- Email: [email protected]
Fuzzy Shape Control Based on Elman Dynamic Recursion Network Prediction Model
Available online at www.sciencedirect.com
-
JOURNAL OF IRON AND STEEL RESEARCH, INTERNATIONAL. 2006, 1 3 ( 1 ) : 31-35
Fuzzy Shape Control Based on Elman Dynamic Recursion Network Prediction Model JIA Chun-yu,
LIU Hong-min
(College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, Hebei , China) Abstract: In the strip rolling process, shape control system possesses the characteristics of nonlinearity, strong coupling, time delay and time variation. Based on self-adapting Elman dynamic recursion network prediction model, the fuzzy control method was used to control the shape on four-high cold mill. T h e simulation results showed that the system can be applied to real time on line control of the shape. Key words: shape prediction; shape control; Elman dynamic recursion network; parameter self-adjusting; fuzzy control
Shape control system is a complicated system with the characteristics of typical multi-variant , time delay, strong coupling and nonlinearity. Due to the difficulty to establish precise analytic model and i he inaccuracies of classical and modern control methods based on empirical models, it is more suitable to adopt intelligent control strategy in shape Therefore, a parameter self-adcontrol system" -7'. lusting fuzzy controller was designed based on the Elman dynamic recursion network predication model to simulate shape control on four-high reversible mill. In this system, the least square method was used to realize mode recognition of shape signal by regressing and smoothly processing the online measured shape according to the polynomial functionr8991 , and further to determine the relationship between the components of shape defects and the control quantities of corresponding shape adjusting system. .4fter regressing, the function of shape signal is expressed as y =u , 2+ u2 z2 (yc,-yh, ) (1) where y is relative length difference; z is standardized width; u l is simple flatness term coefficient of shape; u2 is quadratic term coefficients of shape; yCt 1s measured value of tensile stress at i t h measuring section; and Yhz is regressed value at i t h measuring
+
section.
1
Online Shape Prediction Control
Firstly, the Elman network was used to predict the quadratic term coefficient of shape curve at the next time u Z p , and from the deviation between predicted uZP and target u Z d , the fuzzy operation was conducted to determine the correction quantity AF, of bending force of the work roll. The controlling principle of intelligent prediction of strip shape is shown in Fig. 1 , where e , ec are deviation and change rate of deviation between target and predicted shapes respectively, and J is learning error of the neural network.
Establishment of shape prediction model based on Elman dynamic recursion network Elman dynamic recursion network is applied to the neural network prediction model in Fig. 1 to predict symmetrical shape defect of strip, and the corresponding structure of Elman network is shown in Fig. 2. This network model is composed of 3-layer nerve cells, and the subscript is i ( i = 1 , 2 , 3 ) for input layer, j ( j = l , Z , . * . , m ) for hidden layer, 1 ( 1 = 1 , 2 , , m >for structure layer and s (s= 1) for output 1.1
Foundation Item: Item Sponsored by Provincial Natural Science Foundation of Hebei Province of China (E2004000206) Biography:JIA Chun-yu(1964-), Male, Doctor, Associate Professor; E-mail: jcy@ysu. edu. cn; Revised Date: May 2 3 , 2005
*
32
1 Fig. 1
Vol. 13
Journal of Iron and Steel Research, International
*
J
network predictor
I
Diagram of principle of online shape prediction control
Fig. 2
layer. The number of element in output layer was one, namely the quadratic defect coefficient of shape at time t , uzp(t>.For the input layer, the bending roll of work roll is a main shape control object for online adjusting four-high mill, and the input quantity is six, i. e. real-time measured bending force F,(t-r-l) at time t-r-1, former tension of rolled strip Tf( t - r - 1) at time t - T- 1 , real-time measured rolling force Pd(t-r-1) on drive side and P o ( t - r - l ) on work side at time t - T- 1 together with quadratic defect coefficient u2(t-1) and u2( t - 2 ) of shape at time t-1 and t - 2 , where T is time delay of detection of the shape coefficient. The nodes in structure layer are equal to those in hidden layer. T h e nerve cell func1-e-" , and the nerve tion of hidden layer is f ( x >=1 e-" cell function of the output layer is linear function. So the relationship between input and output is 1:" (t)=[F,(t-~-l) ,Tf(t-T-l) ypd(t-r-1) Po(t-T-l) ,a2 (t-1) ,uz (t-2)11x6 ( t )=1:" ( t )
+
a"
(3) (4)
1
where P is learning sample number. T h e linking values and the threshold values between hidden layer and output layer are adjusted as w,(t )=ws, ( t - 1) +:3)0:2) ( t - 1) (7) s, ( t )=0, ( t - 1 +:3) where 7 is learning speed, and 8;') is sth node's error of the output layer. = ( t )( t ) 1 0 2 3 ) ( t ) c1- oj3)( t ) = [Uzd ( t ) - U z p (t>ic3' (t)[1-1?) ( t ) ] (8) T h e weight values and the threshold values between input layer and hidden layer are adjusted as WJ* (t)=wJ~(t-l)+7$:z)011) (t-1) (9) s, ( t )=e, ( t - 1) $:,) where 8:'' is j t h node's error of the hidden layer.
