- Email: [email protected]
Novel Design Method for the Ball Mill Pulverizing System Based on Fuzzy Reasoning and Auto-Tuning PID Control
Copyright <1::> 2001 IFAC IFAC Conference on New Technologies for Computer Control 19-22 November 2001, Hong Kong
NOVEL DESIGN METHOD FOR THE BALL MILL PULVERIZING SYSTEM BASED ON FUZZY REASONING AND AUTO-TUNING PID CONTROL
·Xiao-Feng Li
Ju-Hua Zhang
Deng-Ying Zhu
Cui Zhang
-Instrument and Power Plant Control Department. Guangdong Power Test and Research Institute. 73 Meihua Road, Guangzhou 510600. China. Email: [email protected]
Abstract: The pulverizing process of a ball mill is rather complex. It is difficult to obtain the optimal control by the conventional control methods, so a new fuzzy self-optimizing control method is presented. The method divides the controller into two parts: the fuzzy adaptive PID control and the supervisory fuzzy control. The self-optimizing inference sub-system of supervisory fuzzy control is proposed for solving imprecise constrains optimization problems, and fuzzy self-optimizing interval and fuzzy se1f-optimizing step are applied to speed the rate of self-optimizing and improve the accuracy of self-optimizing. The fuzzy adaptive PID controller combines fuzzy self-adjusting PID control with fuzzy rough-tuning mechanism. The operation result shows that it is quite suitable for the control of mill and a large amount of electric energy is saved. Copyright 200f IFAC Keywords: Fuzzy Self-Optimizing, Fuzzy Rough Tuning, Mill Level Control, Specifications on Phase and Gain Margin (SPGM), Ball Mill Pulverizes System.
1. INTRODUCTION In most processes there are some extra degrees of freedom that can be used for optimization purposes. The development of optimization techniques requires a reasonably accurate description of the process. The optimal operation point can be difficult to maintain if measure imprecision and model uncertainty are present. Self-optimizing control is an approach to solve this problem by turning the optimization into a set point problem. The key idea is to find a measurable variable with assJred value at optimal operation. If this variable can be found, a feedback control loop will be closed to keep the variable at the set point, and to keep indirectly the process an optimal operation. IThis work has been supported by the Guangdong Power Group Co.• contract JA6098009.
Unfortunately, some variables are difficult to quantitatively measure for many industrial processes including a ball mill for pulverizing system. The ball mill is of strong non linearity, uncertainty, time-variance and serious interconnection (i. e. some of the variables may not be linearly independent) etc. Therefore, it is impossible to establish a precise model for the ball mill. The interactions between operating conditions and the quantity of coal in the mill are complicated and have not been quantitatively studied in a systematic way. Thus in such a multi-variable system, the controlled variable (quantity of coal) is difficult to measure directly, but it can be acquired through the impreCIsIOn relationships between quantity of coal and other easily measured parameters. However. years of industrial practice and research have led to the knowledge for this relationship. This knowledge is represented in the qualitative descriptions and the
505
semi-empirical correlation. In these circumstances, the conventional techniques do not contribute as much as expected to an acceptable (economic) performance of the optimizing control for the ball mill process systems.
increase of pulverization output mcrease, the consumption increases a little. So the unit consumption reduces as pulverization output increases, and it is desirable to keep the mill working at high output level with high economical advantage.
Fuzzy relational model put, the processing of thinking, analyzing and inference into a linguistic analyzing mathematical module, which enables us to convert the natural language into algorithms for computer to accept and operate.
Until recently it was the general understanding that reliable measurement of the mill loading was impossible. Conventional methods such as pressure difference between inlet and outlet, power of driving motor, temperature at outlet, etc. all involve significant disadvantages concerning practical handling and infornlation value.
In this paper, we present an industrial application case, in which a fuzzy relational modeling and self-optimizing approach are applied to a ball mill with available knowledge sources, to optimize the process operation.
In fig. I, the relation between the power input to the driving motor(l), vibration magnitude signal of the front end of the axial(2), difference in pressure between that at the inlet and that at outlet(3) and the pulverization output( 4) with respect to the quantity of coal in the mill are shown, where the horizontal axis is the quantity of the mill. It can be seen that, in operation, the raw coal feeder continuously sends coal into the mill. The quantity of coal in the mill increases and the driving motor power also increases. When pulverization output (rate of pulverized coal output) continuously increases, the maximum of the pulverization output is on the right of the motor power.
