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ORIGINAL ARTICLE
A precise BP neural network-based online model predictive
control strategy for die forging hydraulic press machine
Y. C. Lin
1,2,3
•Dong-Dong Chen
1,2
•Ming-Song Chen
1,2
•
Xiao-Min Chen
1,2
•Jia Li
1,2
Received: 29 January 2016 / Accepted: 12 August 2016 / Published online: 6 September 2016
ÓThe Natural Computing Applications Forum 2016
Abstract The time variance and nonlinearity of forging
processes pose great challenges to high-quality production.
In this study, a one-step-ahead model predictive control
(MPC) strategy based on backpropagation (BP) neural
network is proposed for the precise forging processes. Two
online updated BP neural networks, predictive neural net-
work (PNN) and control neural network (CNN), are
developed to accurately control the die forging hydraulic
press machine. The PNN and CNN are utilized to predict
the output (the velocity of upper die) and determine the
input (the oil pressure of driven cylinders), respectively.
The weights of neural networks are initially trained offline
and then updated online according to an error backpropa-
gation algorithm. In the proposed control strategy, only the
input and output are required, which makes the forging
process easy to be controlled. In addition, because of the
generalized ability and adaptability of neural networks, the
proposed predictive controller can well deal with the time
variance and nonlinearity of forging process. Two forging
experiments demonstrate the feasibility and effectiveness
of the proposed strategy. Moreover, comparing the pro-
posed MPC strategy with the traditional MPC approach and
PID controller, it can be found that the proposed MPC
strategy is the most effective control approach for the
practical forging process.
Keywords BP neural networks Model predictive
control Forging process
1 Introduction
The forging technology has been widely used to manu-
facture the critical components with high performance in
modern industries [1–3]. The hydraulic press machine
(HPM), which provides the forging force to shape forgings,
is one of key equipments in forging technology [2–5]. The
diagram of a typical forging process is shown in Fig. 1,
where the upper die of HPM is driven by three driving
cylinders to make the billet deformed. The cylinders are
driven by the corresponding hydraulic system, including
pumps, valves, and pipes. In order to guarantee the quality
of forgings, the velocity and position of upper die must be
accurately predicted and controlled by servo valves of
hydraulic system.
In the practical forging process, the shape of forging is
often irregular. Thus, the deformation force is nonuniform.
Moreover, the deformation behaviors of billet are very
complex and time-variant, such as the complex
microstructural evolution [6–10] and irregular metal flow
[11–15]. In addition, the driving system of the HPM is
strongly nonlinear [16,17]. The coupling between the
mechanical and hydraulic systems easily makes the forging
process complex and nonlinear. Therefore, due to the time
variance and nonlinearity of forging process, the accurate
control of HPM is a great challenge for the precise forging
process [4,18]. In the past, some control strategies have
been developed to control HPM. The PI control [19], one
of the traditional control approaches, is widely applied in
forging process. Also, the iterative learning control [20]
and sliding mode control [21] are often used to control the
&Y. C. Lin
yclin@csu.edu.cn; linyongcheng@163.com
1
School of Mechanical and Electrical Engineering, Central
South University, Changsha 410083, China
2
State Key Laboratory of High Performance Complex
Manufacturing, Changsha 410083, China
3
Light Alloy Research Institute, Central South University,
Changsha 410083, China
123
Neural Comput & Applic (2018) 29:585–596
https://doi.org/10.1007/s00521-016-2556-5
HPM. However, these control strategies simplify the
forging process to be a linear model which ignores the
influence of unknown disturbances. Therefore, these con-
trol methods cannot meet the requirements of the complex
nonlinear forging process. To better control forging pro-
cess, new control strategies or intelligent control methods
have been developed in recent years. To reduce the diffi-
culty of modeling and controlling forging process, the
system-decomposition-based multi-level control method
[4] and multi-domain modeling method [22] were proposed
to decompose the complex nonlinear system into a series of
linear systems or partition the whole operation region into
some local regions. Meanwhile, due to their superior data
processing ability, the intelligent control methods, includ-
ing neural network method [23–25], fuzzy method
[17,26–28], and support vector machine method [29–31],
have been gradually applied in the modeling and control-
ling of different industrial processes. However, these
methods are hard to be achieved online. Therefore, it is
necessary to develop a precise online control strategy for
the time-variant and nonlinear forging process.