+
Structure of EIman network
o:~) ( t >=azp( t >= I : ~ () t >
put layer at time t respectively; 1;')( t ) and 0:" ( t ) are input and output of hidden layer at time t respectively; 1;')( t ) and 0:')( t ) are input and output of structure layer at time t respectively; Ij3) ( t ) and 0:3) ( t ) are input and output of output layer at time t respectively; wIz is linking weight between input layer and hidden layer; wJlis linking weight between structure layer and hidden layer; w, is linking weight between hidden layer and output layer; 8, and 8, are nerve cell threshold values of hidden layer and output layer respectively. T h e output error function of the network is ~(t)=2~ 1[ a Z d ( t ) - u Z , ( t > ] 2 (6)
(5)
where 1;" ( t ) and 0,") ( t ) are input and output of in-
[c,,
1
+
c,,
1
}
+
a:,) =oy(t)[i-o:2) fey) w i { i - f [ 1 ; 2 )
( t ) 1 3 : 3 ) ~ ,
(t)=
( t ) 1 ) 3 : 3 ) ~ ~(
t)
(10)
T h e weight values between structure layer and hidden layer are adjusted as W,I(t(t>=Ze)ll(t-11)+7$:" (11) where 8;') is lth node's error of structure layer.
8F) = ~ u z d ~ t > - u z p ~ t ~ l w , f '(Ct )~] :xZ ~
Establishment of shape fuzzy control model based on parameter self-adjustment Different control strategies are used to control system due to different characteristics at various stage. General fuzzy controller is designed under specific conditions, so reasonable improvement measures are needed to obtain better control performance. T h e quantized factors R , , k 2 and the proportion factor k , in the fuzzy controller have great influences on the controller. Consequently, they are adjusted to improve the performance of the control system at different 1.2
vo. 1
Fuzzy Shape Control Based on Elman Dynamic Recursion Network Prediction Model
stages. T h e rough adjustment control is selected for arger error and error change rate, while the fine adjustment control is for minor error and its change rate. In this way, the double requests of dynamic state and static state are satisfied. The structure diE
*
33
*
agram of reconstructed system is shown in Fig. 3 , where E and EC are language variants of the shape deviation e and deviation changing rate ec respectively; U is language variant of the bending roll force correction AF,; N is adjusting multiple.
