- Email: [email protected]
Simulation of optimum control for electrodischarge dressing using neural networks
~
Int. J. Mach. Tools Manufact. Vol. 36, No. 2, pp. 173-181, 1996 Elsevier Science Ltd Printed in Great Britain 0890-6955/96t9.50 + .00
Pergamon
SIMULATION OF OPTIMUM CONTROL FOR ELECTRODISCHARGE DRESSING USING NEURAL NETWORKS JEONG-DU KIMi" and EUN-SANG LEEI" (Received 18 May
1994;
in final form
15
March 1 9 9 5 )
Abstract--A neural identifier and a neural controller for optimum control of the electro-discharge dressing systems are proposed. A modeling of a system is obtained from a neural identifier and a neural control structure satisfying stability is proposed. Computer simulation results show that the proposed neural identifier not only gives accurate modeling results but also can find the relationship of the electro-discharge dressing system. In addition, the proposed neural controller gives very effective control according to gap increase by the learning process in spite of the nonlinear characteristics of electro-discharge conditions.
INTRODUCTION
Currently, developments in the mechatronics and optical industry have brought a rapid increase in the use of brittle materials such as silicon, ferrite, ceramics and optical glass. The completion of mirror surface grinding is required for good quality of these brittle materials. Because of high hardness and brittleness cracking and chipping are apt to generate in the grinding of brittle materials [1]. Lapping and polishing are used for mirror surface generation of these materials, but have gradually replaced the high precision grinding [2]. Accordingly, as it becomes possible to produce economically superabrasive diamond and CBN wheel, the brittle materials such as ferrite, ceramic, silicon and optical glass become suitable for grinding. On the other hand, the mirror surface grinding is possible using the superabrasive wheel of more than No. 1000 [3]. The efficient dressing of the superabrasive wheel is difficult due to loading and glazing [4]. And the optimum control according to increase in the gap is important for the dressing of a metal bond grinding wheel using electro-discharge machining. Neural networks have been used as the selection system for machining conditions by E.D.M. [5]. A conventional control method for system linearization using a precise mathematical model requires a perfect understanding of a system. However, by using neural network models we can identify and control a system with some available information [6]. A back-propagation net has been used successfully to model nonlinear chemical systems [7]. A multilayered neural network processor is proposed for training the neural controller to provide the appropriate inputs to the plant [8]. Therefore, back-propagation neural networks are used for the optimum control of gap, electro-discharge voltage and current. This study proposes a neural identifier and a neural controller for constant electrodischarge current and voltage. An appropriate controller output (system input: xo,/on, Ip) is obtained by the learning function. Comparison is performed between a controller using neural networks and that using experimental data for dressing system with gap varying input signal. Computer simulation shows that back-propagation neural networks which have the classification and the generalization function [9] used for the identifier and the controller not only yield accurate results but also can be effectively trained for nonlinear dressing systems with complex characteristics.
?Department of MechanicalEngineering,Korea AdvancedInstitute of Scienceand Technology,373-1, Kusong-dong,Yusong-gu,Taejon, 305-701, Korea. 173
174
Jeong-Du Kim and Eun-Sang Lee BACK-PROPAGATION NEURAL NETWORK FOR OPTIMUM CONTROL
The construction of identifier and controller for optimum control for the dressing of a metal bond grinding wheel is achieved using neural networks. The learning algorithm is a back-propagation error network, and makes use of a set of randomized weights distributed uniformly between -0.5 and 0.5 [10]. Input pattern of the identifier is peak current (Ip), pulse duration ('ton), pulse pause (%n) and gap. Output pattern is gap voltage (V) and current (I). Input pattern of neural network controller is V, I and gap. Output pattern is peak current (Ip), pulse duration ('ton) and pulse pause (Toll). Using sigmoid function f, output Opj of hidden layer unit j is as follows [ 11 ], netpj = Y, WjiOpi--t- 0j
(1)
Opj = ~ (netpj).
(2)
Using connection strengths Wkj and offset Ok of output unit k, output Opk of output layer unit k is as follows, netpk = E WkjOpj + Ok Opk = fk(netpk).
