Journal of Robotics, Networking and Artificial Life, Vol. 5, No. 2 (September 2018) 89-92___________________________________________________________________________________________________________Experimental Evaluation of a Data-Driven Control System using an Electronic ThermalRegulator
Yuka Okubo

Graduate School of Engineering, Hiroshima University,
1-4-1, Kagamiyama, Higashihiroshima city, Hiroshima, Japan
Yoichiro Ashida

Graduate School of Engineering, Hiroshima University,
1-4-1, Kagamiyama, Higashihiroshima city, Hiroshima, Japan
Takuya Kinoshita

Graduate School of Engineering, Hiroshima University,
1-4-1, Kagamiyama, Higashihiroshima city, Hiroshima, JapanToru Yamamoto

Graduate School of Engineering, Hiroshima University,1-4-1, Kagamiyama, Higashihiroshima city, Hiroshima, Japan
E-mail: okubo-yuka@hiroshima-u.ac.jp, ashida-yoichiro@hiroshima-u.ac.jp, kinoshita--takuya@hiroshima-u.ac.jp,yama@hiroshima-u.ac.jp
http://www.hiroshima-u.ac.jp

Abstract

IoT (Internet of Things) has been attracted attention, and several system data can be obtained bycommunication and it is stored in database. The input/output data is expected to be utilized to control
systems in industries. The data-driven technique has been proposed as a way to utilize database forcalculating PID gains. The scheme is effective for non-linear system control, but it is hard to be
implemented to systems. It is due to restricted memory capacity. Therefore, a host computer calculates
PID gains based on the data-driven scheme instead of a control device. The calculated gains are sent to a
general controller from a computer. The effectiveness of the proposed platform is demonstrated by theexperimental examination.
Keywords: PID controller, data-driven controller, electronic thermal regulator, FRIT

PID controller3, 4 is basically applied. In the case of usingPID controller, the PID gains must be tuned considering
the properties of controlled objects. Most of the practicalcontrolled objects have nonlinearity, and it is hard tocontrol them suitably by using the fixed PID controller.
Therefore, the data-driven technique5 having
effectiveness for non-linear systems has been proposed.
Calculating a set of PID gains based on the databasedepending on current operating data, the data-driven
scheme can appropriately control such systems. The data-1. Introduction
In recent years, IoT has been received attention, and thedata of systems obtained through a lot of sensors is hoped
to be utilized to control systems in industries1. Such data,
which is collected by a communication between sensors
and cloud, is stored in database.
On the other hand, the electronic thermal regulators2,
control devise, are employed to control systems, in which

Copyright © 2018, the Authors. Published by Atlantis Press.
This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
89

Journal of Robotics, Networking and Artificial Life, Vol. 5, No. 2 (September 2018) 89-92___________________________________________________________________________________________________________driven technique needs the large memory for database.
Therefore, it is hard to implement this technique to theelectronic thermal regulator due to its restricted memory
capacity. If the computer is utilized for implementing thedata-driven control scheme, the new interface between
the computer and controlled object must be introduced
instead of the electronic thermal regulator. Hence, thedata-driven scheme is hardly implemented to theindustrial field.
In this paper, the construction of the data-driven
control platform using the electronic thermal regulator isfirstly explained, in which the database is introduced inorder to realize the data-driven PID controller. According
to the proposed platform, the host computer calculates
PID gains by the data-driven technique and sends themto the control device. As a result, the aforementioned
memory capacity restriction of the electronic thermalregulator can be avoided. Furthermore, the existing
interfaces between electronic thermal regulator andcontrol objects do not need to be changed.
In this paper, section 2 shows the schematic of thedata-driven control platform. The design of a data-driven
controller is explained in section 3. In section 4, theeffectiveness of the proposed platform is verified byimplementing it for an actual experimental equipment.
The paper ends with concluding remarks in section 5.