-
.*
I
Quantizing
EC
Adjustment _3
Fig. 3
Structure of shape fuzzy control system
1. 2. 1 Design o f f u z z y control query table T h e control input variants are e and ec, and the control output variant is AF,. Synthetically considering the control precision and the response speed, the language variant E , EC and U in shape's control field are divided into seven optimal fuzzy zone, i. e. positive bigness (PB) , positive middle (I'M), positive small (€5) , zero (ZE) , negative middle (NM) , negative small (NS) and negative bigness (NB). A series of control rules are generalized on the basis of the expertise's knowledge and the operator's experience, such as if E= NB and EC= NB then U= PB, accordingly a control rule list is summarized as shown in Table 1. Adopting the composed fuzzy reasoning method for reasoning and the maximum membership degree method for fuzzy , a control query list of the normal fuzzy controller is finally obtained through repeatedly debugging and correcting. 1. 2. 2 Design o f parameter self-adjusting f u z z y registration list In general fuzzy controller, the relationship among the output quantities U ( t ) , E ( t ) and E C ( t ) of the fuzzy controller at some instantaneous time is shown as U(t)=[E(t)xEC(t)].R (13) where x is Descartes's multiply operator; is fuzzy relation composing operator ; E ( t = I N T [e ( t ) k , 1, E C ( t ) =INT[e(t)k,] ; R is fuzzy relation. T h e actual output quantities of corresponding controller are I
>
querylist
Table 1
Fuzzy control rule list EC
E NB NM NS
ZE PS PM PB
NB
NM
NS
ZE
PS
PM
PB
PB PB PM PM PS ZE ZE
PB PB PM PM PS ZE ZE
PB PB PM PS ZE NS NM
PB PM PS ZE NS NM NB
PM PS ZE NM NM NB NB
ZE ZE NS NM NM NB NB
ZE ZE NS NM NM NB NB
(15) T h e above equations show that az is related to k l , k z and k , . When the values of e and ec are bigger, the control system mainly decreases the deviation t o accelerate the dynamic process, so larger control quantity should be selected. T h u s , k , and k z are reduced, and k , is increased. When the values of e and ec are smaller, the system approaches a steady state, especially for higher accuracy and non-overshooting systems such as shape control system, the distinguishabilities of e and ec should be enhanced, and k , and k, need magnifying, which are equivalent to reducing the dead zone of the fuzzy controller. At the same time, reducing k, make the step change of the control quantity small, and the minimum deviation requested can be obtained finally. T h e above analyses show that the change trends of k,and k , are
*
34
Journal of Iron and Steel Research, International
*
opposite to that of k,. For convenience, the change rates of k, and kz can be taken mutual reciprocal to that of k,. In the design of fuzzy adjusting table, the input language variants are the same as those of the control table, still E and EC. T h e adjusting multiple N is an output variable, whose language variant is CB (big contract , CM ( middle contract) , CS ( small contract) , OK (changeless), AS (low magnification), AM (middle magnification) and AB (high magnification) respectively. According to the adjusting rules, the adjusting rule table is established and given in Table 2. T h e fuzzy adjusting table is established with the adjusting rule table. Because this table is stored in the computer, looking up the corresponding table by the input value E and EC when the system is working, the adjusting quantity N will be obtained. T h e steps of the parameter self-adjusting are as follows: (1) quantizing e and ec according to initial k, and k z , ( 2 ) checking the parameter adjusting table to get N , which satisfies k l = k l N , k z = k z N and k , = k , / N , ( 3 ) repeatedly quantizing e and ec with adjusted k, , kz and k , , (4) educing U by using the quantized E and EC to query the control table, (5) educing AF, by k , multiplied by U . Table 2
Rule list of parameter adjusting
Vol. 13
garded as the initial values of the shape online prediction network model and put into the online learning function of the Elman network. At the same time, in order to fully verify the prediction effect in the whole predefined working range of work roll’s bending force, firstly the real-time shape test control program was set in the manual shape control state during rolling, and the working roll’s bending force gradually changed under the allowable range, and the real-time measured values and the corresponding output values of every parameters were online saved as data files during rolling. Fig. 4 shows the online prediction errors of the Elman dynamic recursion network and the static multilayer feed-forward network. T h e forecasting and evaluating index is percentage relative error SPRE,which is defined as following
It is seen that the precision of prediction and the stability of the Elman dynamic recursion network are better than those of the static network. T h e main reason is that the structure cells of the former can memorize the past states of the hidden layers, which acts as the input of the hidden cells at next time together with the network input, making the former have the ability of dynamic memory and reflecting dynamic process of system, and thus obtaining per-
EC
E NB NM NS ZE PS PM PB
NB
NM
NS
ZE
CB
CM CS OK OK OK CS CM
CS OK OK AS OK OK CS
CM CS OK CS
CM CB
PS
PM
PB
OK
CS
OK AM AB AM OK OK
OK OK AS
CM CS OK OK OK CS CM
CB CM
OK OK CS
CS
OK CS CM CB
2 Simulation and Experiment 2. 1 Predicted results According to the measured data of the four-high mill during rolling, the off-line training of Elman network model was made under given error precision condition. In present study, the Elman network structure was 6-6-1 model. T h e initial weights for the off-line training were chosen randomly in the range of [ - 0 . 5 , 0.51. Then, all the weights of network and the thresholds of nerve cells after offline training were substituted into the shape realtime test control application program, which are re-
-10
-5
0
5
10
SPRfi
Fig. 4
Prediction error of shape based on static multilayer feed-forward network (a> and Elman dynamic recursion network (b)
F u z z y Shape Control Based on E l m a n D y n a m i c R e c u r s i o n N e t w o r k Prediction Model
:go. 1
fect effect in prediction. T h e predicted error of shape based on static network algorithmic is about f 1 5 % , however, the error based on Elman neural network algorithmic is about & 7 % , so the latter is preciser.