(3) (4)
From the error between target output tpk and actual output Opk , offset error ~pk of output unit k is as follows, ~pk = (tpk -- Opk)f~(netpk) •
(5)
Using ~pk, Wkj and netpi, offset error ~pj of hidden layer j is ~pj = fj(netpk) • ~pkWkj •
(6)
The connection strengths Wkj and offset Ok are changed as follows, Wkj = Wkj + c~~pkWpj
(7)
Ok = Ok + [3 ~pk.
(8)
The connection strengths Wji and offset Oj are changed as follows, Wji : Wji + ot ~piWpi
(9)
0i = Oj + 138pj.
(10)
Learning pattern is repeated by experimental data for system identification. Momentum method [11] is as follows, W(t) = d + a A W ( t -
1),
(11)
where W(t) is connection strength function, d is error correction scale and a is momentum parameter. For the verification of back-propagation program, the XOR problem is solved first. Sigmoid function becomes a positive number by using 2/(1 + e -a ,¢tpj) _ 1, where a is slope of sigmoid function.
Electro-discharge Dressing using Neural Networks
175
Table 1. Experimental conditions
Grinding machine
Surface grinding machine (wacheon WGS-64)
Wheel
D4000
Wheel speed
1800 rev/min
Table speed
5 m/min
Wheel for truing
GC180 (Brake type Truier)
Power source
Ip = 0-3.75 A "ro./off = 5-200 ).~sec
Electrode
Copper (1/3 of wheel size)
Gap sensor
Model AEC 5505 Photonics Co. (Eddy current type) Resolution: 0.5 p.m
MODELING OF CONTROL SYSTEM
Identification modeling of automatic electro-discharge dressing controller makes use of real experimental values for learning. Table I represents the experimental conditions. Figure 1 shows the automatic control mechanism of gap current and voltage change for electro-discharge dressing. For the measurement of wheel gap an eddy current type gap sensor is installed; a gap signal transmits to the computer via a gap converter. The terminals of an automatic electro-discharge current and voltage controller are linked to the interface board which is connected to A / D and D / A converters. The target of the control system is to keep up the optimum dressing. The result of target is to control
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176
Jeong-Du Kim and Eun-Sang Lee
%,, %ff and Ip for appropriate I and V. Figure 2 shows optimum control system for constant dressing by using a neural network. To get V, I and gap signals from the system, learning data using neural networks, ~'o,, "rolland lp are controlled for optimum dressing. By the error distance of V, I value between desired and control, the error back-propagation progresses in the identifier. After convergence to the desired value, this system can be used on-line for optimum dressing. The back-propagation networks with multilayer are used for identifying and controlling of the system. The optimum control system of electro-discharge dressing is shown in Fig. 3. The output I, V of identifier using neural networks is obtained from each of the 4-8-2-1 networks. The neural network for control is composed of 3-6-2-1 networks. The input units are the gap distance, gap voltage and gap current. The number of hidden layers is selected for minimum output errors by trial and error computing. The output of controller is the peak current, pulse duration and pulse pause which have each of the different connections strength and offset. Namely, this model is composed of several multi-input and single-output (MISO) networks. A general control method can make use of one network for control. Neural network models of the multi-input and multioutput (MIMO) system used in this simulation are networks of three output units for the controller and networks of two output units for the identifier. This MIMO simulation result is compared with MISO results. In electro-discharge dressing system modeling by using back-propagation neural networks, the learning for identification is performed with experimental data, and after the identification process is completed, a neural controller is also trained. This model is counteracted by starting the system with a set of randomized weights distributed uniformly between -0.5 and +0.5. Optimum scale mapping value is the range from 0.7 to 1.8 for learning. Optimum slope of sigmoid function for identifier is 0.9 and controller is 0.05. SIMULATION
The simulation is carried out for the identification and the control of optimum electro-discharge dressing. Figure 4 is the comparison of experimental data and simulation data which are the current and voltage simulation of identifier according to gap change. In spite of steep change of experimental value at 23.7 ~,m gap, the simulation value by using neural networks is similar to the experimental. And by using the networks of two hidden layers the simulation output perfectly approaches the experimental. Using MISO (4-8-2-1) networks excellent identifier results are obtained in comparison with MIMO (4-4-2). Figure 5 shows the comparison between the experimental electro-discharge and this simulation voltage and current according to the variation of peak current in the constant 23.7 tim gap. When one hidden layer is used, a trend is similar but some error exists.
