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Engineering, Technology & Applied Science Research Vol. 9, No. 5, 2019, 4789-4794 4789 
 

www.etasr.com Ta & Dang: A Redundant Recurrent Cerebellar Model Articulation Control System for Industrial … 

 

A Redundant Recurrent Cerebellar Model 

Articulation Control System for Industrial 

Applications 
 

Van-Phuong Ta 

Department of Automatic Control 
HCMC University of Technology And Education 

Ho Chi Minh City, Vietnam 

phuongtv@hcmute.edu.vn 

Xuan-Kien Dang 

Graduate Institute 
HCMC University of Transport 
Ho Chi Minh City, Vietnam 

dangxuankien@hcmutrans.edu.vn 
 

 

Abstract—Because of increasing reliability requirements of the 

applications in industrial areas, the control systems must 

guarantee the stability and robustness during operation and 

continuously maintain control and supervisory process. In order 

to meet the above requirements, this study proposes a redundant 
recurrent cerebellar model articulation control system 

(RRCMACS) for controlling industrial applications, in particular 

the water level and the pressure in a tank. Therein, the stability 

and the robustness of the applications are guaranteed by the 

recurrent cerebellar model articulation controller (RCMAC) and 

the redundant solution maintains continuously control and 

supervisory process. To adapt industrial applications, a 

Programmable Logic Controller (PLC) was used to build the 

control system and industrial networks were used to transfer 
data between the control system and field devices. 

Keywords-recurrent cerebellar model articulation controller 

(RCMAC); redundancy system; industrial communication network; 

uncertainties; non-linear system 

I. INTRODUCTION  

Stability control of level and pressure in a tank are crucial 
tasks in industrial applications [1-3]. Because of the effects of 
the uncertainties due to dynamic perturbations and signal 
noises, the dynamic model of these systems cannot be 
completely obtained [4-7]. Consequently, model-based 
controllers cannot achieve the desired performances [8-10]. To 
overcome these disadvantages, advanced controllers such as 
fuzzy logic controller (FLC) [11, 12], sliding mode control 
(SMC) [13, 14], neural networks (NN) [15, 16], and wavelet 
neural network (WNN) [17-21] have been developed and have 
achieved impressive results in dealing with uncertain systems. 
In the above-mentioned advanced controllers, however, there 
are still difficulties in designing the control systems. For the 
FLC, the selection of fuzzy sets and rules is dependent on the 
prior experience of the system. In the SMC, selection boundary 
of uncertainties or disturbance is a trade-off between stability 
and chattering phenomena. For the NN and WNN, the selection 
of the number of neurons and hidden layers to achieve good 
performance and learning requirements is extremely difficult in 
practical applications. 

Cerebellar Model Articulation Controller (CMAC) is a 
learning structure that mimics human brain [22]. The CMAC 
has been developed and adopted for uncertain non-linear 
Multiple-Input and Multiple-Output (MIMO) systems due to 
properties such as fast learning, good generation capability, and 
simple computation. The augmented effectiveness in 
applications of the CMACs when compared to NNs has been 
proved [23-26]. In recent researches, the wavelet function and 
recurrent technique were incorporated into the CMAC to 
improve the learning capability and dynamic response of the 
traditional CMAC [27-30]. The above adaptive, intelligent 
controllers can deal with the uncertainties and non-linear 
characteristic of the systems to achieve the desired 
performance. The industrial applications of these controllers, 
however, have been limited. In addition, the redundant solution 
has not been mentioned to continuously maintain control and 
supervisory process. This paper proposes an RRCMACS to 
achieve the desired responses and continuously maintain 
control and supervisory process. The recurrent cerebellar model 
articulation (RCMAC) is designed to keep the stability and the 
robustness, and the redundant solution aims to maintain the 
continuous working of the control system. To meet the 
requirements of the industrial area, the PLC was used to build 
the control system and industrial networks were used to 
transfer data between the control system and field devices. 