Model predictive control (MPC) presents a dramatic
advance in theory and application of modern automatic
control [32–35]. Now, MPC has been widely applied in
many industrial fields, such as manufacturing industry
[36,37], chemical control engineering [38–41]. One-step-
Fig. 1 Diagram of the forging process: adiagram of HPM and control system; bforging process
586 Neural Comput & Applic (2018) 29:585–596
123
ahead MPC is one of the simplest MPC strategies. Due to
the simplicity and effectiveness, one-step-ahead MPC has
been successfully used in the predictive control of wind
power [42], hydroturbine governor [43], and uninterrupt-
ible power supply system [44]. In recent years, the neural
network-based model predictive control (NNMPC) strategy
has been proposed and widely applied in industrial process
control [45–47]. Up to now, one-step-ahead NNMPC has
not been applied in the predictive control of HPM in the
forging process.
In this study, a backpropagation (BP) neural network-
based online MPC strategy is firstly developed to control
HPM in the time-variant and nonlinear forging process.
The developed control strategy employs two neural net-
works, predictive neural network (PNN) and control neural
network (CNN), to simplify the traditional MPC. The PNN
is trained to predict the output of system, while the CNN is
updated to determine the optimal input. Finally, the feasi-
bility and effectivity of the developed control strategy are
verified by two practical forging experiments on 4000T
HPM. Moreover, the performances of the proposed and
traditional MPC approaches and PID controller are com-
pared and analyzed.
2 BP neural network-based online model
predictive control
2.1 Model predictive control
Briefly, the flowchart of traditional MPC is shown in Fig. 2,
where u,y, y
d
,y
r
,y
m
, and y
p
denote the input, output, set
value, reference, predictive output, and revised predictive
output, respectively. MPC is mainly composed of predictive
model, reference target planning, feedback compensation,
and rolling optimization [48]. At each control level, the
predictive output y
m
, which is obtained by predictive model,
is used to determine the revised predictive output y
p
by
feedback compensation. Then, the input uis optimally
determined by comparing the revised predictive output y
p
and reference y
r
. The whole process will be online iterative
until the output of system reaches the set value y
d
.
In this study, the BP neural network-based MPC, which
follows the course of traditional MPC, is a one-step-ahead
control strategy. The sequence for determining the pre-
dictive output y
m
, revised predictive output y
p
, reference y
r
,
input u, and output yis shown in Fig. 3. The solid line and
dash line represent the past and future processes, respec-
tively. At each control level, the predictive output y
m
is
firstly determined by the predictive model, and then the
revised predictive output y
p
, reference y
r
, and input uare
obtained by the feedback compensation, reference target
planning, and rolling optimization, respectively. Finally,
the output yis obtained in the process. Meanwhile, the next
control level is starting and the new predictive output y
m
is
predicted by the predictive model.
2.2 Predictive neural network
Although the proposed control strategy follows the struc-
ture of traditional MPC, the PNN is used to replace the
predictive model in traditional MPC to predict the output of
system. Then, the control of forging process can be sim-
plified to some extent. The architecture of PNN is shown in
Fig. 4. Here, the PNN has 5 inputs, 11 neurons in the
Fig. 2 Flowchart of traditional MPC (u,y, y
d
,y
r
,y
m
, and y
p
denote
the input, output, set value, reference, predictive output, and revised
predictive output)
Fig. 3 Sequence for determining the predictive output y
m
, revised
predictive output y
p
, reference y
r
, input u, and output y
Neural Comput & Applic (2018) 29:585–596 587
123
hidden layer, and 1 output. Additionally, the PNN model
can be expressed as:
ymðkþ1Þ¼fp½uðk2Þ;uðk1Þ;uðkÞ;yðk1Þ;yðkÞ ð1Þ
where yðk1Þand yðkÞare the (k-1)th and kth practical
outputs of the system, respectively. uðk2Þ,uðk1Þ, and
uðkÞare the (k-2)th, (k-1)th, and kth inputs for the
system, respectively. ymðkþ1Þdenotes the (k?1)th
predictive output of the system.