Back-propagation by output error
Actual I,V
Desired I, V
r
(EDM Conlroller)
N
Ik
v W Fig. 2. Optimum control system for dressing by using neural network.
Electro-discharge Dressing using Neural Networks
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Thus, in this neural network one hidden layer is added for the reduction of error. The output of simulation yields below 3% error by using each of connection strength and offset value. When the peak current between metal bond wheel and electrode is varied, the electro-discharge current and voltage have a nonlinear term about the condition of wheel and electrode, but simulation results using the MISO network follow after the nonlinear actual tendency. Therefore, the simulation for optimum electro-discharge dressing is useful in the application of actual control system. Figure 6 shows the tendency of current and voltage according to pulse duration in the condition of constant peak current. The neural network (4-8-2-1) output follows after a tendency of experiment exactly, and the output error of experiment and simulation is reduced prominently. By using the system identification through learning method the results of simulation are approximately the same as that of experiment and the identifier for the optimum control of electro-discharge dressing traces well the nonlinear behavior of the system according to each condition. Figure 7 shows the experimental trend similarly, but the output error using the MIMO network (3-3-3) is large in the neural network controller with electro-discharge 21.2 p,m gap. Thus by the addition of a hidden layer and the use of single output, the output error is reduced greatly. In fixing electro-discharge 100 p,m (%,) pulse duration, the simulation value of pulse duration by using a multi-output network, a large error occurred according to the variation of electro-discharge voltage. Using neural network (3-6-2-1) of a single output diminishes the output error.
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It turns out that the addition of a hidden layer and the separation of output unit become more effective for the optimum control of electro-discharge dressing. Because of the decrease of gap current with the increase of electro-discharge gap, for optimum electro-discharge dressing it is important to keep this current constant. Figure 8 shows the control current by neural network of controller ( 3 - 6 - 2 - 1 ) and network of identifier ( 4 - 8 - 2 - 1 ) through learning when we specify desired current as 0.8, 1.2 and 1.6 A. As the gap increases, the control current on desired (Id) shows a
Electro-discharge Dressing using Neural Networks 40
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little error but is kept constant. This peak current (Ip) represents the input of identifier and the output of neural network controller for the dressing control by gap increase. The peak current must rise extremely at the 24 gm gap for maintaining a constant current. By controlling the peak current (Ip) using neural networks, the control current (I) for optimum dressing approaches the desired current. Therefore, the optimum control using neural networks is very useful for maintaining a stable dressing effect. From this simulation, the identifier and controller with multi-input and single-output
180
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neural networks become more effective structures and they give more accurate results for the control of the nonlinear electro-discharge dressing system. CONCLUSIONS Using back-propagation networks the identification of electro-discharge dressing control system generates a little error of simulation value in comparison with the experimental value. But, a trend between simulation and experiment is similar. After convergence by learning, the simulation value of neural network controller follows the trend of the nonlinear experimental value exactly. Therefore, this neural network controller can be applied to a real dressing system. From this simulation the identifier and controller with multi-input and single-output neural networks become more effective structures and give more accurate results for the control of nonlinear electro-discharge dressing systems. Computer simulation shows that back-propagation neural networks which have the approximation and general function used for the identifier and the controller not only yield reasonable results but also can find the unknown electro-discharge dressing system with nonlinear characteristics. T h e r e f o r e the optimum control of electro-discharge dressing is useful in using neural networks in spite of the nonlinear characteristics of the dressing gap, electrode, pulse power source and metal bond wheel. REFERENCES [1] A. B. Oroenou and J. D. B. Veldkamp, Grinding brittle materials, Philips Tech. Rev. 38, 131-144 (1979). [2] H. Ohmori, Elid mirror surface grinding technologywith electrolytic in-processdressing, Elid Grinding Research Group, pp. 8-31 (1991). [3] The trend and future of mirror like grinding, Material Fabrication Laboratory, pp. 147-148 (1991). [4] R. Komanduri and W. R. Reed, A new technique of dressing and conditioning resin bonded superabrasire grinding wheel, Ann. CIRP 29, 239-243 (1980). [5] Y. Konishi, M. Hasegawa and I. Sugimoto, Recognition of EDM process using neural network, Int. JSPE 25(3), 206-207 (1991). [6] K. S. Narendra and K. Parthasrsthy, Identificationand control of dynamicsystem using neural network, IEEE Trans., Neural Networks, pp. 4-27 (1990). [7] N. V. Bhat, P. A. Minderman, T. McAvoy and N. S. Wang, Modeling chemical process systems via neural computation, IEEE Control Sys. Mag., pp. 24-30 (1990).
