired boiler units to
improve their economical and control performances. However,
compared with an oil-fired boiler or pulverized coal fired boiler, a
CFB boiler has the different characteristics: 1. more difficult to
develop the mechanism model; 2. its combustion process response
is much more slower, in other words, it is a large inertia process; 3.
significant difference in combustion mode and lower temperature
firing. Thus, it was difficult to keep the original pattern ‘transplant’
above-mentioned hierarchical control technologies or reference
governor approaches into the CFB boiler thermal power units.
In this paper, a two layers hierarchical control structure based
on an existing PI-type fuel-load control loop of the CFB boiler was
developed. A reference governor in the upper layer was designed to
supervise the CFB boiler's some important state variables and to
yield timely the modified instruction signal fed to the PI controller
loop in the lower layer. Because the fuzzy methods are suitable for
solving the non-modeling problems [27,28] and fuzzy hyperbolic
model (FHM) method can express a complex nonlinear process
[29,30], a Takagi-Sugeno fuzzy hyperbolic static model (FHSM)
method was selected as its supervised algorithm in the reference
governor, so that the upper layer can yield theoretically a right
compensation signal for the external load command to ask the fuel
feed rate for CFB boiler under any operating conditions. Thus, the
complex nonlinearity, large inertia performance in CFB boiler will
be addressed.
The remaining sections of this paper are organized as follows:
First, a 480t/h coal fried CFB boiler and its control problems were
described, and then a hierarchical structure on CFB boiler unit's
load control loop was designed and the system stability was
analyzed. Next, the supervisor's algorithm was implemented in the
DCS of CFB boiler and the system regulations were shown. Fourthly,
the experiment results were presented. Finally, some conclusions
were drawn.
911
nozzles in the bottom of the furnace, and two secondary air fans to
provide combustion air to the middle of the furnace. Its schematic
diagram was shown in Fig. 1.
Fuels of the CFB boiler were the mixtures such as coal, coal refuses and coal washing mud etc, and its low calorific value and high
moisture in the mixtures led to a very long settling time in the
transition process of parameters change. In other words, the CFB
combustion was a nonlinear and large inertia process, which was
backed up by an actual data gathered from a test in Fig. 2. In the test,
when the fuel feed rate was step up form 74 to 90 t/h (tons per
hour) by manual operation in 500 s, the process response data of
the output power, main steam pressure, bed temperature, fluidized
air flow rate and oxygen content were recorded and drawn: For the
output power, it took about 1220 s to approach to the last stable
point while the fuel feed rate being risen up. And for the main
steam pressure and bed temperature, it was about 1300 s and
1100 s respectively. In addition, the fluidized air rate was increased
about 11000 Nm3/h (normal cubic meters per hour) to match the
increment of the fuel feed rate which caused the oxygen content in
flue gas to decrease about 2.5%. Nevertheless, both the fluidized air
rate and oxygen content return almost to their previous values
while the output power closed to the new stable point.
2.2. CFB boiler control problems
For the complexity such as nonlinearity and large inertia performance etc in the combustion process, the existing PID-type
control loops in the DCS of the CFB boiler were unable to do well
Fig. 1. Schematic diagram of CFB boiler.
2. CFB boiler and control problems
2.1. CFB boiler description
The considered CFB boiler was a 480t/h coal-fired drum-type
boiler in the thermal power plant of Ruiping in Henan Province,
China. Such boilers were widely utilized to supply heating and
electric power in China. Its specified steam mass flow rate is 480t/h
at a pressure of 13.7Mpa and in the bed temperature ranges from
800 C to 950 C. It included three key components: a membrane
water-wall furnace, two steam-cooled cyclones and a heat recovery
area housing the primary and secondary super-heater, re-heater
and economizer. There are six fuel silos and three limestone silos
positioned along the boiler front wall with a chain feeder under
each one, which are controlled to drop the fuel and limestone
mixtures onto a chain convey and to deliver the coal to drop chute/
screw feeder. There are two primary air fans to supply air from
Fig. 2. Response to coal feed rate step up from 74 to 90 t/h.