2.2
Control effect
Based on the precision of the shape online prediction model based on the Elman dynamic recursion network, analog simulation of real-time control was made. Fig. 5 shows the shape real-time control of the parameter self-adjusting fuzzy prediction algorithm and general fuzzy control algorithm based on the Elman network model and the PID control algorithm. It can be seen that the shape control method has better rectification ability and steady performance.
.
PID control
---- General fuzzy control
2 m
-Parameter self-adjusting fuzzy control
-30 0
Fig. 5
3
10
20 Time/s
30
40
50
Real-time control effect of shape
Conclusions
(1) T h e parameter self-adjusting fuzzy control method is an effective method for controlling shape based on the Elman dynamic recursion network prediction model during rolling. According to the expertise’s knowledge, the operator’s experience and the self-learning, the prediction control of shape can be realized. (2) T h e Elman dynamic recursion network can predict the dynamic system, and doesn’t depend on the experiences of measured object. T h e Elman net-
-
35
work has high efficiency of learning, fast velocity of approach and strong ability of generalization, so it can be used t o the prediction of smaller network structure, especially for the dynamic prediction of nonlinear shape control system. ( 3 ) T h e real-time online correction of the quantized factors of the designed fuzzy controller can not only quicken the response speed but also improve the distinguishability with better adaptability and robustness. References: ZHANG Ji-li, QU Jin-ping, SUN Dexing, et al. T h e Method of the Real-Time Multi-Step Prediction and Control of BP Network for thc Delayed-Time System [J]. J of Harbin Institute of Technology, 2000, 7 ( 2 ) : 82-86. I,IU Bao-kun, WANG Hui, CAO Ming, et al. Direct Optimizing Predictive Control Based on Neural Network [J]. Information and Control, 1998, 27(5): 386-389 (in Chinese). I,IN Mao-qiong, CHEN Zeng-qiang , YUAN Zhu-zhi. SelfTuning Control for Neural Network Predictive Deviation Compensation Based on Damped Least Square [J]. Information and Control, 2000, 29(1): 27-33 (in Chinese). LIU Xi-mei, YU Fei. Predictive Control Based on Neural Networks [J]. Journal of Qingdao Institute of Chemical T e c h n o b gy, 1999, 20(3): 284-287 (in Chinese). T A N Yong-hong. Self-Adaption Control Based on BP Neural Network [J]. Control Theory and Application, 1994, 11(1): 84-88 (in Chinese). FAN Yu-hong, REN Chang-ming. Research of Predictive Control Based on B P Networks for Nonlinear System [J]. Journal of Tianjin University, 1999, 32(6) : 720-723 (in Chinese). WANG Chang-hong, XU Li-xin. A Local Recursion Neural Network Model and Its Application for Identification of Dynamic Systcm [J]. Journal of Harbin Institute of Technology, 1998, 3 0 ( 4 ) : 21-24 (in Chinese). LlAN Jia-chuang. Shape Control Theory and Foundation [J]. Journal Northeast Heavy Machinery Institute, 1978, l(1) : 120 (in Chinese). ZHANG Jun-zhe. ASEA Cold Strip Flatness Control System [J]. Metallurgical Industry Automation, 1990, 14(2) : 23-29 (in Chinese). FENG Dong-qing , XIE Song-he. Fuzzy Intelligent Control [MI. Beijing: Chemical Industry Press, 1998 (in Chinese).