Electro-discharge Dressing using Neural Networks
181
[8] D. Psaltis, A. Sideris and A. A. Yamamura, A multilayered neural network controller, IEEE Control Sys. Mag., pp. 17-21 (1988). [9] M. Lee, S. Y. Lee and C. H. Park, Neural controller of nonlinear dynamic systems using higher neural networks, Electron. Lett. 28(3), 276-277 (1992). [10] J. A. Freeman and D. M. Skapura, Neural Networks, pp. 89-105. Addison-Wesley, Reading, MA (1991). [11] M. Y. Park and H. S. Choi, Neurocomputer, pp. 17-73. Daeyoungsa (1991).
Int. J. Mach. Tools Manufact. Vol. 36, No. 2, pp. 173-181, 1996 Elsevier Science Ltd Printed in Great Britain 0890-6955/96t9.50 + .00
Pergamon
SIMULATION OF OPTIMUM CONTROL FOR ELECTRODISCHARGE DRESSING USING NEURAL NETWORKS JEONG-DU KIMi" and EUN-SANG LEEI" (Received 18 May
1994;
in final form
15
March 1 9 9 5 )
Abstract--A neural identifier and a neural controller for optimum control of the electro-discharge dressing systems are proposed. A modeling of a system is obtained from a neural identifier and a neural control structure satisfying stability is proposed. Computer simulation results show that the proposed neural identifier not only gives accurate modeling results but also can find the relationship of the electro-discharge dressing system. In addition, the proposed neural controller gives very effective control according to gap increase by the learning process in spite of the nonlinear characteristics of electro-discharge conditions.
INTRODUCTION
Currently, developments in the mechatronics and optical industry have brought a rapid increase in the use of brittle materials such as silicon, ferrite, ceramics and optical glass. The completion of mirror surface grinding is required for good quality of these brittle materials. Because of high hardness and brittleness cracking and chipping are apt to generate in the grinding of brittle materials [1]. Lapping and polishing are used for mirror surface generation of these materials, but have gradually replaced the high precision grinding [2]. Accordingly, as it becomes possible to produce economically superabrasive diamond and CBN wheel, the brittle materials such as ferrite, ceramic, silicon and optical glass become suitable for grinding. On the other hand, the mirror surface grinding is possible using the superabrasive wheel of more than No. 1000 [3]. The efficient dressing of the superabrasive wheel is difficult due to loading and glazing [4]. And the optimum control according to increase in the gap is important for the dressing of a metal bond grinding wheel using electro-discharge machining. Neural networks have been used as the selection system for machining conditions by E.D.M. [5]. A conventional control method for system linearization using a precise mathematical model requires a perfect understanding of a system. However, by using neural network models we can identify and control a system with some available information [6]. A back-propagation net has been used successfully to model nonlinear chemical systems [7]. A multilayered neural network processor is proposed for training the neural controller to provide the appropriate inputs to the plant [8]. Therefore, back-propagation neural networks are used for the optimum control of gap, electro-discharge voltage and current. This study proposes a neural identifier and a neural controller for constant electrodischarge current and voltage. An appropriate controller output (system input: xo,/on, Ip) is obtained by the learning function. Comparison is performed between a controller using neural networks and that using experimental data for dressing system with gap varying input signal. Computer simulation shows that back-propagation neural networks which have the classification and the generalization function [9] used for the identifier and the controller not only yield accurate results but also can be effectively trained for nonlinear dressing systems with complex characteristics.
?Department of MechanicalEngineering,Korea AdvancedInstitute of Scienceand Technology,373-1, Kusong-dong,Yusong-gu,Taejon, 305-701, Korea. 173
174
Jeong-Du Kim and Eun-Sang Lee BACK-PROPAGATION NEURAL NETWORK FOR OPTIMUM CONTROL
The construction of identifier and controller for optimum control for the dressing of a metal bond grinding wheel is achieved using neural networks. The learning algorithm is a back-propagation error network, and makes use of a set of randomized weights distributed uniformly between -0.5 and 0.5 [10]. Input pattern of the identifier is peak current (Ip), pulse duration ('ton), pulse pause (%n) and gap. Output pattern is gap voltage (V) and current (I). Input pattern of neural network controller is V, I and gap. Output pattern is peak current (Ip), pulse duration ('ton) and pulse pause (Toll). Using sigmoid function f, output Opj of hidden layer unit j is as follows [ 11 ], netpj = Y, WjiOpi--t- 0j
(1)
Opj = ~ (netpj).