912
X. Zhuo et al. / Energy 162 (2018) 910e917
as one would wish. In particular, the effect of the fuel-load control
system was dissatisfactory: the serious fluctuations of the main
steam pressure and bed temperature of the CFB boiler can not be
depressed while its output power was regulated into a neighbourhood of some set-points. Shown in Fig. 3. The fluctuant
amplitude values of the main steam pressure and bed temperature
exceeded 3.5Mpa and 46 C respectively, which had seriously
affected the lifetime of the CFB boiler.
In addition, some factors such as the variety of fuel and time
varying parameters etc would make this PID controller loop be out
of step with the coal feed rate required or even produce a reverse
regulation. This would certainly lead to the sharpened fluctuation
of the main steam pressure and bed temperature, and finally the
skilled technicians were asked to intervene and switch the operation to manual mode to avoid the system collapse. That was shown
as Fig. 4. Therefore, the CFB boiler was basically operated under the
PID controller loops with manual auxiliary mode.
3. Hierarchical structure on CFB boiler unit's load control
loop
In this section, a two layers hierarchical structure on the loadfuel control loop was presented to improve the control performance of the CFB boiler thermal power unit. Upper layer was supervisory level and lower layer was regulation level. Shown as
Fig. 5. In the supervisory level, a reference governor as supervisor
was designed to acquired real-time values of the CFB boiler's main
steam pressure and bed temperature and produce a compensation
signal for the external load command of the lower layer. Motivated
by the ideas in the literature [29e32], a Takagi-Sugeno fuzzy hyperbolic tangent static model algorithm for the reference governor
Fig. 5. The hierarchical control structure on CFB boiler unit's PI type fuel-load control
loop.
was developed to cope with the complex nonlinearity and large
inertia performance in the dynamic response of CFB boiler. The
regulation level was the existing load-fuel control loop with a
traditional PI controller which can function only under the manual
auxiliary.
3.1. Hierarchical structure expression
1. Supervisor's algorithm: a T-S fuzzy hyperbolic tangent static
model was selected as following:
The i-th rule: If z1 isFi1 , and … zg isFig .
Then
ri ðtÞ ¼ ci1 tanhðk1 x1 ðtÞÞ þ / þ cin tanhðkn xn ðtÞÞ
i ¼ 1; 2; /; s
(1)
Herez1 /zg are the known premise variables which don't depend on
the inputxðtÞ, Fij is the fuzzy set, ri ðtÞ2Ris the output variable of the
supervisor, xðtÞ2Rn is the input vector andtanhðki xi ðtÞÞ ¼
eki xi ðtÞ eki xi ðtÞ ,
eki xi ðtÞ þeki xi ðtÞ
cij is a coefficient.
By using the fuzzy inference method with a singleton fuzzification and product inference and center average defuzzification,
the overall T-S hyperbolic tangent static model can be written as:
rðtÞ ¼
s
X
wi ,ri ðtÞ ¼ H,tanhðkxðtÞÞ
(2)
i¼1
m
Herewi ¼ Ps i ðzÞ , mi ðzÞ ¼
i¼1
Fig. 3. Control effect of CFB boiler's fuel-load loop with PI controller.
mi ðzÞ
g
Y
F~ij ðzÞ, F~ij ðzÞis the membership func-
j¼1
P
tion of fuzzy set Fij . His a 1 nmatric and H ¼ ½ si¼1 wi ,ci1 ; /;
Ps
tanhðkxðtÞÞ2Rn1
and
tanhðkxðtÞÞ ¼
i¼1 wi ,cin ,
½tanhðk1 ,x1 ðtÞÞ; /; tanhðkn ,xn ðtÞÞT , ki is a positive constant.
2. PI controller's expression
Zt
uðtÞ ¼ dP ,eðtÞ þ dI ,
eðtÞdt
(3)
0
Here uðtÞ2Ris the output of PI controller, dP anddI are the proportion
coefficient and integration coefficient respectively. The error eðtÞ ¼
Nref NE ðtÞ þ rðtÞ, Nref is the external load command andNE ðtÞis the
output power of CFB boiler generation unit.
3. Pant's expression
Fig. 4. A case that PID control loop was out of step with fuel required.