In the PNN, Wp1 2R115and Wp2 2R111 denote the
input–hidden and hidden–output connection weight matri-
ces, respectively. Also, bp1 2R111and bp2 2R11rep-
resent the input–hidden and hidden–output bias terms. The
activation function used in PNN is shown as:
gðxÞ¼ 1
1þexð2Þ
Then, the state and output equations of PNN are
np1i¼X
5
j¼1
Wp1ijUjþbp1ii¼1;2;11 ð3Þ
hp1i¼gðnp1iÞi¼1;2;11 ð4Þ
np2 ¼X
11
i¼1
Wp2ihp1iþbp2 ð5Þ
ymðkþ1Þ¼gðnp2Þð6Þ
where Urepresents the inputs of the PNN ½uðk2Þ;
uðk1Þ;uðkÞ;yðk1Þ;yðkÞ; np1 and hp1 denote the input
and output of the hidden layer, respectively; np2 and ym
denote the input and output of the output layer,
respectively.
2.3 Control neural network
In the proposed control strategy, the CNN is used to gen-
erate the optimal control signal, which is simpler and lower
time-consuming compared to the traditional rolling opti-
mization method. The architecture of CNN is shown in
Fig. 5. Here, the CNN has 4 inputs, 9 neurons in the hidden
layer, and 1 output. Then, the CNN model can be expressed
as:
uðkþ1Þ¼fc½yrðkþ1Þ;ypðkþ1Þ;uðk1Þ;uðkÞ ð7Þ
where uðk1Þ,uðkÞ, and uðkþ1Þare the (k-1)th, kth,
and (k?1)th practical inputs of the system, respectively.
yrðkþ1Þand ypðkþ1Þdenote the (k?1)th reference and
revised predictive output of the system, respectively.
In the CNN, Wc1 2R94and Wc2 2R19denote the
input–hidden and hidden–output connection weight matri-
ces, respectively. Also, bc1 2R91and bc2 2R11repre-
sent the input–hidden and hidden–output bias terms. The
activation function used in CNN is the same as that used in
PNN.
So, the state and output equations of CNN are
nc1i¼X
4
j¼1
Wc1ijYjþbc1ii¼1;2;9ð8Þ
hc1i¼gðnc1iÞi¼1;2;9ð9Þ
nc2 ¼X
9
i¼1
Wc2ihc1iþbc2 ð10Þ
uðkþ1Þ¼gðnc2Þð11Þ
where Yrepresents the inputs of CNN ½yrðkþ1Þ;
ypðkþ1Þ;uðk1Þ;uðkÞ, and nc1, hc1, nc2, and uðkþ1Þ
denote the input of hidden layer, the output of hidden layer,
the input of output layer, and the output of output layer,
respectively.
Fig. 4 Architecture of PNN
Fig. 5 Architecture of CNN
588 Neural Comput & Applic (2018) 29:585–596
123
2.4 Online update of PNN
According to the procedure of MPC, when the (k?1)th
practical output of system, i.e., yðkþ1Þ, is observed, the
weight matrices and bias terms of the PNN can be updated
online to predict the next time predictive output of system.
For the PNN, the cost function can be defined as:
E¼1
2yðkþ1Þymðkþ1Þ½
2ð12Þ
According to the backpropagation algorithm, the
weights of PNN can be updated as:
wiðkþ1Þ¼wiðkÞþDwiðkÞð13Þ
DwiðkÞ¼g
oEðkÞ
owiðkÞð14Þ
where grepresents the learning rate.