(2)
Using connection strengths Wkj and offset Ok of output unit k, output Opk of output layer unit k is as follows, netpk = E WkjOpj + Ok Opk = fk(netpk).
(3) (4)
From the error between target output tpk and actual output Opk , offset error ~pk of output unit k is as follows, ~pk = (tpk -- Opk)f~(netpk) •
(5)
Using ~pk, Wkj and netpi, offset error ~pj of hidden layer j is ~pj = fj(netpk) • ~pkWkj •
(6)
The connection strengths Wkj and offset Ok are changed as follows, Wkj = Wkj + c~~pkWpj
(7)
Ok = Ok + [3 ~pk.
(8)
The connection strengths Wji and offset Oj are changed as follows, Wji : Wji + ot ~piWpi
(9)
0i = Oj + 138pj.
(10)
Learning pattern is repeated by experimental data for system identification. Momentum method [11] is as follows, W(t) = d + a A W ( t -
1),
(11)
where W(t) is connection strength function, d is error correction scale and a is momentum parameter. For the verification of back-propagation program, the XOR problem is solved first. Sigmoid function becomes a positive number by using 2/(1 + e -a ,¢tpj) _ 1, where a is slope of sigmoid function.
Electro-discharge Dressing using Neural Networks
175
Table 1. Experimental conditions
Grinding machine
Surface grinding machine (wacheon WGS-64)
Wheel
D4000
Wheel speed
1800 rev/min
Table speed
5 m/min
Wheel for truing
GC180 (Brake type Truier)
Power source
Ip = 0-3.75 A "ro./off = 5-200 ).~sec
Electrode
Copper (1/3 of wheel size)
Gap sensor
Model AEC 5505 Photonics Co. (Eddy current type) Resolution: 0.5 p.m
MODELING OF CONTROL SYSTEM
Identification modeling of automatic electro-discharge dressing controller makes use of real experimental values for learning. Table I represents the experimental conditions. Figure 1 shows the automatic control mechanism of gap current and voltage change for electro-discharge dressing. For the measurement of wheel gap an eddy current type gap sensor is installed; a gap signal transmits to the computer via a gap converter. The terminals of an automatic electro-discharge current and voltage controller are linked to the interface board which is connected to A / D and D / A converters. The target of the control system is to keep up the optimum dressing. The result of target is to control
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Fig. 1. Automatic control mechanism of gap current and voltage change for electro-discharge dressing.
176
Jeong-Du Kim and Eun-Sang Lee
%,, %ff and Ip for appropriate I and V. Figure 2 shows optimum control system for constant dressing by using a neural network. To get V, I and gap signals from the system, learning data using neural networks, ~'o,, "rolland lp are controlled for optimum dressing. By the error distance of V, I value between desired and control, the error back-propagation progresses in the identifier. After convergence to the desired value, this system can be used on-line for optimum dressing. The back-propagation networks with multilayer are used for identifying and controlling of the system. The optimum control system of electro-discharge dressing is shown in Fig. 3. The output I, V of identifier using neural networks is obtained from each of the 4-8-2-1 networks. The neural network for control is composed of 3-6-2-1 networks. The input units are the gap distance, gap voltage and gap current. The number of hidden layers is selected for minimum output errors by trial and error computing. The output of controller is the peak current, pulse duration and pulse pause which have each of the different connections strength and offset. Namely, this model is composed of several multi-input and single-output (MISO) networks. A general control method can make use of one network for control. Neural network models of the multi-input and multioutput (MIMO) system used in this simulation are networks of three output units for the controller and networks of two output units for the identifier. This MIMO simulation result is compared with MISO results. In electro-discharge dressing system modeling by using back-propagation neural networks, the learning for identification is performed with experimental data, and after the identification process is completed, a neural controller is also trained. This model is counteracted by starting the system with a set of randomized weights distributed uniformly between -0.5 and +0.5. Optimum scale mapping value is the range from 0.7 to 1.8 for learning. Optimum slope of sigmoid function for identifier is 0.9 and controller is 0.05. SIMULATION
The simulation is carried out for the identification and the control of optimum electro-discharge dressing. Figure 4 is the comparison of experimental data and simulation data which are the current and voltage simulation of identifier according to gap change. In spite of steep change of experimental value at 23.7 ~,m gap, the simulation value by using neural networks is similar to the experimental. And by using the networks of two hidden layers the simulation output perfectly approaches the experimental. Using MISO (4-8-2-1) networks excellent identifier results are obtained in comparison with MIMO (4-4-2). Figure 5 shows the comparison between the experimental electro-discharge and this simulation voltage and current according to the variation of peak current in the constant 23.7 tim gap. When one hidden layer is used, a trend is similar but some error exists.