II. SYSTEM DESCRIPTION 

A. Structure and Operation of the Redundant System 

The structure of the redundant system and a photograph of 
its implementation are shown in Figures 1 and 2 respectively. 
The redundant system includes a primary station (PS) and a 
standby station (SS), which continuously maintain the control 
and supervisory process of the control system. In particular, the 
system used DeviceNet Network to control and monitor the 
pressure and water level in a tank. The ControlNet network was 
used to transfer diagnostic information between the PS and SS 
to take over control as satisfying prescribed conditions. At the 
beginning of the process, the station that started earlier takes 
the role of the PS and takes control over the system, while the 
other station works as the SS. During operation, if the PS 

Corresponding author: Van-Phuong Ta



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www.etasr.com Ta & Dang: A Redundant Recurrent Cerebellar Model Articulation Control System for Industrial … 

 

faults, the SS will take over to maintain control and the 
supervisory process of the system. In addition, the RCMAC 
was utilized to guarantee the stability and robustness of the 
system during operation. The RCMAC was downloaded to 
both stations, thus the effectiveness of the control and 
supervisory process was the same with in both stations. 

 

 
Fig. 1.  Structure of the redundant system 

 
Fig. 2.  Experiments of the RCMACS 

B. Control Takeover 

During operation, the controllers monitor the working 
conditions of each other. A “Heartbeat” parameter is used to 
measure the strength of the controllers. When this parameter 
falls down under a prescribed threshold, it means the 
controllers are having faults while handling the system. In 
particular, assuming that the PS owns the control system at the 
beginning of the process, it monitors the connections of the 
devices in the system during operation. If there are fault 
connections suddenly inhibiting these devices, the SS can 
communicate with them in order to control the system. In 
addition, the SS always monitors the status of the PS. 
Whenever the PS has problems with connections, the SS 
immediately takes over control of the system. Figure 3 
describes the process of control takeover between the PS and 
SS. The flowchart of control takeover is shown in Figure 4. 

III. RCMAC 

Along with continuously maintaining the control and 
supervisory process of the system, stability and robustness of 
the system are also a crucial task in the industrial applications. 
This duty is handled by the RCMAC. The dynamic model of 
practical applications is extremely difficult to define. 

 
Fig. 3.  Take over control between two CPU 

 
Fig. 4.  The flowchart of control takeover  

In this study, the dynamic equation of the pressure control 
system and the water level control system are identified by the 
Matlab tool. The linearized dynamic models, including 
uncertainties of the system are given by (1) and (2), 
respectively: 

y(t)+0.045y(t)+0.0017y(t)+UD(t) = 0.0045u(t)�� �  (1) 

y(t)+0.00035y(t)+0.001y(t)+UD(t) = 0.165u(t)�� �  (2) 

where u(t)  andy(t) are control signal and the pressure in the 

Tank or water level. UD(t) is the lumped uncertainties and 

linearization error. Equations (1) and (2) can be rewritten in 
state equation form as: 

0 0

T
T T

x= F (x) + G (x)u + UD(x)

y = x;  = x x




   

��

�

 

x
 (3) 



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In the case of 
0
F (x) , 

0
G (x) , and well-known uncertainties 

(x)UD , an ideal controller can be designed as [27, 30]: 

-1

0 d 0 1 2i
G (x) y F (x) UD(x) K e+K eu = − − +  �� �  (4) 

where 
1 2

K ,  K  are selected to the error dynamic equation 

1 2
Ke+ e+K e = 0�� �  satisfying the Hurwitz criterion. 