The plant refers to a CFB boiler unit which has strong
X. Zhuo et al. / Energy 162 (2018) 910e917
nonlinearity and complexity, in the section, we use a fuzzy hyperbolic tangent dynamic model describe it as follows:
_
xðtÞ
¼ A,tanhðkxðtÞÞ þ B,uðtÞ
(4)
Here xðtÞ ¼ ½x1 ðtÞ; /; xn ðtÞ T , tanhðkxðtÞÞ ¼ ½tanhðk1 x1 ðtÞ Þ; /;
913
loop system (6) is globally asymptotically stable.
Proof:
Pn R t
2
Let VðtÞ ¼
i¼1 ð 0 tanhðki xi ðtÞÞdtÞ be a quadratic Lyapunov
function andxi denotesxi ðtÞ for a brief description, then the time
derivative of VðtÞ was:
tanhðkn xn ðtÞ Þ T , A2Rnn , B2Rn1 , uðtÞ2R.
_
VðtÞ
¼ 2,
n
X
0
ki ,sech ðki xi Þ,tanhðki xi Þ,@
i¼1
3.2. Stability analysis
Zt
2
1
tanhðki xi Þdt A,x_i
0
(7)
For the two layers hierarchical control system, when the output
powerNE ðtÞ of CFB boiler unit was equal to its load commandNref ,
i.e. Nref ¼ NE ðtÞ, the output uðtÞ of PI controller's expression (3) was
rewritten as:
the
Rt
rðtÞ dt
(5)
tanhðxðtÞÞ dt
0
tanhðk1 x1 Þdt; /; tanhðkn xn Þ,
Rt
T
tanhðkn xn Þdt and
2
_
can be
the matrix PðxÞ ¼ diagðki ,sech ðki xi ÞÞnn , then VðtÞ
expressed:
0
Zt
¼ dP H,tanhðxðtÞÞ þ dI H,
XðxÞ ¼
½tanhðk1 x1 Þ,
Zt
uðtÞ ¼ dP ,rðtÞ þ dI ,
Let
vector-
0
_
VðtÞ
¼ XT ðxÞPðxÞx_ þ x_ T PðxÞXðxÞ
(8)
Substituting (6) into (8), we get:
0
Rt
Here
0 tanhðkxðtÞÞdt ¼
Rt
Rt
T
½ 0 tanhðk1 x1 ðtÞÞdt; /; 0 tanhðkn xn ðtÞÞdt .
Substituting (5) into (4), thus the overall closed loop system can
be expressed as:
_
xðtÞ
¼ ðA þ dP ,BHÞtanhðxðtÞÞ þ dI ,BH
2
_ ¼ XT ðxÞPðxÞ4ðA þ dP ,BHÞtanhðkxÞ þ dI ,BH
VðtÞ
Zt
0
2
þ4ðA þ dP ,BHÞtanhðkxÞ þ dI ,BH
Zt
Zt
3
tanhðkxÞdt 5
3T
tanhðkxÞdt 5 PðxÞXðxÞ
0
tanhðxðtÞÞ dt
(6)
(9)
0
By transforming (9), we get:
The asymptotic stability condition of this closed loop system can
be summarized as follows:
8
0
1
>
>
>
B
C
>
>
>
B
C
>
<
B
C
1
B
C
T
_
VðtÞ ¼ X ðxÞ PðxÞðA þ dP ,BHÞ,diag BZ t
C
>
B
C
>
>
B
C
tanhðk
x
Þdt
>
i
i
>
@
A
>
0
>
:
0
B
B
B
B
þdiag BZ
B
B
@
0
nn
9
>
>
>
>
>
>
>
=
T
T T
, A þ dP ,H B PðxÞ XðxÞ
>
>
>
>
>
>
>
;
1
C
C
C
1
C
C
t
C
tanhðki xi Þdt C
A
1
þXT ðxÞ dI ,PðxÞBH,diag
tanhðki xi Þ
nn
þ diag
nn
1
tanhðki xi Þ
nn
Theorem: for the nonlinear system (4) with a PI control (5), if
there exists a diagonal and positive definite matrixP > 0such as
LMIPðxÞQ þ Q T PT ðxÞ < 0is satisfied, here matrixQ ¼ ðA þ
dP ,BHÞ,L1 ðxÞ þ dI ,BH,L2 ðxÞ, dP and dI are the proportion and
integration coefficients of the PI controller respectively, L1 ðxÞ ¼
!