2. MEASUREMENT OF MILL LOADING AND OPERATION CHARACTERISTICS OF THE BALL MILL The ball mill, as compared to other types of pulverizing facilities, has the advantages of high reliability, long service life, and low maintenance and is widely used in China. Its shortcoming is of high-energy consumption for pulverization. The consumption is high at no-load running. With the
.
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ptimal ~e!atinj~oint move
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-~:.,..; • : -:,.:
IyII
Fig. l. Operation characteristics of the ball mill Obviously, to bring the operating point near the maximum pulverization will not only save electrical energy input, but also enhance the pulverization capability. From curve(2), it can be seen that when the quantity of coal in the mill is small, vibration
signal is large as the hitting and collision between ball and coal, and between ball and ball are heavy. When the quantity of coal in the mill increases, the vibration signal becomes smaller. Curve(4) show that when coal quantity increases, the pulverization
506
output increases , and when the pulverization output passes the maximum, the pulverization output drop and the quantity of in-feed raw coal exceeds the pulverization capability, the quantity of coal in the mill increases rapidly, and the mill will be choked. Curve(3) show that before the pulverization output reaches the maximum, the pressure difference changes slowly and steadily. When the pulverization output passes the maximum, and the in-feed raw coal further increases, the pressure difference increase slowly at first and then rapidly till the mill is blocked. From the field tests it has been found that the equipment based on piezoelectric vibration pickup was preferable for measuring ball mill material level, which only give the imprecision correlation.
the mill and the measurable variables. They only give the imprecision correlation . But We can fuse them together and make a credible quantity of coal. In the new fuzzy self-optimizing approach, a self-optimizing step is represented a<; the variant step length and self-optimizing interval is represented as the variant advance interval. It is expected that the specific self-optimizing step length (OS) and self-optimizing interval (OT) depend on the concentrations of ~P, ml-OP, but the exact forms of the dependence are unknown: OS=Fs(~P, OT=Fr(~P,
In fig. 1, the operation can be divided into three regions: I, II and Ill. In region 1, the unit energy consumption of the mill is high with low pulverization. In region m, the mill is vulnerable to block. In region n, the operation is most desirable. Thus, to achieve optimal results requires an operating point close to the region III. Tf blockage occurs the process must be stopped and the mill manually cleaned, thus operators run the process far away from this optimal point. This results in high operational energy costs.
ml-OP) ml-OP)
(2) (3)
Fuzzy sets and membership functions of the process variables are used to characterize degree to approach the steady operating constraint value. For example, equation 4 is a membership function representing a fuzzy constraint "the pressure difference ~P less than or approximately equal to the operating constraint value of pressure difference ~PL'" with a tolerance 1: JlM (SP)= 11 { 1+exp[(~P-ML)l1]}
(4)
Table 1 Rule set for adjusting the self-optimizing step length (OS). Z stands for zero
We nominally operate at the optimum but the optimal operating point has moved due to some unknown variations of the coal quality. We want to compute the optimal move in the available manipulative variable in order to follow the real optimum. With model uncertainty and imprecisely measurable variables it may be difiicult to tell which direction the free variable should be move in order to bring the process closer to the real optimum. In this case, a fuzzy self-optimizing control replaced the fixed setpoints control [Li 2001] .
~P
OS
ml-OP
S
M
B
SS
S
M
B
S
SS
S
M
M
Z
S
S
B BB
Z
SS
S
Z
Z
SS
Table 2 Rule set for adjusting the self-optimizing interval (OT). I stand for infinite
3. FUZZY SELF-OPTIMIZING ON THE MILL The objective here is to maximize the quantity of coal in the mill while maintaining the manipulated operation variables within a desired range. The optimizing control problem cau be formulated as:
~P<~Plimit
OT
maxE(ML) ,ilL
m1-0P
(1)
Subject to the inequality constraints: X. PL<)(P<)(PH, XTL
S
M
B
SS
B
S
S
S
B
M
S
M
I
M
M
B
B
M
BB
I
B
Thus, the fuzzy linguistic models are used to approximate the unknown functions Fs and Fr. The model consists of if-then rules. In the fuzzy set, two kinds of rules are used: "optimizing step kind" and "optimizing interval kind". The optimizing step kind rule is with the following form:
X~P!0(6.Plh
The optimization objectives are not always clearly defined in the pulverizing process of the ball mill because the quantity of coal in the mill is difiicult to measure directly. From the section 2, we know that the mapping exists between the quantity of coal in
If (ml-OP is Xi and ~P-LlPL is Yi) Then (increment of
507
to constraint value, the step length closed to zero and the interval closed to infinite, the self-optimizing schedule halted.
the optimizing step is .1SP i }. The optimizing interval kind rule is with the following fonn: If (ml-OP is Xj and M-.1P L is Yj ) Then (optimizing interval is Tj ).