Back-propagation by output error
Actual I,V
Desired I, V
r
(EDM Conlroller)
N
Ik
v W Fig. 2. Optimum control system for dressing by using neural network.
Electro-discharge Dressing using Neural Networks
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Thus, in this neural network one hidden layer is added for the reduction of error. The output of simulation yields below 3% error by using each of connection strength and offset value. When the peak current between metal bond wheel and electrode is varied, the electro-discharge current and voltage have a nonlinear term about the condition of wheel and electrode, but simulation results using the MISO network follow after the nonlinear actual tendency. Therefore, the simulation for optimum electro-discharge dressing is useful in the application of actual control system. Figure 6 shows the tendency of current and voltage according to pulse duration in the condition of constant peak current. The neural network (4-8-2-1) output follows after a tendency of experiment exactly, and the output error of experiment and simulation is reduced prominently. By using the system identification through learning method the results of simulation are approximately the same as that of experiment and the identifier for the optimum control of electro-discharge dressing traces well the nonlinear behavior of the system according to each condition. Figure 7 shows the experimental trend similarly, but the output error using the MIMO network (3-3-3) is large in the neural network controller with electro-discharge 21.2 p,m gap. Thus by the addition of a hidden layer and the use of single output, the output error is reduced greatly. In fixing electro-discharge 100 p,m (%,) pulse duration, the simulation value of pulse duration by using a multi-output network, a large error occurred according to the variation of electro-discharge voltage. Using neural network (3-6-2-1) of a single output diminishes the output error.
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25
Gap(/_~rn) Fig. 4. S i m u l a t i o n
of identifier
a c c o r d i n g t o g a p (lp = 3.75 A , ,o. imental v a l u e ; S i m : S i m u l a t i o n
= 100 I~se¢, %n = 5 I~sec). Exp: Expervalue.
60
2.5 '''....
"-~.~ 48
.... " ..... -~'~-~ ~ ~
4 42 " ~'"" • ..
• ""
21
17
0 ;::>
24
/f
<
.<
I/// :t/--
....'"" 4 2 4 _ 2 1.3
12
Exp. Sim.
I
09
MISO . . . .
. M~°._:.U:LLIJ i
~
~
h
2 35
2.7
305
3 4
0.5 175
~p (A) Fig. 5. S i m u l a t i o n o f i d e n t i f i e r a c c o r d i n g t o p e a k c u r r e n t . ( G a p = 23.7 p,m, % , = 100 I~sec, % n = 5 I~sec.)
It turns out that the addition of a hidden layer and the separation of output unit become more effective for the optimum control of electro-discharge dressing. Because of the decrease of gap current with the increase of electro-discharge gap, for optimum electro-discharge dressing it is important to keep this current constant. Figure 8 shows the control current by neural network of controller ( 3 - 6 - 2 - 1 ) and network of identifier ( 4 - 8 - 2 - 1 ) through learning when we specify desired current as 0.8, 1.2 and 1.6 A. As the gap increases, the control current on desired (Id) shows a
Electro-discharge Dressing using Neural Networks 40
179 2.9
4- 4- 2
\
'
28
1 46
"~'"~. 24
~
4-4-2 ~
9 1
0 98
"...................
Sire.
MI~O....... 20
i
40
I
~
104
72
,, ....