2.4.1 Update of hidden–output weights
The weight-updating formula of hidden–output can be
expressed as:
DWp2i¼g
oE
oWp2i
¼g
oE
oymðkþ1Þ
oymðkþ1Þ
onp2
onp2
oWp2i
ð15Þ
where oE
oymðkþ1Þ¼ yðkþ1Þymðkþ1Þ½,oymðkþ1Þ
onp2 ¼
ymðkþ1Þð1ymðkþ1ÞÞ,onp2
oWp2i¼hp1i
So, DWp2ican be expressed by,
DWp2i¼gyðkþ1Þymðkþ1Þ½ymðkþ1Þ
ð1ymðkþ1ÞÞ hp1i
ð16Þ
Similarly, the bias-term-updating formula of hidden–
output can be expressed as:
Dbp2 ¼g
oE
obp2 ¼g
oE
oymðkþ1Þ
oymðkþ1Þ
onp2
onp2
obp2 ð17Þ
where onp2
obp2 ¼1:
Therefore, Dbp2 can be calculated as,
Dbp2 ¼gyðkþ1Þymðkþ1Þ½ymðkþ1Þ
ð1ymðkþ1ÞÞ ð18Þ
2.4.2 Update of input–hidden weights
The weight-updating formula of input–hidden can be
expressed as:
DWp1ij ¼g
oE
oWp1ij
¼g
oE
oymðkþ1Þ
oymðkþ1Þ
onp2
onp2
ohp1i
ohp1i
onp1i
onp1i
oWp1ij
ð19Þ
where onp2
ohp1i¼Wp2i,ohp1i
onp1i¼hp1ið1hp1iÞ,onp1i
oWp1ij ¼
Uj:
So, DWp1ij can be expressed by,
DWp1ij ¼gyðkþ1Þymðkþ1Þ½ymðkþ1Þ
ð1ymðkþ1ÞÞ Wp2ihp1ið1hp1iÞUj
ð20Þ
Similarly, the bias-term-updating formula of input–hid-
den can be expressed as:
Dbp1i¼g
oE
obp1i
¼g
oE
oymðkþ1Þ
oymðkþ1Þ
onp2
onp2
ohp1i
ohp1i
onp1i
onp1i
obp1i
ð21Þ
where onp1i
obp1i¼1:
Therefore, Dbp1ican be calculated as,
Dbp1i¼gyðkþ1Þymðkþ1Þ½ymðkþ1Þ
ð1ymðkþ1ÞÞ Wp2ihp1ið1hp1iÞ
ð22Þ
2.5 Online update of CNN
In the traditional MPC, the control signal is always
obtained by rolling optimization method in real time. Then,
the weight matrices and bias terms of CNN should also be
updated online to determine the next time input of system.
For the CNN, according to the objective function of rolling
optimization method, the cost function is defined as:
J¼1
2yrðkþ1Þypðkþ1Þ
2ð23Þ
According to the backpropagation algorithm, the
weights of CNN can be updated as:
wiðkþ1Þ¼wiðkÞþDwiðkÞð24Þ
DwiðkÞ¼g
oJðkÞ
owiðkÞð25Þ
2.5.1 Update of hidden–output weights
The weight-updating formula of hidden–output can be
expressed as:
DWc2i¼g
oJ
oWc2i
¼g
oJ
oypðkþ1Þ
oypðkþ1Þ
oymðkþ1Þ
oymðkþ1Þ
ouðkÞ
ouðkÞ
oWc2i
ð26Þ
where oJ
oypðkþ1Þ¼ yrðkþ1Þypðkþ1Þ
,oypðkþ1Þ
oymðkþ1Þ¼1,
Neural Comput & Applic (2018) 29:585–596 589
123
oymðkþ1Þ
ouðkÞ¼oymðkþ1Þ
onp2
onp2
ohp1
ohp1
onp1
onp1
ouðkÞ
¼ymðkþ1Þð1ymðkþ1ÞÞ Wp2 hp1
ð1hp1ÞWp1i3
ouðkÞ
oWc2i
¼ouðkÞ
onc2