-
JOURNAL OF IRON AND STEEL RESEARCH, INTERNATIONAL. 2006, 1 3 ( 1 ) : 31-35
Fuzzy Shape Control Based on Elman Dynamic Recursion Network Prediction Model JIA Chun-yu,
LIU Hong-min
(College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, Hebei , China) Abstract: In the strip rolling process, shape control system possesses the characteristics of nonlinearity, strong coupling, time delay and time variation. Based on self-adapting Elman dynamic recursion network prediction model, the fuzzy control method was used to control the shape on four-high cold mill. T h e simulation results showed that the system can be applied to real time on line control of the shape. Key words: shape prediction; shape control; Elman dynamic recursion network; parameter self-adjusting; fuzzy control
Shape control system is a complicated system with the characteristics of typical multi-variant , time delay, strong coupling and nonlinearity. Due to the difficulty to establish precise analytic model and i he inaccuracies of classical and modern control methods based on empirical models, it is more suitable to adopt intelligent control strategy in shape Therefore, a parameter self-adcontrol system" -7'. lusting fuzzy controller was designed based on the Elman dynamic recursion network predication model to simulate shape control on four-high reversible mill. In this system, the least square method was used to realize mode recognition of shape signal by regressing and smoothly processing the online measured shape according to the polynomial functionr8991 , and further to determine the relationship between the components of shape defects and the control quantities of corresponding shape adjusting system. .4fter regressing, the function of shape signal is expressed as y =u , 2+ u2 z2 (yc,-yh, ) (1) where y is relative length difference; z is standardized width; u l is simple flatness term coefficient of shape; u2 is quadratic term coefficients of shape; yCt 1s measured value of tensile stress at i t h measuring section; and Yhz is regressed value at i t h measuring
+
section.
1
Online Shape Prediction Control
Firstly, the Elman network was used to predict the quadratic term coefficient of shape curve at the next time u Z p , and from the deviation between predicted uZP and target u Z d , the fuzzy operation was conducted to determine the correction quantity AF, of bending force of the work roll. The controlling principle of intelligent prediction of strip shape is shown in Fig. 1 , where e , ec are deviation and change rate of deviation between target and predicted shapes respectively, and J is learning error of the neural network.
Establishment of shape prediction model based on Elman dynamic recursion network Elman dynamic recursion network is applied to the neural network prediction model in Fig. 1 to predict symmetrical shape defect of strip, and the corresponding structure of Elman network is shown in Fig. 2. This network model is composed of 3-layer nerve cells, and the subscript is i ( i = 1 , 2 , 3 ) for input layer, j ( j = l , Z , . * . , m ) for hidden layer, 1 ( 1 = 1 , 2 , , m >for structure layer and s (s= 1) for output 1.1
Foundation Item: Item Sponsored by Provincial Natural Science Foundation of Hebei Province of China (E2004000206) Biography:JIA Chun-yu(1964-), Male, Doctor, Associate Professor; E-mail: jcy@ysu. edu. cn; Revised Date: May 2 3 , 2005
*
32
1 Fig. 1
Vol. 13
Journal of Iron and Steel Research, International
*
J
network predictor
I
Diagram of principle of online shape prediction control
Fig. 2
layer. The number of element in output layer was one, namely the quadratic defect coefficient of shape at time t , uzp(t>.For the input layer, the bending roll of work roll is a main shape control object for online adjusting four-high mill, and the input quantity is six, i. e. real-time measured bending force F,(t-r-l) at time t-r-1, former tension of rolled strip Tf( t - r - 1) at time t - T- 1 , real-time measured rolling force Pd(t-r-1) on drive side and P o ( t - r - l ) on work side at time t - T- 1 together with quadratic defect coefficient u2(t-1) and u2( t - 2 ) of shape at time t-1 and t - 2 , where T is time delay of detection of the shape coefficient. The nodes in structure layer are equal to those in hidden layer. T h e nerve cell func1-e-" , and the nerve tion of hidden layer is f ( x >=1 e-" cell function of the output layer is linear function. So the relationship between input and output is 1:" (t)=[F,(t-~-l) ,Tf(t-T-l) ypd(t-r-1) Po(t-T-l) ,a2 (t-1) ,uz (t-2)11x6 ( t )=1:" ( t )
+
a"
(3) (4)
1
where P is learning sample number. T h e linking values and the threshold values between hidden layer and output layer are adjusted as w,(t )=ws, ( t - 1) +:3)0:2) ( t - 1) (7) s, ( t )=0, ( t - 1 +:3) where 7 is learning speed, and 8;') is sth node's error of the output layer. = ( t )( t ) 1 0 2 3 ) ( t ) c1- oj3)( t ) = [Uzd ( t ) - U z p (t>ic3' (t)[1-1?) ( t ) ] (8) T h e weight values and the threshold values between input layer and hidden layer are adjusted as WJ* (t)=wJ~(t-l)+7$:z)011) (t-1) (9) s, ( t )=e, ( t - 1) $:,) where 8:'' is j t h node's error of the hidden layer.