136
0 5
168
200
Ton (/.~sec) Fig. 6. Simulation of identifier according to pulse duration. (Gap = 21.2 izm, Ip = 3.75 A, %ff = 5 p.sec.)
3.75
3.1
.
~ii'"'..
150
120
3-3-3 ~ '
""',:: . . . . . . . . . . ./.
3-6-2-1 .....
245
"~'~"..,. ,
90
3-a-3
Z
". J
"',..
Ip
8o ~
1.8
116
I .... 0.,5
.....
25
I
30
L
t
t
31
37
43
~.
49
0
55
Voltage Fig. 7. Simulation of controUcr according to voltage. (Gap = 21.2 p.m.)
little error but is kept constant. This peak current (Ip) represents the input of identifier and the output of neural network controller for the dressing control by gap increase. The peak current must rise extremely at the 24 gm gap for maintaining a constant current. By controlling the peak current (Ip) using neural networks, the control current (I) for optimum dressing approaches the desired current. Therefore, the optimum control using neural networks is very useful for maintaining a stable dressing effect. From this simulation, the identifier and controller with multi-input and single-output
180
Jeong-Du Kim and Eun-Sang Lee 1.8
4.5
16
1.4
35
1.2
3
v 1 ca
25
"~ 09 i.
l 6A
08
2
m L) 0.6
1 2A
04
08A
15
r~ca
Id (desired current) - -
I (controlcurrent) - - Ip (peakcurrent)
02
0 16
18'
210
212
~I 4
0.5
26
0
Gap ( /l m) Fig. 8. Simulation result for the control of desired current
(ld = 0.8,
1.2, 1.6 A).
neural networks become more effective structures and they give more accurate results for the control of the nonlinear electro-discharge dressing system. CONCLUSIONS Using back-propagation networks the identification of electro-discharge dressing control system generates a little error of simulation value in comparison with the experimental value. But, a trend between simulation and experiment is similar. After convergence by learning, the simulation value of neural network controller follows the trend of the nonlinear experimental value exactly. Therefore, this neural network controller can be applied to a real dressing system. From this simulation the identifier and controller with multi-input and single-output neural networks become more effective structures and give more accurate results for the control of nonlinear electro-discharge dressing systems. Computer simulation shows that back-propagation neural networks which have the approximation and general function used for the identifier and the controller not only yield reasonable results but also can find the unknown electro-discharge dressing system with nonlinear characteristics. T h e r e f o r e the optimum control of electro-discharge dressing is useful in using neural networks in spite of the nonlinear characteristics of the dressing gap, electrode, pulse power source and metal bond wheel. REFERENCES [1] A. B. Oroenou and J. D. B. Veldkamp, Grinding brittle materials, Philips Tech. Rev. 38, 131-144 (1979). [2] H. Ohmori, Elid mirror surface grinding technologywith electrolytic in-processdressing, Elid Grinding Research Group, pp. 8-31 (1991). [3] The trend and future of mirror like grinding, Material Fabrication Laboratory, pp. 147-148 (1991). [4] R. Komanduri and W. R. Reed, A new technique of dressing and conditioning resin bonded superabrasire grinding wheel, Ann. CIRP 29, 239-243 (1980). [5] Y. Konishi, M. Hasegawa and I. Sugimoto, Recognition of EDM process using neural network, Int. JSPE 25(3), 206-207 (1991). [6] K. S. Narendra and K. Parthasrsthy, Identificationand control of dynamicsystem using neural network, IEEE Trans., Neural Networks, pp. 4-27 (1990). [7] N. V. Bhat, P. A. Minderman, T. McAvoy and N. S. Wang, Modeling chemical process systems via neural computation, IEEE Control Sys. Mag., pp. 24-30 (1990).
Electro-discharge Dressing using Neural Networks
181
[8] D. Psaltis, A. Sideris and A. A. Yamamura, A multilayered neural network controller, IEEE Control Sys. Mag., pp. 17-21 (1988). [9] M. Lee, S. Y. Lee and C. H. Park, Neural controller of nonlinear dynamic systems using higher neural networks, Electron. Lett. 28(3), 276-277 (1992). [10] J. A. Freeman and D. M. Skapura, Neural Networks, pp. 89-105. Addison-Wesley, Reading, MA (1991). [11] M. Y. Park and H. S. Choi, Neurocomputer, pp. 17-73. Daeyoungsa (1991).