onc2
oWc2i
¼uðkÞð1uðkÞÞ hc1i
So, DWc2ican be expressed by,
DWc2i¼g½yrðkþ1Þypðkþ1Þ ymðkþ1Þ
ð1ymðkþ1ÞÞ Wp2 hp1 ð1hp1Þ
Wp1i3uðkÞð1uðkÞÞ hc1ið27Þ
Similarly, the bias-term-updating formula of hidden–
output can be expressed as:
Dbc2 ¼g
oJ
obc2
¼g
oJ
oypðkþ1Þ
oypðkþ1Þ
oymðkþ1Þ
oymðkþ1Þ
ouðkÞ
ouðkÞ
obc2 ð28Þ
where ouðkÞ
obc2 ¼ouðkÞ
onc2
onc2
obc2 ¼uðkÞð1uðkÞÞ 1:
Therefore, Dbc2 can be calculated as,
Dbc2 ¼gyrðkþ1Þypðkþ1Þ
ymðkþ1Þ
ð1ymðkþ1ÞÞ Wp2 hp1 ð1hp1Þ
Wp1i3uðkÞð1uðkÞÞ ð29Þ
2.5.2 Update of input–hidden weights
The weight-updating formula of input–hidden can be
expressed as:
DWc1ij ¼g
oJ
oWc1ij
¼g
oJ
oypðkþ1Þ
oypðkþ1Þ
oymðkþ1Þ
oymðkþ1Þ
ouðkÞ
ouðkÞ
oWc1ij
ð30Þ
where ouðkÞ
oWc1ij ¼ouðkÞ
onc2
onc2
ohc1i
ohc1i
onc1i
onc1i
oWc1ij ¼uðkÞð1uðkÞÞ
Wc2ihc1ið1hc1iÞYj:
So, DWc1ij can be expressed by,
DWc1ij ¼g½yrðkþ1Þypðkþ1Þ ymðkþ1Þ
ð1ymðkþ1ÞÞ Wp2 hp1 ð1hp1ÞWp1i2
uðkÞð1uðkÞÞ Wc2ihc1ið1hc1iÞYj
ð31Þ
Similarly, the bias-term-updating formula of input–hid-
den can be expressed as:
Dbc1i¼g
oJ
obc1i
¼g
oJ
oypðkþ1Þ
oypðkþ1Þ
oymðkþ1Þ
oymðkþ1Þ
ouðkÞ
ouðkÞ
obc1i
ð32Þ
where ouðkÞ
obc1i¼ouðkÞ
onc2
onc2
ohc1i
ohc1i
onc1i
onc1i
obc1i¼uðkÞð1uðkÞÞ
Wc2ihc1ið1hc1iÞ1:
Therefore, Dbc1ican be calculated as,
Dbc1i¼g½yrðkþ1Þypðkþ1Þ ymðkþ1Þ
ð1ymðkþ1ÞÞWp2 hp1 ð1hp1ÞWp1i2
uðkÞð1uðkÞÞWc2ihc1ið1hc1iÞ
ð33Þ
2.6 Implementation of BP neural network-based
online MPC strategy
The BP neural network-based online MPC strategy follows
the course of traditional MPC. However, two improve-
ments in the proposed control strategy have been achieved,
i.e., simplifying the controller and reducing time con-
sumption, which can satisfy the online and accurate control
of the time-variant and nonlinear forging process. The
flowchart of BP neural network-based MPC strategy is
shown in Fig. 6. It can be summarized as follows:
Fig. 6 Flowchart of BP neural network-based MPC strategy
590 Neural Comput & Applic (2018) 29:585–596
123
Step 1 Initialization of model parameters. Initialize the
learning rate g, softness parameter a, and initial input
u(1).
Step 2 Offline training of PNN. At the first control level,
the PNN should be trained to determine the initial
predictive output y
m
(1).