The constraint value of the variable is with a little margin away from the steady operating boundary. This gives the system some degree of tolerance to cope with stochastic fluctuation of process variables.
Thus a set of rules, as show in table I and table 2, may be used to adjust the step length (OS) and the interval (OT), respectively. The rule base of the model contains rules for all possible combinations of the antecedent linguistic terms (SS, S. M. B. etc.). and the membership functions have been extracted from the process measurementc; by fuzzy set.
4. FUZZY ROUGH-TUNING MECHANISM Fuzzy self-adjusting PID controller schemes have enjoyed considerable success both in academia and industry since their development [He 1993, Li 2000]. They have been widely applied to systems subject to stochastic disturbance. For the global optimizing control, it turned out that it is very hard to achieve acceptable control perfonnance by the fuzzy self-adjusting pro systems. They cannot effectively deal with the strong nonlinearities of global optimizing control. Due to the strong nonlinearities of the optimizing control, it is well motivated to study control schemes in which optimal linear controllers are applied in combination with various control scheduling methods. Thus, a controller scheduling procedure based on the interpolation of the PID control law rather than the PlO parameter of the control law is more successful for the optimizing control. This procedure bears a close resemblance to an approach in the modeling context. in which a nonlinear model is formed by interpol~tion between local linear models.
In this approach, the step length and the interval of self-optimizing are variants based on the distance between the variable of the operating point and the steady operating constraint value, which are represented as descending and ascending functions, respectively. The setpoints at each step are the variables to be adjusted by the fuzzy self-optimizing system and become the new values. When the variable of the operating point moves from the inside to the boundary of a constraining region, the step length function decreased gradually close to zero and the interval function increased gradually close to infinite, the fuzzy self-optimizing procedure forces the system to slow down the ascending rate of the optimizing set-point. This means that it changes from the fully allowable to completely forbidden state. When the variable of the operating point close
Supervisory fuzzy control Fuzzy self-optimi
zcr ~
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. __ '_'_ 0_0_._0_ 0_'_'_'_'---'_'- ---- '- _._._ ._._
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ID co trol
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+"-
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+
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+
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Material level ~ dP! fuzzy adaptive PlO 1-4.....--~....,.. ....
Pressure auto-tuning PlO
lH.
:->"" I
Temperature fuzzy adaptive PlO
l._._._._._._._._._._._._._~~~~~lfj
Fig. 2.
Control scheme for discussion of propose algorithm
508
In this section, a new Fuzzy self-adaptive PID controller based on fuzzy rough-tuning approach will be presented that can effectively deal with changes in operating condition occurrence. To cope with the noniinearities, a set of PID control laws can be designed by using the SPGM tuning formulas for various stationary points of the self-optimizing course and the global control is implemented by smoothly aggregating the laws with their relevant contribution with respect to the various operating conditions. The aggregation of control structure yields a nonlinear control system for the optimizing pulverizes operation. The essence of fuzzy rough-tuning mechanism is that at every time instance, the mechanism evaluates the trend of the operating conditions to detect the possible deviation from a prescribed operating condition. The aggregation of control structl're yields a nonlinear control system for the optimizing pulverizes operation. If a deviation is found, the appropriate control law according to the local operating condition of the deviation will be generated instantaneously to adapt it.
SO-SP nis {82%, 97%}; the universes of discourse of XP n is {86.014, 89.139}, the universes of discourse of TOn is {50.37, 142.31}, and the universes of discourse of Tin is {115 .75, 297.86}.
5. APPLICATION ON BALL MILL PULVERIZER SYSTEM Fig. 3 is the real time curves in manual operation. It can be seen that the curves jump up and down demonstrating the improper action of the manual control with unsteady ball mill operation.
It is well known that the optimizing set-point of the
material level (ML-SP) has mostly influence on quantity of coal in the mill. The relationship between optimizing set-point and control law will change when the operating condition changes, and may result in a new set of PID parameters. Therefore, we are able to build the fuzzy rule in the following fom1.
9
o
4
6 Time (hour)
Fig. 3. The real-time curve of the parameters during operation.
_."-_1..........