+
Structure of EIman network
o:~) ( t >=azp( t >= I : ~ () t >
put layer at time t respectively; 1;')( t ) and 0:" ( t ) are input and output of hidden layer at time t respectively; 1;')( t ) and 0:')( t ) are input and output of structure layer at time t respectively; Ij3) ( t ) and 0:3) ( t ) are input and output of output layer at time t respectively; wIz is linking weight between input layer and hidden layer; wJlis linking weight between structure layer and hidden layer; w, is linking weight between hidden layer and output layer; 8, and 8, are nerve cell threshold values of hidden layer and output layer respectively. T h e output error function of the network is ~(t)=2~ 1[ a Z d ( t ) - u Z , ( t > ] 2 (6)
(5)
where 1;" ( t ) and 0,") ( t ) are input and output of in-
[c,,
1
+
c,,
1
}
+
a:,) =oy(t)[i-o:2) fey) w i { i - f [ 1 ; 2 )
( t ) 1 3 : 3 ) ~ ,
(t)=
( t ) 1 ) 3 : 3 ) ~ ~(
t)
(10)
T h e weight values between structure layer and hidden layer are adjusted as W,I(t(t>=Ze)ll(t-11)+7$:" (11) where 8;') is lth node's error of structure layer.
8F) = ~ u z d ~ t > - u z p ~ t ~ l w , f '(Ct )~] :xZ ~
Establishment of shape fuzzy control model based on parameter self-adjustment Different control strategies are used to control system due to different characteristics at various stage. General fuzzy controller is designed under specific conditions, so reasonable improvement measures are needed to obtain better control performance. T h e quantized factors R , , k 2 and the proportion factor k , in the fuzzy controller have great influences on the controller. Consequently, they are adjusted to improve the performance of the control system at different 1.2
vo. 1
Fuzzy Shape Control Based on Elman Dynamic Recursion Network Prediction Model
stages. T h e rough adjustment control is selected for arger error and error change rate, while the fine adjustment control is for minor error and its change rate. In this way, the double requests of dynamic state and static state are satisfied. The structure diE
*
33
*
agram of reconstructed system is shown in Fig. 3 , where E and EC are language variants of the shape deviation e and deviation changing rate ec respectively; U is language variant of the bending roll force correction AF,; N is adjusting multiple.