Fig. 1. The schematic of a data-driven control platform.

showing the historical data of the system. � � 1 isdefined by the following equation:� � 1 ≔ Ā�� 1 , … ,�� � ,Ā � 1 , … ,�� � , (2)where �� is the control input, and � , Ā are the ordersof the system output and the control input, respectively.
In this paper, the following control law with a PID
structure is introduced:�������� � ��� ���3� �� � ��� � � ��,
where �� denotes the control error signal defined by
the following equation:�� � � � �,
4
where �� is the reference signal. The �, �, and � inequation (3) express the proportional gain, integral time,and derivative time, respectively. � , � and �
similarly denote the proportional gain, integral gain andderivative gain. The � shows the backward operator.
are the sampling time and� and ̀ ≔ 1 �
differencing operator.

2. Construction of the data-driven control
platform
The schematic of a data-driven control platform isshown in Fig. 1. In this paper, the electronic thermal
regulator plays a role of a controller. The electronic
thermal regulator receives control outputs, e.g.
temperature, humidity or pressure through a sensor anddetermines the control input. In the proposed platform,
the reference signal and control I/O data are sent to thehost computer having a database from the electronic
thermal regulator. The host computer sends a set of PID
gains calculated on data-driven scheme to the electronic
thermal regulator. Since the host computer sends PID
gains instead of the control input, the electronic thermal
regulator can control systems using last PID gains even
if the communication is interrupted.

3.2. Design of a data-driven controller[STEP1] Generate an initial database: In the data-driven
control, the control parameters are calculated from thehistorical closed-loop data stored in a database. If there
are no stored information vectors in the database, thedata-driven scheme cannot work. To create initial
database, it is required to obtain the closed-loop data. Thedata stored in the form of the following equation:� t ≔ � �, Ā � , Ā 1,2, ⋯ ,� 05

3. Design of the data-driven controller
3.1. Controlled Object
The controlled object can be described by the following
nonlinear system:���� 𝑓. � � 1 ,(1)where �� is system output, �⋅ denotes the function ofnonlinearity and � � 1 is an information vector6� � ≔ � �,� �,� � ,where � 0 is the number of information vectors stored
in the initial database. The query is defined by thefollowing equation:

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Journal of Robotics, Networking and Artificial Life, Vol. 5, No. 2 (September 2018) 89-92___________________________________________________________________________________________________________� � ≔ Ā�� 1 , Ā �, Ā �, … , Ā � � 1 ,,7Ā � 1 , …, Ā � � 1[STEP2] Calculate distances and Select neighbors: Thedistances between query � � and every informationvector � �in the database, where � �, are calculatedby the following equation:� � �, Ā �� �� �,max � � m in � �8
� 1, 2, ⋯ , Ā �where � � is the number of information vectors in thedatabase at �. The max � � denotes the maximum
value of � elements in all information vectors. Similarly,the min � � expresses the minimum value of �elements in all information vectors. The k -pieces vectors
with the smallest �are selected from all informationvectors. The selected information vectors and PID gains
corresponding to the information vectors are neighborvectors.
[STEP3] Calculate PID gains: The suitable PID gains
around the query are calculated by applying the steepest
descent method to selected neighbor vectors in STEP 2.
���� �,�1,Fig. 2. The appearance of the temperature control equipment.

When �� 1 is minimized, the PID gains can becalculated such that � � and � � are equal. Inequation (13), the fictitious reference output � � isused so that the closed-loop system including a controller
has a desired characteristic of the reference model. � �is shown by the following equation:
� �1
�̃ �.
14
� ���
� � is a user-specified polynomial included in thereference model and arbitrarily designed in advance suchthat the model has the desired characteristic.
15� � ≔ 1 �� � � ,9�

where � in equation (9) is weight for � �corresponding to the � information vector � � asfollows:
�,10�
∑ �
where � expresses the distance calculated by equation(8) between the query and � information vector.

2exp

� e xp≔�≔ 0.25 1 Ā Ā̀cos0.51Ā

�⎫
⎪
⎬
⎪
⎭

.