IF set-point is SO-SP n THEN XP is XP n and Tl is Tin and T D is Tdn.
-- --
Where XP n , Tin and T cln are the linguistic values of PID parameters; SO-SPn is the linguistic value of set-point.
.... ~ .
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~.
---;~-~-P;;~~: Jifl~--·--~-~,~ .
Table 3 Fuzzy rough-tuning rules ML-SP
Material Le\'el Loop
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..... .....
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..:
-c. .
XP
s
B
S
S
B
S
B
B
Time (hour)
Fig. 4. The real-time curve of the paranleters during SPGM+SFT.
The particular examination that was used in Table 3 is given in Table 4. The universes of discourse of
Table 4 Tuning value of material level control loop under difference coal quantity
SO-SP XP
TI
TD
97%
76.833
234.57
202.57
89.139
297.86
142.31
94.899
359.03
94.757
82%
71.403
91.152
69.361
86.014
115.75
50.37
93.558
139.52
33.644
Results of the SFT PID controllers are shown in Fig.
4. The SFT PID controllers can keep very small
509
deviations of Temperature, Pressure, Coal level and Pressure difference respectively. On Aug. l8, 2000, the optimization results were tested in the mill operation under FSO+FST +FRT control, which is shown in Fig.5. Fig. 6 shows the variation of coal level under FSO+FST control.
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.
~
. i-:·.,:"~::;:,:,~:··---7···
---
1I
: : : l ; i L __ --~dc'=:;::.::;:::1S;CQaI:-lc~lA . i--o........:.~- ..u h= ~:•.';':t;;-?t-.\,r 7". I{v"...... -; -~::"v~f::r.::-i
7
6
·..,·! _
5
6
o
Fig.6. The real-time curve of the parameters during FSO+FST. An optimization strategy for the operation of a complex pulverizing system is realized by Fuzzy self-optimizing control and fuzzy adaptive PID control system. This new fuzzy control system has been successfully commissioned, and remarkable improvement of the system behavior is reached. It is an ideal control system for the ball mill pulverizing system.
o
Time [hour]
Fig.5. The real-time curve of the parameters during FSO+FST+FRT. Fig. 6. shows the variation of coal level under FSO+FST control. It can be clearly seen that the stability of the coal level is widely improved by the FSO+FST+FRT control. In the same way, the coal level deviation from the setpoints of fuzzy self-optimizing is tightly regulated and optimizing time is shortened.
REFERENCES He S. Z., S. H Tan, C. C Hang. and P. Z. Wang (1993). Control of Dynamical Processes Using A on-line Rule-Adaptive Fuzzy Control System,
The FSO+FST+FRT control system proves itself to be capable of promoting solvent quality, saving energy and providing more reliable function. The results were encouraged, increasing in production rate, saving in energy within a reasonable operating condition. In the trial production period from 2000 Jan to 2000 Nov, the fuzzy self-optimizing control system managed to get unit energy consumption for pulverizing reduced by 14.87%. Compared to the manual operation, the FSO+FST+FRT control system saves about RMB 560, 000 in energy and produce costs per year in the No. I boiler of Meixin Power Plant.
6.
0:---
Time [hour]
C'C-.·!.•. ~:=~,_J.ij.~~;h==t:~~ 9
10
1··. - -
Fuzzy Sets and System, 54, 11-22. Li X. F. (2000). Application of The Fuzzy Adaptive PID to A Power Plant. iFAC Symposium on Power Plant and Power Systems Control 2000, Brussels, Belgium. April 26-29. Li X. F. (2000) The Realization of Fuzzy Self-Tuning PID Control Based on DCS, industrial lnstnlmentation & Automation (Chinese) 155, 31-33. Li X. F. (2001). Fuzzy Self-Optimizing Control System and Its Application. Control and Instruments in Chemical Industrial (Chinese), 179,27-30. Narendra K., S. (1995) Adoption and Learning Using Multiple Models, Switching and Tuning. IEEE tralZS. 011 control system, 37-51. Skogestad S., etc. (1999) Plantwide Control: The Search for The Self-Optimizing Control Structure. i4th IFAC World Congress, Beijing, July 1999, 325-330.
CONCLUSIONS
The ball mill control system has been running in the Meixin Power Plant since January 4 in 2000. The running results show that it has possessed characteristics of reasonable design, operating convenience, quick response and good stability.