However, the uncertainties, UD(x)  cannot be defined in the 

practical systems, thus the ideal controller 
i
u  does not 

guarantee the desired performance. To deal with the 
uncertainties, a proposed control system is depicted in Figure 3. 
In this system, the recurrent cerebellar model articulation 
controller uRCMAC is combined with a compensator controller 
uCC to achieve stability and robustness. Therein, the uRCMAC is 
developed to mimic the ideal controller and by its learning 
capability to achieve stability while the compensator controller 
is designed to attenuate efficiently the effects of uncertainties to 
obtain robustness. The total proposed control system has the 
following form: 

RCMAC CCi
u = u -u -u   (5) 

The control diagram and the structure of the RCMAC are 
shown in Figures 5 and 6 respectively. The RCMAC aims to 

learn the uncertainties, UD(x) , which always exist in practical 

applications, in order to minimize the errors of the system. To 
reduce the number of the variables in the computation of the 
control system, error, derivation of error, and integral of error 
are integrated to form the error sliding surface, S which is 
minimized by the RCMAC during learning [30]. According to 
the learning capability of the RCMAC, the error sliding surface 
will converge to zero at the appropriately selected learning rate. 
However, due to the uncertainties’ effects, the error sliding 
surfaces often oscillate around zero point and easily diverge in 
the presence of disturbances or noise. Therefore, a compensator 
controller was combined with the RCMAC to guarantee the 
robustness of the system during operation [28, 30]. This 

RCMAC (Figure 6) includes input space S , association 

memory space A , receptive field space R , weight memory 

space W , and output spaces O . The function value of each 
space in the RCMAC is represented as [30]: 

rik i rik ik
s (t) = s (t)+w µ (t -1)  (6) 

( )
2

ri ik

ik rik 2

ik

s -m
µ (s ) = exp -

σ

 
 
  

 (7) 

n

ik ik rik

i=1

µb = (s )∏  (8) 

nj nnk

j jk ik rik

j=1 k=1 i=1

µO = w (s )∑∑ ∏  (9) 

The parameters of the controller are adjusted by the 
RCMAC’s learning to achieve good performance in the 

presence of the lumped uncertainties UD(x) . 

 
Fig. 5.  Control diagram of the RCMAC 

 
Fig. 6.  Structure of the RCMAC 

In this paper, 
Ts s�  is selected as an error function and the 

back-propagation algorithm is utilized to adjust the parameters 
of the controller as follows: 

0 ISM RCMAC CC

T T T

T

d 1 2

( ) (x)( )

(

S S S S

S UD(x) K e+K e)

= − − +

+

−

− +��

�

�

0
F x G u u u

x
 (10) 

i

T T

RCMAC

kj w w

kj RCMAC kj

n

T

w 0 ik ri

i=1

S S S S
w η η

w w

η S (x)( µ (S ))

∆
∂∂ ∂

= − = −
∂ ∂ ∂

= ∏

� � u

u

G

 (11) 

( )

T T

RCMAC ik
ik m m

ik RCMAC ik ik

ri ikT

m 0 kj 2

ik

µS S S S
m η η

m µ m

S -m
η S (x)w 2

σ

∆
∂ ∂∂ ∂

= − = −
∂ ∂ ∂ ∂

=

� � u

u

G

(12) 



Engineering, Technology & Applied Science Research Vol. 9, No. 5, 2019, 4789-4794 4792 
 

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( )

T T

RCMAC ik

ik σ σ

ik RCMAC ik ik

σ kj

2

ri ikT

3

ik

µS S S S
η η

µ

η (x)w
S -m

S 2
σ

∆σ
σ σ

∂ ∂∂ ∂
= − = −

∂ ∂ ∂ ∂

=

� �

0

u

u

G

 (13) 

( )

rik rik

rik

T T

RCMAC ik ri

rik w w

rik RCMAC ik ri rik

w kj

ri ikT

i(k-1)2

ik

µ SS S S S
w η η

w µ S w

η (x)w
S -m

S 2 µ
σ

∆
∂ ∂ ∂∂ ∂

= − = −
∂ ∂ ∂ ∂ ∂

=

� �

0

u

u

G

(14) 

To maintain the robustness of the control system as the 
error function is tending to zero, a sliding mode control-based 
compensator controller can be designed as: 

-1

CC 0
ˆu = G (x)Btanh(S)  (15) 

whereBis the error boundary and B̂is an estimation of B. In 
practical industrial applications, the error boundary cannot be 
exactly measured. Moreover, selecting the boundary error is a 
trade-off between the output chattering phenomenon and the 
stability of the control system. Consequently, the error 
boundary is estimated in this study as [28, 30]: 

B
B̂ = η S
�

 (16) 

With the estimating rule given in (15), the stability of the 
system is guaranteed in the sense of Lyapunov-like Lemma 
[31]. 