-
.*
I
Quantizing
EC
Adjustment _3
Fig. 3
Structure of shape fuzzy control system
1. 2. 1 Design o f f u z z y control query table T h e control input variants are e and ec, and the control output variant is AF,. Synthetically considering the control precision and the response speed, the language variant E , EC and U in shape's control field are divided into seven optimal fuzzy zone, i. e. positive bigness (PB) , positive middle (I'M), positive small (€5) , zero (ZE) , negative middle (NM) , negative small (NS) and negative bigness (NB). A series of control rules are generalized on the basis of the expertise's knowledge and the operator's experience, such as if E= NB and EC= NB then U= PB, accordingly a control rule list is summarized as shown in Table 1. Adopting the composed fuzzy reasoning method for reasoning and the maximum membership degree method for fuzzy , a control query list of the normal fuzzy controller is finally obtained through repeatedly debugging and correcting. 1. 2. 2 Design o f parameter self-adjusting f u z z y registration list In general fuzzy controller, the relationship among the output quantities U ( t ) , E ( t ) and E C ( t ) of the fuzzy controller at some instantaneous time is shown as U(t)=[E(t)xEC(t)].R (13) where x is Descartes's multiply operator; is fuzzy relation composing operator ; E ( t = I N T [e ( t ) k , 1, E C ( t ) =INT[e(t)k,] ; R is fuzzy relation. T h e actual output quantities of corresponding controller are I
>
querylist
Table 1
Fuzzy control rule list EC
E NB NM NS
ZE PS PM PB
NB
NM
NS
ZE
PS
PM
PB
PB PB PM PM PS ZE ZE
PB PB PM PM PS ZE ZE
PB PB PM PS ZE NS NM
PB PM PS ZE NS NM NB
PM PS ZE NM NM NB NB
ZE ZE NS NM NM NB NB
ZE ZE NS NM NM NB NB
(15) T h e above equations show that az is related to k l , k z and k , . When the values of e and ec are bigger, the control system mainly decreases the deviation t o accelerate the dynamic process, so larger control quantity should be selected. T h u s , k , and k z are reduced, and k , is increased. When the values of e and ec are smaller, the system approaches a steady state, especially for higher accuracy and non-overshooting systems such as shape control system, the distinguishabilities of e and ec should be enhanced, and k , and k, need magnifying, which are equivalent to reducing the dead zone of the fuzzy controller. At the same time, reducing k, make the step change of the control quantity small, and the minimum deviation requested can be obtained finally. T h e above analyses show that the change trends of k,and k , are
*
34
Journal of Iron and Steel Research, International
*
opposite to that of k,. For convenience, the change rates of k, and kz can be taken mutual reciprocal to that of k,. In the design of fuzzy adjusting table, the input language variants are the same as those of the control table, still E and EC. T h e adjusting multiple N is an output variable, whose language variant is CB (big contract , CM ( middle contract) , CS ( small contract) , OK (changeless), AS (low magnification), AM (middle magnification) and AB (high magnification) respectively. According to the adjusting rules, the adjusting rule table is established and given in Table 2. T h e fuzzy adjusting table is established with the adjusting rule table. Because this table is stored in the computer, looking up the corresponding table by the input value E and EC when the system is working, the adjusting quantity N will be obtained. T h e steps of the parameter self-adjusting are as follows: (1) quantizing e and ec according to initial k, and k z , ( 2 ) checking the parameter adjusting table to get N , which satisfies k l = k l N , k z = k z N and k , = k , / N , ( 3 ) repeatedly quantizing e and ec with adjusted k, , kz and k , , (4) educing U by using the quantized E and EC to query the control table, (5) educing AF, by k , multiplied by U . Table 2
Rule list of parameter adjusting
Vol. 13
garded as the initial values of the shape online prediction network model and put into the online learning function of the Elman network. At the same time, in order to fully verify the prediction effect in the whole predefined working range of work roll’s bending force, firstly the real-time shape test control program was set in the manual shape control state during rolling, and the working roll’s bending force gradually changed under the allowable range, and the real-time measured values and the corresponding output values of every parameters were online saved as data files during rolling. Fig. 4 shows the online prediction errors of the Elman dynamic recursion network and the static multilayer feed-forward network. T h e forecasting and evaluating index is percentage relative error SPRE,which is defined as following
It is seen that the precision of prediction and the stability of the Elman dynamic recursion network are better than those of the static network. T h e main reason is that the structure cells of the former can memorize the past states of the hidden layers, which acts as the input of the hidden cells at next time together with the network input, making the former have the ability of dynamic memory and reflecting dynamic process of system, and thus obtaining per-
EC
E NB NM NS ZE PS PM PB
NB
NM
NS
ZE
CB
CM CS OK OK OK CS CM
CS OK OK AS OK OK CS
CM CS OK CS
CM CB
PS
PM
PB
OK
CS
OK AM AB AM OK OK
OK OK AS
CM CS OK OK OK CS CM
CB CM
OK OK CS
CS
OK CS CM CB
2 Simulation and Experiment 2. 1 Predicted results According to the measured data of the four-high mill during rolling, the off-line training of Elman network model was made under given error precision condition. In present study, the Elman network structure was 6-6-1 model. T h e initial weights for the off-line training were chosen randomly in the range of [ - 0 . 5 , 0.51. Then, all the weights of network and the thresholds of nerve cells after offline training were substituted into the shape realtime test control application program, which are re-
-10
-5
0
5
10
SPRfi
Fig. 4
Prediction error of shape based on static multilayer feed-forward network (a> and Elman dynamic recursion network (b)
F u z z y Shape Control Based on E l m a n D y n a m i c R e c u r s i o n N e t w o r k Prediction Model
:go. 1
fect effect in prediction. T h e predicted error of shape based on static network algorithmic is about f 1 5 % , however, the error based on Elman neural network algorithmic is about & 7 % , so the latter is preciser.