Step 3 Obtain y
m
(k?1) by PNN. In the whole process,
the predictive output y
m
(k?1) can be iteratively
determined by PNN.
Step 4 Feedback compensation. Due to the nonlinearity,
time-variant characteristic, and unknown disturbances of
practical forging process, the predictive output
y
m
(k?1) is hard to match the actual output y(k?1).
It may be make the control process unstable. The
predictive error between the actual and predictive
outputs should be used to revise the predictive output.
The formula can be given by:
ypðkþ1Þ¼ymðkþ1ÞþhðyðkÞymðkÞÞ ð34Þ
where his the weight coefficient. Generally, h¼1.
Step 5 Reference target planning. In each control
horizon, the reference target y
r
(k?1) should be
presented before the practical output y(k?1) is
observed. The reference target planning formula is
expressed as:
yrðkþ1Þ¼ayðkÞþð1aÞydð35Þ
where y
d
is the value of goal setting and a(0\a\1) is
the softness parameter. If ais large, the predictive con-
trol is strongly robust. However, it will lead to the slow
response speed of system. Otherwise, the response speed
of system will become fast, but it will cause the system
overshoot and oscillation. In this study, the softness
parameter ais set as 0.1 in order to quickly reach the
goal.
Step 6 Obtain u(k?1) by CNN. The initial input u(1) is
determined by initialization. However, in the later
process, the input u(k?1) is iteratively obtained by
CNN.
Step 7 Observe y(k?1). The practical output y(k?1)
is utilized in the next control horizon.
Step 8 Update the weights of neural networks. The
methods to update online the weights of PNN and CNN
are presented in Sect. 2.4 and 2.5, respectively.
Step 9 Return to Step 3 to carry out the next time step
prediction and control.
Remark 1 Generally, for the traditional MPC, the rolling
optimization mainly deals with the optimal problem with
constraints, and the quadratic programming (QP) method is
often used to solve the problem. However, in this study, the
CNN is used to replace QP method to obtain the optimal
input for the system. This is because the QP method costs
much more time than the CNN. Moreover, the constraints
for this problem are satisfied naturally when training the
neural networks. So, the CNN not only simplifies the
complex problem to be an input–output question, but also
reduces the time consumption.
3 Experimental verifications
Two experiments were performed on 4000T HPM (as shown
in Fig. 7) to confirm the feasibility and effectiveness of the
proposed control strategy. The pump station, which can
produce the maximal 25 MPa oil pressure, provides power
for the entire system. The oil pressures of three cylinders
located above the work plate are controlled by servo valves.
These servo valves receive control signals from a PLC
(SIMATICS7-300), a control panel equipped with a PC, and
the data acquisition board for pressure, displacement, and
velocity. The pressure sensors (E-ART-6/400, range
0–400 bar) installed at the inlet of the driven cylinders are
used to collect pressure data. The displacement sensors
(magnetostrictive sensors: RPS 1650M D70 1S1 G8400,
resolution 0.001 mm) installed at the vertical columns are
used to collect displacement data. The sampling period of all
sensors is one second. The practical pressure of driven
cylinders and the velocity of upper die are defined as the
input and output of the system, respectively. In this study,
the first experiment is mainly utilized to validate the feasi-
bility, while the second experiment is used to confirm the
effectiveness of the proposed control strategy.
3.1 Experiment 1
The first experiment data are shown in Figs. 8and 9.In
order to validate the feasibility of the proposed control
strategy, the input (the pressure of driven cylinders) and the
output (the velocity of upper die) are used to train the PNN
initially. Then, according to the proposed control strategy,
the forging process is simulated using the trained PNN. The
values of parameters g¼0:005, h¼1, and a¼0:1. The
value of goal setting is shown as:
Neural Comput & Applic (2018) 29:585–596 591
123
yd¼0:1 mm/s 0\t200 s
0:05 mm/s 200 s\t300 s
ð36Þ
Figure 10 shows the comparison of the real and pre-
dictive outputs. It is clear that the predictive output is
closely consistent with the real output. Furthermore, the
predictive output is more stable than the real output. In
addition, the predictive output is closer to the reference
than the real output. Due to the predictive characteristic of
MPC approach, the control system can timely change the
velocity of upper die from 0.1 to 0.05 mm/s. Meanwhile,
there is no large oscillation in the change process. Also, the
errors between the real and predictive outputs are mainly
distributed around 0 except the sudden change point. So,
the BP neural network-based MPC strategy is feasible, and
it can effectively predict and control the forging process on
4000T HPM.