510
NOVEL DESIGN METHOD FOR THE BALL MILL PULVERIZING SYSTEM BASED ON FUZZY REASONING AND AUTO-TUNING PID CONTROL
·Xiao-Feng Li
Ju-Hua Zhang
Deng-Ying Zhu
Cui Zhang
-Instrument and Power Plant Control Department. Guangdong Power Test and Research Institute. 73 Meihua Road, Guangzhou 510600. China. Email: [email protected]
Abstract: The pulverizing process of a ball mill is rather complex. It is difficult to obtain the optimal control by the conventional control methods, so a new fuzzy self-optimizing control method is presented. The method divides the controller into two parts: the fuzzy adaptive PID control and the supervisory fuzzy control. The self-optimizing inference sub-system of supervisory fuzzy control is proposed for solving imprecise constrains optimization problems, and fuzzy self-optimizing interval and fuzzy se1f-optimizing step are applied to speed the rate of self-optimizing and improve the accuracy of self-optimizing. The fuzzy adaptive PID controller combines fuzzy self-adjusting PID control with fuzzy rough-tuning mechanism. The operation result shows that it is quite suitable for the control of mill and a large amount of electric energy is saved. Copyright 200f IFAC Keywords: Fuzzy Self-Optimizing, Fuzzy Rough Tuning, Mill Level Control, Specifications on Phase and Gain Margin (SPGM), Ball Mill Pulverizes System.
1. INTRODUCTION In most processes there are some extra degrees of freedom that can be used for optimization purposes. The development of optimization techniques requires a reasonably accurate description of the process. The optimal operation point can be difficult to maintain if measure imprecision and model uncertainty are present. Self-optimizing control is an approach to solve this problem by turning the optimization into a set point problem. The key idea is to find a measurable variable with assJred value at optimal operation. If this variable can be found, a feedback control loop will be closed to keep the variable at the set point, and to keep indirectly the process an optimal operation. IThis work has been supported by the Guangdong Power Group Co.• contract JA6098009.
Unfortunately, some variables are difficult to quantitatively measure for many industrial processes including a ball mill for pulverizing system. The ball mill is of strong non linearity, uncertainty, time-variance and serious interconnection (i. e. some of the variables may not be linearly independent) etc. Therefore, it is impossible to establish a precise model for the ball mill. The interactions between operating conditions and the quantity of coal in the mill are complicated and have not been quantitatively studied in a systematic way. Thus in such a multi-variable system, the controlled variable (quantity of coal) is difficult to measure directly, but it can be acquired through the impreCIsIOn relationships between quantity of coal and other easily measured parameters. However. years of industrial practice and research have led to the knowledge for this relationship. This knowledge is represented in the qualitative descriptions and the
505
semi-empirical correlation. In these circumstances, the conventional techniques do not contribute as much as expected to an acceptable (economic) performance of the optimizing control for the ball mill process systems.
increase of pulverization output mcrease, the consumption increases a little. So the unit consumption reduces as pulverization output increases, and it is desirable to keep the mill working at high output level with high economical advantage.
Fuzzy relational model put, the processing of thinking, analyzing and inference into a linguistic analyzing mathematical module, which enables us to convert the natural language into algorithms for computer to accept and operate.
Until recently it was the general understanding that reliable measurement of the mill loading was impossible. Conventional methods such as pressure difference between inlet and outlet, power of driving motor, temperature at outlet, etc. all involve significant disadvantages concerning practical handling and infornlation value.
In this paper, we present an industrial application case, in which a fuzzy relational modeling and self-optimizing approach are applied to a ball mill with available knowledge sources, to optimize the process operation.
In fig. I, the relation between the power input to the driving motor(l), vibration magnitude signal of the front end of the axial(2), difference in pressure between that at the inlet and that at outlet(3) and the pulverization output( 4) with respect to the quantity of coal in the mill are shown, where the horizontal axis is the quantity of the mill. It can be seen that, in operation, the raw coal feeder continuously sends coal into the mill. The quantity of coal in the mill increases and the driving motor power also increases. When pulverization output (rate of pulverized coal output) continuously increases, the maximum of the pulverization output is on the right of the motor power.
2. MEASUREMENT OF MILL LOADING AND OPERATION CHARACTERISTICS OF THE BALL MILL The ball mill, as compared to other types of pulverizing facilities, has the advantages of high reliability, long service life, and low maintenance and is widely used in China. Its shortcoming is of high-energy consumption for pulverization. The consumption is high at no-load running. With the
.
%
/
/
/
/
ptimal ~e!atinj~oint move
.............