16

�denotes the rise-time, and �is a parameter relevant todumping. It is required that �is set to between 1/2 and1/3 sum of time constant and dead time. �is desired toset to between 0 and 2. When � 0, the step response is
the Binomial model response. When � 1 , the step
response shows the Butterworth model response.
In equation (14), the fictitious reference input �̃ � iscalculated by the input-output relation of controller� � . The � � is expressed as follows:17�� � � � ⋯ � � ,where �is the control law order. �equals 2 in the casewhere PID controller is used. The input-output relationof a controller is shown by the following equation:���̃ �� � ,18� �∆�̃ ��� ∆Ā � � �.
19
the fictitious reference signal �̃ � is obtained bydeformation of equation (18).

3.3. Off-line learning by FRIT

The fictitious reference iterative tuning (FRIT)6 is atechnique calculating directly the control parameters
arefrom a pair of I/O data. The new PID gains �obtained by updating the database stored PID gains � .
The following steepest descent method is applied tomodify the PID gains:
��� 1
�
�,
11
�
��
≔ �, Ā , Ā ,where � denotes the learning rates for each control
parameters. The �� 1 expresses the error criterion asfollows:112�� 1 ≔ �� 12
� 1 .
13
�� 1 ≔ Ā � 1 �91

Journal of Robotics, Networking and Artificial Life, Vol. 5, No. 2 (September 2018) 89-92___________________________________________________________________________________________________________

4. Experimental control results

Table 1: User-specified parameters for the experiment.

In this paper, the data-driven control platform wasapplied to the temperature equipment shown in Fig. 2.
The electronic thermal regulator E5CC-QQ2ASM andthe interface converter K3SC-10 for connection between
the electronic thermal regulator and a host computer wasutilized, which they made by OMRON Corporation. The
temperature equipment equips with a ceramic heater andan aluminum block. The control output �� is thetemperature of the aluminum and is measured with athermocouple of K-type. The control input �� is duty
ratio which determines how much to heat through a relay.
The reference signal Ā � was set to �� 6 0 [℃] andthe sampling time � was set to 2 [s]. After the control
output can track to the reference signal, a disturbance wasapplied that non-heated aluminum contacts and cools theheated one.
The PID parameters for generating initial databasewere denoted as follows:
0.021, Ā1.29.
20
� 2 .07, ĀThe initial data vectors were stored database according toequation (5). The user-specified parameters for theexperiment are shown in Table 1.
The desired polynomial Ā � was designed as��211 1.91Ā 0 .91� ,Orders of the information
vectorNumber of neighbors
Learning rates
Initial Number of data

� 1
� 2
� 6
� 1 .0 10
� 1 .0 10
� 1 .0 10
�01138Fig. 3. The control results by the proposed platform, and by afixed PID controller.

where � and �were set to � 90 and � 0 . The
control results of using the fixed PID gains and theproposed platform are respectively shown in Fig. 3. The
upper figure shows that solid line is the control output by
the proposed platform, dotted line is the desired control
output, dash line is the reference signal and chain line isthe control output using the fixed PID gains. The control
result of using fixed PID controller cannot track to thedesired control output and the disturbance let it cool 13℃
approximately at � 700 . In comparison with two
results, the rise-time of the proposed scheme is shorter
than one of the fixed PID controller. Therefore, theeffectiveness of data-driven control platform was verified.

adjusted only the case where the control performance isdeteriorated, will be considered.
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3. K. J. Astrom, T, Hagglund, Advanced PID Control,International Society of Automation, (2005)
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29-39
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5. Conclusion
In this paper, the effectiveness of the data-drivencontrol platform has been verified. In the proposedplatform, it is handily permitted advance control law thata host computer sends PID gains to the electronic thermalregulator using an existing interface. Even if PID gains
cannot be sent to the electronic thermal regulator, asystem is controlled using the last PID gains. In this paper,
the PID gains are adjusted at every step. In future work,
the control design method, in which PID gains are92