3.2 Experiment 2
The second experiment is mainly utilized to confirm the
effectiveness of the proposed control strategy. Then, the
weight matrices and bias terms of PNN and CNN, which
were trained in the first experiment, are utilized as the
initial weight matrices and bias terms of PNN and CNN
for the second experiment. The initial weight matrices and
Fig. 7 Practical 4000T HPM
Fig. 8 Input of experiment 1
Fig. 9 Output of experiment 1
592 Neural Comput & Applic (2018) 29:585–596
123
bias terms of PNN for the second experiment are shown
as:
Wp1 ¼
152:0825 96:1193 46:6102 1:1991 4:1598
33:3517 22:6898 78:7413 265:7069 19:9291
185:9030 116:1661 188:3240 243:9329 105:1505
39:8815 5:1406 39:0562 11:8511 4:6203
55:9892 4:3900 53:6012 11:5856 6:6535
129:4756 74:6679 47:0959 0:7381 2:0258
242:9268 148:3639 186:7155 83:2754 29:2461
45:5106 2:1035 46:3862 11:4372 5:4132
121:6556 54:2411 154:8974 271:6618 114:3594
9:7958 71:5477 85:9566 13:9572 35:4460
6:0859 27:2676 42:9174 12:8681 32:3842
0
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
@
1
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
A
bp1 ¼
8:5749
42:5462
269:0954
1:5034
0:7899
7:2662
41:1325
1:2146
297:5819
32:8845
29:8884
0
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
@
1
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
A
;Wp2 ¼
55:8785
0:3617
62:4863
103:2579
70:4858
65:5863
0:8769
174:5329
62:1414
36:6314
40:8731
0
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
@
1
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
A
;bp2 ¼16:2396
The initial weight matrices and bias terms of CNN for
the second experiment are shown as:
Wc1 ¼
0:4657 0:1298 2:6725 5:0892
0:9548 0:2316 0:8359 0:5324
0:5629 0:8085 3:8450 3:6620
0:0350 0:2595 2:7894 3:2570
0:9671 0:3586 0:7828 1:5243
0:8506 0:6154 0:8587 0:1697
0:8945 0:0317 0:2684 0:8443
0:1653 0:2322 0:4686 1:5278
0:3535 0:1326 1:0371 0:4182
0
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
@
1
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
A
bc1 ¼
0:7020
0:8743
0:9597
6:4460
0:5119
1:0556
0:2901
0:0048
1:6241
0
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
@
1
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
A
;Wc2 ¼
4:4250
0:1883
3:0983
5:8189
0:7624
0:4408
2:0776
2:8230
1:2392
0
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
@
1
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
A
;bc2 ¼1:5004
Fig. 10 Experiment 1: athe
real and predictive outputs;
bthe error between the real and
predictive outputs
Fig. 11 Experiment 2: athe
real output vs. predictive output;
bthe error between the real and
predictive outputs
Neural Comput & Applic (2018) 29:585–596 593
123
Also, the values of g,h, and aare the same with those of
experiment 1. The value of goal setting is shown as:
yd¼0:1 mm/s 0\t40 s
0:05 mm/s 40 s\t100 s
ð37Þ
Figure 11 shows the comparisons between the real and
predictive outputs in experiment 2. It is obvious that the
predictive output agrees well with the real output, and the
real and predictive outputs are all tracking the reference
velocity. Moreover, the control system can timely change
the velocity of upper die from 0.1 to 0.05 mm/s without
large oscillation. Also, the errors between the real and
predictive outputs are mainly distributed around 0. The
input of experiment 2, as shown in Fig. 12, is obtained by
the CNN developed in this control strategy. So, this
experiment clearly indicates that the forging process can be
effectively predicted and controlled by the proposed con-
trol strategy in this study.