/
.· L
,-:: ~ :
.......... r · ,' ::: f: " .':'1: . . .' :::;!, ·.r . , ::: '~ I :Power 0 f' motor • . 1.'
.. .....; . c ~
•
J •
,
• • •• (
• . J'.
I
-: ·h
':- : .
• I·
':-
2:Vibration signal
:- L::: :t! . \1 ': f ·: ~: ~ ~ 3:Dlfference pressure
\ :
2~1
' . 1.', : : :~ :
4
~
\
I\. I I
i :: : ~ I :> I
• I·
:- L '
:-. . J.:, :::t7; :: 4:p.uIVeriZation I. I
\.
· I' . . ~/.
.. ...:..i~·
: :
. .
· ~r .
r:(: output
1· .10. : .. .). .. -- .... ,. {~I'.": : : ~: - -:;ar~""'~"-:'-:" - -.-r. ~ .•:
. . ~-=..:=r~: I:
~,,--:,":,.......
. . . +",:."
...... -.:... .. ..,,-
I I
I
•
-
'.......
......
..{". ': :0,,0 ::f~ :- LIII :::t: . O.r. ' M ...•.
....:.,L-. . ,-
II
. I-
I
Coal quantity in the mill
I
-~:.,..; • : -:,.:
IyII
Fig. l. Operation characteristics of the ball mill Obviously, to bring the operating point near the maximum pulverization will not only save electrical energy input, but also enhance the pulverization capability. From curve(2), it can be seen that when the quantity of coal in the mill is small, vibration
signal is large as the hitting and collision between ball and coal, and between ball and ball are heavy. When the quantity of coal in the mill increases, the vibration signal becomes smaller. Curve(4) show that when coal quantity increases, the pulverization
506
output increases , and when the pulverization output passes the maximum, the pulverization output drop and the quantity of in-feed raw coal exceeds the pulverization capability, the quantity of coal in the mill increases rapidly, and the mill will be choked. Curve(3) show that before the pulverization output reaches the maximum, the pressure difference changes slowly and steadily. When the pulverization output passes the maximum, and the in-feed raw coal further increases, the pressure difference increase slowly at first and then rapidly till the mill is blocked. From the field tests it has been found that the equipment based on piezoelectric vibration pickup was preferable for measuring ball mill material level, which only give the imprecision correlation.
the mill and the measurable variables. They only give the imprecision correlation . But We can fuse them together and make a credible quantity of coal. In the new fuzzy self-optimizing approach, a self-optimizing step is represented a<; the variant step length and self-optimizing interval is represented as the variant advance interval. It is expected that the specific self-optimizing step length (OS) and self-optimizing interval (OT) depend on the concentrations of ~P, ml-OP, but the exact forms of the dependence are unknown: OS=Fs(~P, OT=Fr(~P,
In fig. 1, the operation can be divided into three regions: I, II and Ill. In region 1, the unit energy consumption of the mill is high with low pulverization. In region m, the mill is vulnerable to block. In region n, the operation is most desirable. Thus, to achieve optimal results requires an operating point close to the region III. Tf blockage occurs the process must be stopped and the mill manually cleaned, thus operators run the process far away from this optimal point. This results in high operational energy costs.
ml-OP) ml-OP)
(2) (3)
Fuzzy sets and membership functions of the process variables are used to characterize degree to approach the steady operating constraint value. For example, equation 4 is a membership function representing a fuzzy constraint "the pressure difference ~P less than or approximately equal to the operating constraint value of pressure difference ~PL'" with a tolerance 1: JlM (SP)= 11 { 1+exp[(~P-ML)l1]}
(4)
Table 1 Rule set for adjusting the self-optimizing step length (OS). Z stands for zero
We nominally operate at the optimum but the optimal operating point has moved due to some unknown variations of the coal quality. We want to compute the optimal move in the available manipulative variable in order to follow the real optimum. With model uncertainty and imprecisely measurable variables it may be difiicult to tell which direction the free variable should be move in order to bring the process closer to the real optimum. In this case, a fuzzy self-optimizing control replaced the fixed setpoints control [Li 2001] .