1
1
R
, L2 ðxÞ ¼ diag tanhðk
, then the closed
diag t
xÞ
0
tanhðki xi Þdt
i i
nn
nn
,dI ,HT BT PðxÞ XðxÞ
0
1
B
C
B
C
1
LetL1 ðxÞ ¼ LT1 ðxÞ ¼ diagBR t
C
@ 0 tanhðki xi ÞdtA
diag
1
tanhðki xi Þ
, L2 ðxÞ ¼ LT2 ðxÞ ¼
nn
_
, then VðtÞ
can be expressed as:
nn
914
X. Zhuo et al. / Energy 162 (2018) 910e917
o
_
VðtÞ
¼ XT ðxÞfPðxÞ,ðA þ dP ,BHÞL1 ðxÞ þ L1 ðxÞ, AT þ dP ,HT BT PðxÞ XðxÞ
o
þXT ðxÞfdI ,PðxÞBHL2 ðxÞ þ L2 ðxÞ,dI ,HT BT PðxÞ XðxÞ
T
þ dP ,BHÞ,L
1 ðxÞ þ dI ,BH,L
i 2 ðxÞ
o
h ¼ X ðxÞfPðxÞ½ðA
þ LT1 ðxÞ, AT þ dP ,HT BT þ dI ,LT2 ðxÞ,HT BT PðxÞ XðxÞ
trix PðxÞ is a diagonal and positive define matrix, i.e. PðxÞ ¼
that the derivativesp_ T ðtÞandT_ b ðtÞmade the another contribution
torðtÞ. Hence, the algorithm of the reference governor can be
expressed in (12) and its structure was shown in Fig. 7.
PT ðxÞ > 0.
(
Since PðxÞ ¼ diag
If
we
ki
sech2 ðki xi Þ
let
and ki > 0, sech2 ðki xi Þ > 0, mann
matrixQ ¼
the
ðA þ
_
dI ,BH,L2 ðxÞ, then VðtÞ
can be expressed as:
dP ,BHÞ,L1 ðxÞ þ
n
o
_
VðtÞ
¼ XT ðxÞ PðxÞQ þ Q T PT ðxÞ XðxÞ
(10)
roffs ðtÞ ¼ a1 , tanh k1 ,ðpT pT0 Þ3 þ b1 ,tanh k3 ,ðTb Tb0 Þ3
rdiff ðtÞ ¼ a2 , tanh k2 ,ðp_ T Þ3 þ b1 ,tanh k4 ,ðT_ b Þ3
(12)
When the linear matrix inequality PðxÞQ þ Q T PT ðxÞ < 0 is
_ < 0. It completes the proof.
satisfied, then VðtÞ
,
P
P
P
Here a1 ¼ si¼1 wi ci1 ; a2 ¼ si¼1 wi ci2 ; b1 ¼ si¼1 wi ci3 Ps
3.3. Reference governor construction in the DCS
b2 ¼
wi ,ri ðtÞ
i¼1
s
X
b
To describe how to realize the system regulation by the reference governor in supervisory level. We define the two generalized
variables: JðtÞ and vJðtÞ. Let JðtÞ ¼ tanh k1 ,ðpT pT0 Þ3 þ
b
# "
s
X
tanh k1 $ðpT pT0 Þ3
wi ci1
wi ci2
wi ci3
¼
þ
3
i¼1
tanh k2 $ðp_ T Þ
i¼1
i¼1
# "
#"
" s
s
s
X
X
tanh k1 $ðpT pT0 Þ3
P
þ
wi ci1
wi ci3
wi ci2
¼
3
i¼1
tanh k3 $ðTb Tb0 Þ
i¼1
i¼1
¼ roffs ðtÞ þ rdiff ðtÞ
"
i¼1 wi ci2
4. System regulation
tiveT_ b ðtÞ, the expression (2) can be written as follows:
s
X
i¼1 wi ci4
b
Letx1 ðtÞ ¼ ðpT ðtÞ pT0 Þ3 denotes the cube of deviation of main
3
_
denotes its cube of derivasteam pressure andx2 ðtÞ ¼ ðpðtÞÞ
3
tivep_ T ðtÞ; x3 ðtÞ ¼ ðTb ðtÞ Tb0 Þ denotes the cube of deviation of bed
temperature and x ðtÞ ¼ ðT_ ðtÞÞ3 denotes its cube of deriva-
rðtÞ ¼
,
Ps
Ps
;
Remark: in expression (12), the coefficientsa1 anda2 were
negative
values
so
that
the
compensation
signalsroffs ðtÞandrdiff ðtÞwere opposite to the change direction of the
pressurepT ðtÞand temperatureTb ðtÞ. the coefficients b1 2½ 0; 1 and b2 2½ 0; 1 were the weight factors which describe the proportions occupied byT ðtÞandT_ ðtÞ.