3.3 Comparisons and discussions
In this section, the performance of the BP neural network-
based online MPC approach is compared with those of the
PID controller and traditional MPC approach. In this study,
the parameters of PID controller (including proportional,
integral, and derivative constants) are 105.32, 732.91, and
213.56, respectively. For the traditional MPC, the predic-
tion and control horizons are 5 and 3, respectively. Fig-
ure 13 shows the tracking performance of the proposed
MPC approach, PID controller, and traditional MPC
approach. It is obvious that the velocity of upper die con-
trolled by the proposed MPC approach is closer to the
reference trajectory than those controlled by the PID con-
troller, as well as traditional MPC approach. In particular,
the PID controller depicts the higher overshoot than the
proposed MPC. As shown in Fig. 13b, the tracking error of
the proposed MPC approach is smaller than those of the
PID controller and traditional MPC approach. Also,
Table 1shows the root-mean-square errors (RMSEs) of the
proposed MPC approach, PID controller, and traditional
MPC approach. It is clear that the RMSE of the proposed
MPC is the smallest, which implies that the performance of
the proposed MPC approach is the best.
The BP neural network-based online MPC approach
employs the advantages of neural network, such as general-
ization capability, adaptation, and fault tolerance property.
Due to these advantages, the proposed MPC approach could
effectively handle the problems caused by unknown distur-
bances. This is because the proposed MPC approach is based
on the practical experimental data, and the PNN and CNN
have contained the influences of unknown disturbances on
the inputs and outputs when they are trained. In addition,
because the PNN and CNN are updated online, the proposed
MPC approach is an online controller, which could timely
identify the disturbances and update the weights of neural
networks to eliminate the influences caused by unknown
disturbances. However, the traditional MPC and PID con-
troller cannot deal with the influences of unknown distur-
bances. Therefore, the proposed MPC approach is a very
effective controller for the practical forging process.
Fig. 12 Input of experiment 2
Fig. 13 Comparisons of the
proposed MPC, PID controller,
and the traditional MPC: athe
real outputs and reference; bthe
tracking errors
594 Neural Comput & Applic (2018) 29:585–596
123
4 Conclusions
A precise BP neural network-based online MPC strategy is
proposed to control the time-variant and nonlinear forging
process on 4000T HPM in this study. Two BP neural
networks, predictive neural network (PNN) and control
neural network (CNN), are established to deal with the
time-variant and nonlinear forging process. The PNN is
used to predict the output of system, and the CNN is used
to replace the traditional rolling optimization to determine
the input of system. Due to the advantages of neural net-
works, such as generalization capability, high speed,
adaptation, and fault tolerance property, the proposed
control strategy has such features as simple structure, fast
acting, and adaptability. Moreover, the constraints are
satisfied and the unknown disturbances are compensated
naturally by the feedback approach. Two forging experi-
ments on 4000T HPM confirm the feasibility and effec-
tiveness of the proposed control strategy. Compared to the
traditional MPC approach and PID controller, the proposed
MPC approach is the most effective control strategy for the
practical forging process.
Acknowledgments This work was supported by the National Natural
Science Foundation Council of China (Grant No. 51375502), the
National Key Basic Research Program (Grant No. 2013CB035801),
the Project of Innovation-driven Plan in Central South University
(Grant No. 2016CX008), the Natural Science Foundation for Distin-
guished Young Scholars of Hunan Province (Grant No. 2016JJ1017),
Program of Chang Jiang Scholars of Ministry of Education (No.
Q2015140), and the Hunan Provincial Innovation Research Funds for
Postgraduate (Grant No. CX2016B045), China.
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