IV. EXPERIMENTAL RESULTS 

A. Water Level Stability Control System 

The water level control system is represented in Figure 7. 
The system includes a pump powered by a DeviceNet 
Network-controlled inverter. The water level in the tank is 
monitored by a Level Transmitter (LT). The LT’s signal is 
connected to the inverter. All processes are performed by the 
control stations via the DeviceNet network. Data in the control 
stations are monitored by computers and a Human Machine 
Interface (HMI) via an Ethernet network. The initial parameters 
of the RCMAC of the control system are: 

w m σ wr B k
η = η = η = η = η = 0.001,n = 7

 

1 2
K = 0.035,K = 0.054

 

m [ 0.6 0.4 0.2 0 0.2 0.4 0.6]= − − −
 

w [ 0.4 0.25 0.15 0 0.15 0.25 0.4]= − − −
 

[0.3 0.3 0.3 0.3 0.3 0.3 0.3]σ =
 

rik
w [ 0.4 0.25 0.15 0 0.15 0.25 0.4]= − − −

 

The response of the water level in the tank is shown in 
Figure 8. The experimental result shows that the RCMACS can 
control the water level in the tank and achieve different desired 
set points. Besides, the redundant solution guarantees the 
continuous control and supervisory process in case the 

controllers get faults. In particular, during the operation, if the 
PS is in the program mode, fault or outage power, the SS will 
take over the control of the system and maintain the process 
continuously.  

 

 
Fig. 7.  Water level control system 

 
Fig. 8.  The response of the water level in the tank 

B. Pressure Stability Control System 

The pressure stability control system is presented in Figure 
9. The system includes a pressure pump powered by a 
DeviceNet Network-controlled inverter. The pressure in the 
tank is qualified by a pressure transmitter (PT). The PT’s signal 
is connected to the inverter. All processes are performed by the 
control stations via the DeviceNet network. 

 

 
Fig. 9.  Pressure stability control system 



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The initial parameters of the RCMAC are the same with the 
case of water level control. The experimental results of the 
pressure stability control system are shown in Figure 10. The 
experimental results prove that the RCMACS can control the 
pressure in the tank and achieve the desired different references 
in reality. Along with achieving good responses, the redundant 
solution also guarantees the continuous control and supervisory 
process in case of fault in the controllers. 

 

 
Fig. 10.  The response of the pressure in the tank 

V. CONCLUSION AND FUTURE WORK 

Water level control system and pressure stability control 
system were controlled to achieve the desired trajectories by 
the redundant recurrent cerebellar model articulation control 
system. The parameters of the controller were learned and 
turned in real time, and the stability and robustness of the 
control system are guaranteed in the Lyapunov sense. The 
exchange data between the control stations and the field 
devices were transferred via the industrial DeviceNet Network. 
This solution not only reduces the effects of noise and signal 
attenuation during operation, but also increases the distance 
between the control stations and sensors and actuators. 
Furthermore, the redundant solution was proposed in this study 
to maintain continuously the control and supervisory process. 
Two control stations were used to operate concurrently. 
Whenever one station faults, the other will quickly take over 
control of the system. Therefore, the continuous operation of 
the control system is guaranteed. 

The use of historical data records, however, is one of the 
most crucial tasks in practical industrial applications. This is 
useful for users in finding and troubleshooting faults during 
operation. Future research work will include the 
implementation of this task. 

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