In this subsection, a reference governor was constructed so that
the supervisor's algorithm (2) can be implemented in the DCS of
CFB boiler. To cope with the complex nonlinearity and large inertia
performance in CFB boiler effectively, the hyperbolic tangent
function of cubic state variables were selected as supervisor's algorithm. This kind functions can be expressed by y ¼ tanhðk,x3 Þ
shown in Fig. 6.
4
i¼1 wi ci1
s
P
#"
#
tanh k3 $ðTb Tb0 Þ3
wi ci4
i¼1
tanh k4 $ðT_ b Þ3
#
#"
s
tanh k2 $ðp_ T Þ3
P
wi ci4
i¼1
tanh k4 $ðT_ b Þ3
s
P
#"
(11)
b1 ,tanh k3 ,ðTb Tb0 Þ3 , which integrate the main steam pressure
"
In
"
expression
(11),
roffs ðtÞ ¼
s
X
wi ci1
s
P
#
wi ci3
i¼1
i¼1
#
tanh k1 ,ðpT pT0 Þ3
described that the errors pT ðtÞ pT0 and
tanh k3 ,ðTb Tb0 Þ3
Tb ðtÞ Tb0 made the contribution to the compensation signal rðtÞ,
#
" s
#"
s
X
tanh k2 ,ðp_ T Þ3
P
described
wi ci2
wi ci4
and rdiff ðtÞ ¼
i¼1
tanh k4 ,ðT_ b Þ3
i¼1
errorpT ðtÞ pT0 with the bed temperature error Tb ðtÞ Tb0 to
reflect the drift away from their set points. Let vJðtÞ ¼
tanh k2 ,ðp_ T Þ3 þ b2 ,tanh k4 ,ðT_ b Þ3 , which integrate the one
order derivativep_ T ðtÞ of main steam pressure with the one order
derivativeT_ b ðtÞ of bed temperature to reflect their change directions. Then, the system regulation can be classified into five
cases, and each case corresponding to one regulation region of the
reference governor in the supervisor level. The five regulation regions were numbered as A, B, C, D and O region and shown in Fig. 8.
X. Zhuo et al. / Energy 162 (2018) 910e917
915
In the five cases of system regulation, Case 1 corresponding to O
Region and Case 2 corresponding to A Region and Case 3 corresponding to B Region and Case 4 corresponding to C Region and
Case 5 corresponding to D Region. The regulation process as
follows:
Fig. 6. Curve of y ¼ tanhðk,x3 Þ with k ¼ 0:1
Fig. 7. Block diagram of reference governor in supervisory level.
Fig. 8. Regulation regions of reference governor in supervisory level.
Case 1: when the regulation of reference governor in the supervisory level was located in O Region, the generalized variables JðtÞ/0 and vJðtÞ/0. This shown that the main steam
pressurepT ðtÞ and bed temperatureTb ðtÞ almost approach to
their set-points respectively, i.e. pT ðtÞypT0 and Tb ðtÞyTb0 ,
meanwhile, their one order derivatives were very small, almost
zero, i.e. p_ T ðtÞy0and T_ b ðtÞy0. According to the expression (11)
or (12) the compensation signal rðtÞy0. Hence, the coal feed
rate of CFB boiler will remain almost unchanged.
Case 2: when the regulation of reference governor was located
in A Region, the generalized variables JðtÞ < 0 and vJðtÞ 0.