~P
OS
ml-OP
S
M
B
SS
S
M
B
S
SS
S
M
M
Z
S
S
B BB
Z
SS
S
Z
Z
SS
Table 2 Rule set for adjusting the self-optimizing interval (OT). I stand for infinite
3. FUZZY SELF-OPTIMIZING ON THE MILL The objective here is to maximize the quantity of coal in the mill while maintaining the manipulated operation variables within a desired range. The optimizing control problem cau be formulated as:
~P<~Plimit
OT
maxE(ML) ,ilL
m1-0P
(1)
Subject to the inequality constraints: X. PL<)(P<)(PH, XTL
S
M
B
SS
B
S
S
S
B
M
S
M
I
M
M
B
B
M
BB
I
B
Thus, the fuzzy linguistic models are used to approximate the unknown functions Fs and Fr. The model consists of if-then rules. In the fuzzy set, two kinds of rules are used: "optimizing step kind" and "optimizing interval kind". The optimizing step kind rule is with the following form:
X~P!0(6.Plh
The optimization objectives are not always clearly defined in the pulverizing process of the ball mill because the quantity of coal in the mill is difiicult to measure directly. From the section 2, we know that the mapping exists between the quantity of coal in
If (ml-OP is Xi and ~P-LlPL is Yi) Then (increment of
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to constraint value, the step length closed to zero and the interval closed to infinite, the self-optimizing schedule halted.
the optimizing step is .1SP i }. The optimizing interval kind rule is with the following fonn: If (ml-OP is Xj and M-.1P L is Yj ) Then (optimizing interval is Tj ).
The constraint value of the variable is with a little margin away from the steady operating boundary. This gives the system some degree of tolerance to cope with stochastic fluctuation of process variables.
Thus a set of rules, as show in table I and table 2, may be used to adjust the step length (OS) and the interval (OT), respectively. The rule base of the model contains rules for all possible combinations of the antecedent linguistic terms (SS, S. M. B. etc.). and the membership functions have been extracted from the process measurementc; by fuzzy set.
4. FUZZY ROUGH-TUNING MECHANISM Fuzzy self-adjusting PID controller schemes have enjoyed considerable success both in academia and industry since their development [He 1993, Li 2000]. They have been widely applied to systems subject to stochastic disturbance. For the global optimizing control, it turned out that it is very hard to achieve acceptable control perfonnance by the fuzzy self-adjusting pro systems. They cannot effectively deal with the strong nonlinearities of global optimizing control. Due to the strong nonlinearities of the optimizing control, it is well motivated to study control schemes in which optimal linear controllers are applied in combination with various control scheduling methods. Thus, a controller scheduling procedure based on the interpolation of the PID control law rather than the PlO parameter of the control law is more successful for the optimizing control. This procedure bears a close resemblance to an approach in the modeling context. in which a nonlinear model is formed by interpol~tion between local linear models.
In this approach, the step length and the interval of self-optimizing are variants based on the distance between the variable of the operating point and the steady operating constraint value, which are represented as descending and ascending functions, respectively. The setpoints at each step are the variables to be adjusted by the fuzzy self-optimizing system and become the new values. When the variable of the operating point moves from the inside to the boundary of a constraining region, the step length function decreased gradually close to zero and the interval function increased gradually close to infinite, the fuzzy self-optimizing procedure forces the system to slow down the ascending rate of the optimizing set-point. This means that it changes from the fully allowable to completely forbidden state. When the variable of the operating point close
Supervisory fuzzy control Fuzzy self-optimi
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Fig. 2.
Control scheme for discussion of propose algorithm
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In this section, a new Fuzzy self-adaptive PID controller based on fuzzy rough-tuning approach will be presented that can effectively deal with changes in operating condition occurrence. To cope with the noniinearities, a set of PID control laws can be designed by using the SPGM tuning formulas for various stationary points of the self-optimizing course and the global control is implemented by smoothly aggregating the laws with their relevant contribution with respect to the various operating conditions. The aggregation of control structure yields a nonlinear control system for the optimizing pulverizes operation. The essence of fuzzy rough-tuning mechanism is that at every time instance, the mechanism evaluates the trend of the operating conditions to detect the possible deviation from a prescribed operating condition. The aggregation of control structl're yields a nonlinear control system for the optimizing pulverizes operation. If a deviation is found, the appropriate control law according to the local operating condition of the deviation will be generated instantaneously to adapt it.
SO-SP nis {82%, 97%}; the universes of discourse of XP n is {86.014, 89.139}, the universes of discourse of TOn is {50.37, 142.31}, and the universes of discourse of Tin is {115 .75, 297.86}.
5. APPLICATION ON BALL MILL PULVERIZER SYSTEM Fig. 3 is the real time curves in manual operation. It can be seen that the curves jump up and down demonstrating the improper action of the manual control with unsteady ball mill operation.