2.2
Control effect
Based on the precision of the shape online prediction model based on the Elman dynamic recursion network, analog simulation of real-time control was made. Fig. 5 shows the shape real-time control of the parameter self-adjusting fuzzy prediction algorithm and general fuzzy control algorithm based on the Elman network model and the PID control algorithm. It can be seen that the shape control method has better rectification ability and steady performance.
.
PID control
---- General fuzzy control
2 m
-Parameter self-adjusting fuzzy control
-30 0
Fig. 5
3
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20 Time/s
30
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Real-time control effect of shape
Conclusions
(1) T h e parameter self-adjusting fuzzy control method is an effective method for controlling shape based on the Elman dynamic recursion network prediction model during rolling. According to the expertise’s knowledge, the operator’s experience and the self-learning, the prediction control of shape can be realized. (2) T h e Elman dynamic recursion network can predict the dynamic system, and doesn’t depend on the experiences of measured object. T h e Elman net-
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work has high efficiency of learning, fast velocity of approach and strong ability of generalization, so it can be used t o the prediction of smaller network structure, especially for the dynamic prediction of nonlinear shape control system. ( 3 ) T h e real-time online correction of the quantized factors of the designed fuzzy controller can not only quicken the response speed but also improve the distinguishability with better adaptability and robustness. References: ZHANG Ji-li, QU Jin-ping, SUN Dexing, et al. T h e Method of the Real-Time Multi-Step Prediction and Control of BP Network for thc Delayed-Time System [J]. J of Harbin Institute of Technology, 2000, 7 ( 2 ) : 82-86. I,IU Bao-kun, WANG Hui, CAO Ming, et al. Direct Optimizing Predictive Control Based on Neural Network [J]. Information and Control, 1998, 27(5): 386-389 (in Chinese). I,IN Mao-qiong, CHEN Zeng-qiang , YUAN Zhu-zhi. SelfTuning Control for Neural Network Predictive Deviation Compensation Based on Damped Least Square [J]. Information and Control, 2000, 29(1): 27-33 (in Chinese). LIU Xi-mei, YU Fei. Predictive Control Based on Neural Networks [J]. Journal of Qingdao Institute of Chemical T e c h n o b gy, 1999, 20(3): 284-287 (in Chinese). T A N Yong-hong. Self-Adaption Control Based on BP Neural Network [J]. Control Theory and Application, 1994, 11(1): 84-88 (in Chinese). FAN Yu-hong, REN Chang-ming. Research of Predictive Control Based on B P Networks for Nonlinear System [J]. Journal of Tianjin University, 1999, 32(6) : 720-723 (in Chinese). WANG Chang-hong, XU Li-xin. A Local Recursion Neural Network Model and Its Application for Identification of Dynamic Systcm [J]. Journal of Harbin Institute of Technology, 1998, 3 0 ( 4 ) : 21-24 (in Chinese). LlAN Jia-chuang. Shape Control Theory and Foundation [J]. Journal Northeast Heavy Machinery Institute, 1978, l(1) : 120 (in Chinese). ZHANG Jun-zhe. ASEA Cold Strip Flatness Control System [J]. Metallurgical Industry Automation, 1990, 14(2) : 23-29 (in Chinese). FENG Dong-qing , XIE Song-he. Fuzzy Intelligent Control [MI. Beijing: Chemical Industry Press, 1998 (in Chinese).