This shown that the main steam pressurepT ðtÞ and/or bed
temperatureTb ðtÞ were less than their set-point values respectively, i.e. pT ðtÞ < pT0 and/or Tb ðtÞ < Tb0, and their one order derivative were greater than or equal to zero. i.e.p_ T ðtÞ 0 and/or
T_ b ðtÞ 0. According to the expression (11) or (12), the
compensation signalrðtÞin A Region will make the coal feed
control signal changed appropriately to drive the main steam
pressure pT ðtÞand/or bed temperature Tb ðtÞto approach to their
set-points at an appropriate speed. The regulation process was
shown in Fig. 9.
Case 3: when the regulation of reference governor was located
in B Region, the generalized variables JðtÞ < 0 and vJðtÞ 0.
This shown that the main steam pressurepT ðtÞ and/or bed
temperatureTb ðtÞ were less than their set-point values respectively, i.e. pT ðtÞ < pT0 and/or Tb ðtÞ < Tb0, and their one order derivative were less than or equal to zero. i.e.p_ T ðtÞ 0 and/or
T_ b ðtÞ 0. According to the expression (11) or (12), the
compensation signalrðtÞin B Region will make the coal feed
control signal increased rapidly to reverse the variables' tend
further away from their set-points, and to drive them to
approach to their set-points at an appropriate speed. The
regulation process was shown in Fig. 10.
Case 4: when the regulation of reference governor was located
in C Region, the generalized variables JðtÞ > 0 and vJðtÞ 0.
This shown that the main steam pressurepT ðtÞ and/or bed
temperature Tb(t) were greater than their set-point values
respectively, i.e. pT(t) >pT0 and/or Tb(t) >Tb0, and their one order
derivative were less than or equal to zero. i.e. dpT(t)/dt 0 and/or
dTb(t)/dt ≤0. According to the expression (11) or (12), the
compensation signal r(t) in C Region will make the coal feed
control signal changed appropriately to drive the main steam
Fig. 9. Curve of main steam pressure (or bed temperature) in Case 2.
916
X. Zhuo et al. / Energy 162 (2018) 910e917
Fig. 10. Curve of main steam pressure (or bed temperature) in Case 3.
pressure pT(t) and/or bed temperature Tb(t) to approach to their
set-points at an appropriate speed. The regulation process was
shown in Fig. 11.
Case 5: when the regulation of reference governor was located
in D Region, the generalized variables JðtÞ > 0 and vJðtÞ 0.
This shown that the main steam pressure pT ðtÞ and/or bed
temperatureTb ðtÞ were greater than their set-point values
respectively, i.e. pT ðtÞ > pT0 and/or Tb ðtÞ > Tb0, and their one order derivative were less than or equal to zero. i.e. p_ T ðtÞ 0 and/
or T_ b ðtÞ 0. According to the expression (11) or (12), the
compensation signal rðtÞ. in D Region will make the coal feed
control signal decreased rapidly to reverse the variables' tend
further away from their set-points, and to drive them to
approach to their set-points at an appropriate speed. The
regulation process was shown in Fig. 12.
5. Experiment results
To examine the practicability of the proposed hierarchical control structure for the PID control loop of CFB boiler unit, as the
supervisor, the reference governor with a T-S fuzzy hyperbolic
static model (T-S FHSM) algorithm was implemented on the DCS of
CFB boiler unit in Ruiping thermal power plant. The parameters'
values in reference governor were decided as follows:
According to the actual data, the deviation value of main steam
pressure pT ðtÞ pT0 2½ 2:0; þ2:0 .Mpa and the derivative
p_ T ðtÞ2½ 0:0006; þ0:0006 . Mpa/sec, and the deviation value of
bed temperature Tb ðtÞ Tb0 2½ 50; þ50 . Centigrade and the
derivative T_ ðtÞ2½ 0:01; þ0:01 . Centigrade/sec. If these regions
b
were translated into the interval ½ 3:0; þ3:0 , the values of parameters will be decided as a1 ¼ a2 ¼ 0:02., b1 ¼ b2 ¼ 0:3 and
k1 ¼ k2 ¼ k3 ¼ k4 ¼ 0:1.
Fig. 11. Curve of main steam pressure (or bed temperature)in Case 4.
Fig. 12. Curve of main steam pressure (or temperature) in Case 5.