It is well known that the optimizing set-point of the
material level (ML-SP) has mostly influence on quantity of coal in the mill. The relationship between optimizing set-point and control law will change when the operating condition changes, and may result in a new set of PID parameters. Therefore, we are able to build the fuzzy rule in the following fom1.
9
o
4
6 Time (hour)
Fig. 3. The real-time curve of the parameters during operation.
_."-_1..........
IF set-point is SO-SP n THEN XP is XP n and Tl is Tin and T D is Tdn.
-- --
Where XP n , Tin and T cln are the linguistic values of PID parameters; SO-SPn is the linguistic value of set-point.
.... ~ .
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11
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.
i
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~.
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Table 3 Fuzzy rough-tuning rules ML-SP
Material Le\'el Loop
.
; Fl!l:dcr re ....olution (;\uto)
..... .....
..... : ....... '
~ ,
..:
-c. .
XP
s
B
S
S
B
S
B
B
Time (hour)
Fig. 4. The real-time curve of the paranleters during SPGM+SFT.
The particular examination that was used in Table 3 is given in Table 4. The universes of discourse of
Table 4 Tuning value of material level control loop under difference coal quantity
SO-SP XP
TI
TD
97%
76.833
234.57
202.57
89.139
297.86
142.31
94.899
359.03
94.757
82%
71.403
91.152
69.361
86.014
115.75
50.37
93.558
139.52
33.644
Results of the SFT PID controllers are shown in Fig.
4. The SFT PID controllers can keep very small
509
deviations of Temperature, Pressure, Coal level and Pressure difference respectively. On Aug. l8, 2000, the optimization results were tested in the mill operation under FSO+FST +FRT control, which is shown in Fig.5. Fig. 6 shows the variation of coal level under FSO+FST control.
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.
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7
6
·..,·! _
5
6
o
Fig.6. The real-time curve of the parameters during FSO+FST. An optimization strategy for the operation of a complex pulverizing system is realized by Fuzzy self-optimizing control and fuzzy adaptive PID control system. This new fuzzy control system has been successfully commissioned, and remarkable improvement of the system behavior is reached. It is an ideal control system for the ball mill pulverizing system.
o
Time [hour]
Fig.5. The real-time curve of the parameters during FSO+FST+FRT. Fig. 6. shows the variation of coal level under FSO+FST control. It can be clearly seen that the stability of the coal level is widely improved by the FSO+FST+FRT control. In the same way, the coal level deviation from the setpoints of fuzzy self-optimizing is tightly regulated and optimizing time is shortened.
REFERENCES He S. Z., S. H Tan, C. C Hang. and P. Z. Wang (1993). Control of Dynamical Processes Using A on-line Rule-Adaptive Fuzzy Control System,
The FSO+FST+FRT control system proves itself to be capable of promoting solvent quality, saving energy and providing more reliable function. The results were encouraged, increasing in production rate, saving in energy within a reasonable operating condition. In the trial production period from 2000 Jan to 2000 Nov, the fuzzy self-optimizing control system managed to get unit energy consumption for pulverizing reduced by 14.87%. Compared to the manual operation, the FSO+FST+FRT control system saves about RMB 560, 000 in energy and produce costs per year in the No. I boiler of Meixin Power Plant.
6.
0:---
Time [hour]
C'C-.·!.•. ~:=~,_J.ij.~~;h==t:~~ 9
10
1··. - -
Fuzzy Sets and System, 54, 11-22. Li X. F. (2000). Application of The Fuzzy Adaptive PID to A Power Plant. iFAC Symposium on Power Plant and Power Systems Control 2000, Brussels, Belgium. April 26-29. Li X. F. (2000) The Realization of Fuzzy Self-Tuning PID Control Based on DCS, industrial lnstnlmentation & Automation (Chinese) 155, 31-33. Li X. F. (2001). Fuzzy Self-Optimizing Control System and Its Application. Control and Instruments in Chemical Industrial (Chinese), 179,27-30. Narendra K., S. (1995) Adoption and Learning Using Multiple Models, Switching and Tuning. IEEE tralZS. 011 control system, 37-51. Skogestad S., etc. (1999) Plantwide Control: The Search for The Self-Optimizing Control Structure. i4th IFAC World Congress, Beijing, July 1999, 325-330.
CONCLUSIONS
The ball mill control system has been running in the Meixin Power Plant since January 4 in 2000. The running results show that it has possessed characteristics of reasonable design, operating convenience, quick response and good stability.
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