The verification experiments were conducted in two respects:
(1). Test1 was to compare the control performances between the
existing PI control loop with manual auxiliary and the proposed
hierarchical T-S FHSM control scheme. (2). Test2 was to evaluate
the control effect of the proposed hierarchical T-S FHSM control
scheme in a long period operation.
Test1 was a comparison experiment in which the CFB boiler first
was operated more than 2 h under the existing PI type load-fuel
control loop with manual auxiliary, then switched to the proposed hierarchical T-S FHSM control mode. The result was shown in
Fig. 13. Under the existing PI control system with manual auxiliary
mode, the main steam pressurepT ðtÞ was in the range 8.75e10.0
Mpa
and
its
maximum
peak-valley
deviation
DpTmax ¼ pTmax pTmin was 1.25 Mpa; and the bed temperature
Tb ðtÞwas in the range 854e887 C and its maximum peak-valley
deviation wasDTbmax ¼ 330 C. However, while the CFB boiler was
controlled by the proposed hierarchical T-S FHSM control system,
the pressurepT ðtÞwas in the range 9.1e9.6Mpa and its maximum
peak-valley deviation wasDpTmax ¼ 0:5Mpa; the bed temperature
Tb ðtÞwas in the range 865e878 C and its maximum peak-valley
deviation wasDTbmax ¼ 130 C. By comparison, the proposed hierarchical T-S FHSM control system can improve the control performance of the load-fuel control loop in CFB boiler obviously.
Test2 was an evaluation experiment in which the CFB boiler was
operated more than 12 h under the proposed hierarchical T-S FHSM
control system. The result was shown in Fig. 14. During the
experiment, the output power was kept around 107 MW. For the
main steam pressurepT ðtÞand bed temperature Tb ðtÞ, their
maximum peak-valley deviations were DpTmax ¼ 2:4Mpaand
Fig. 13. Comparison of PI control with manual auxiliary mode vs. hierarchical T-S
FHSM control mode.
X. Zhuo et al. / Energy 162 (2018) 910e917
917
References
Fig. 14. Operation of CFB boiler unit under hierarchical T-S FHSM control mode.
DTbmax ¼ 550 C respectively in the first 2 h, but in the next 10 h, the
maximum peak-valley deviations were DpTmax ¼ 1:3Mpa and
DTbmax ¼ 390 C respectively. Compared with the result in Fig. 3
which was controlled by the existing PI control loop with manual
auxiliary, the proposed hierarchical T-S FHSM control scheme can
weaken the fluctuation of the main steam pressure and bed temperature apparently in a long period and make the controlled
system more stable. In addition, the proposed control system can
also bear some short-time coal chocking phenomenon in the
operation.
6. Conclusions
In this paper, we proposed a two layers hierarchical control
structure for the existing PID type load-fuel control loop of CFB
boiler thermal power unit. In the upper layer, a reference governor
with Takagi-Sugeno fuzzy hyperbolic tangent static model control
algorithm was developed as the supervisor to yield the compensation for the external load command of the existing PI type loadfuel control loop in the lower layer, which regulated the coal feed
rate to meet the demand of output power of the thermal power
unit. To overcome the large inertia performance and complex
nonlinearity of CFB boiler, the reference governor in the upper layer
take the hyperbolic tangent function of cubic of the state variables
as the core of the algorithm so that the calculated compensation
was both timely and appropriate for the dynamic control in the
lower layer.
After construction, the proposed hierarchical control scheme
can be implemented in the DCS of the CFB boiler thermal power
unit and some experiments had been conducted. The results of both
the comparison experiment and a long period operation evaluation
experiment shown that the proposed hierarchical T-S FHSM control
scheme can improve the control performance of the PI type loadfuel control system obviously, weaken the fluctuation in the main
steam pressure and bed temperature apparently and make the
controlled system more stable.
Acknowledgment
This work was supported by the Science and Technology Partnership Program, Ministry of Science and Technology of China
(KY201401003), the National Nature Science Foundation of China
(No. 51576082), the Hubei Provincal Nature Science Foundation of
China (No.2016CFC757) and the Foundation of State Key Laboratory
of Coal Combustion (No. FSKLCC1116).
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