Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 1 (June 2017) 14–17___________________________________________________________________________________________________________Design of a Data-Oriented Kansei Feedback Control System
Takuya Kinoshita

Graduate School of Engineering, Hirosihma University,
1-4-1, Kagamiyama, Higashihiroshima city, Hiroshima, Japan
Toru Yamamoto

Faculty of Engineering Division of Electrical, Systems and Mathematical Engineering, Hirosihma University,
1-4-1, Kagamiyama, Higashihiroshima city, Hiroshima, Japan
E-mail: takuya-kinoshita@hiroshima-u.ac.jp, yama@hiroshima-u.ac.jp
http://www.hiroshima-u.ac.jp

Abstract
In the development of the aging society, it is important for patients with hemiplegia to introduce adaptive welfareequipment. However, it is difficult to determine the suitable reference signal for each person. In this study, thedesign of a data-oriented cascade control system based on Kansei is proposed. In the proposed control system, there
are two controllers which are a data-driven controller and a fixed controller. In particular, a data-driven controller
determines the suitable reference signal based on Kansei.
Keywords: PID controller, Data-driven controller, Kansei, off-line learning.

in the proposed scheme, the Ankle Foot Orthosis2(AFO) supports torque 𝜏𝐴 . In this paper, Kansei signal
is defined as walking comfortabley(𝑡) whose
maximum value is 1. Note that it is important toestimate reference signal of brain 𝑟𝜃1 (𝑡) because𝑟𝜃1 (𝑡) is unknown. Therefore, a data-base controller(primary controller) is applied to calculate the estimatedreference signal w(𝑡).

1. Introduction
In the development of aging society, it is important forpatients with hemiplegia to introduce the adaptive
welfare equipment. However, it is difficult to support
them by using general welfare equipment because there
are a lot of individual disabilities. Therefore, anadaptive welfare equipment is required in near future.
Nevertheless, it is difficult to determine the suitablereference signal for each person. In this study, thedesign of a data-oriented cascade control system basedon Kansei is proposed. In the proposed control system,
there are two controllers which are a data-driven
controller1 and a fixed controller. In particular, adata-driven controller1 determines the suitable reference
signal of a welfare equipment based on Kansei.

3. Controlled object

2. Schematic figure of the proposed control
system

Fig.2 shows the schematic figure of tow vertical joint
manipulator is shown as leg model. 𝐼1 , 𝐼2 are ankle’s
and knee’s moment of inertia, respectively. 𝑚0 , 𝑚1 , 𝑚2
are weight of upper body, lower leg and femur,respectively. 𝐿1 , 𝐿2 are the length of lower leg andfemur, and 𝑙1 , 𝑙2 are the length of gravitational centerof lower leg and femur, respectively. The torque𝜏1 and 𝜏2 are corresponding to angle 𝜃1 and 𝜃2 . The
equation of walking motion is expressed as follows:Fig. 1 shows the schematic figure of the proposedcontrol system. It is difficult for the patient withhemiplegia to move their foot by only torque τ𝐵 . Hence,−𝑚02 𝐿1 𝑙2 𝐶(𝜃2 ) ⋅ (2𝜃1̇ 𝜃2̇ + 𝜃22̇ )+��
𝑚02 𝐿1 𝑙2 𝐶(𝜃2 ) ⋅ 𝜃12̇𝐼 + 𝐼2 + 𝑚0 𝐿21 + 2𝑚02 𝐿1 𝑙2 𝐶(𝜃2 ) 𝐼2 + 𝑚02 𝐿1 𝑙2 𝐶(𝜃2 ) 𝜃1̈
�1
�� �𝐼2𝐼2 + 𝑚02 𝐿1 𝑙2 𝐶(𝜃2 )𝜃2̈Copyright © 2017, 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/).
14Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 1 (June 2017) 14–17___________________________________________________________________________________________________________Fig. 3. Block diagram of the FRIT.

inner loop is designed as the following fixed PDcontroller.
𝜏𝐴 (𝑡) = 𝐾𝑃2 𝑒(𝑡) + 𝐾𝐷2 Δ𝑒 (𝑡)(6)𝑒(𝑡) ≔ 𝑤(𝑡) − 𝜃1 (𝑡),(7)where 𝐾𝑃2 and 𝐾𝐷2 respectively are proportional gain
and derivative gain.

Fig. 1. Schematic figure of the proposed control system.

4.2. Design procedure of a data-driven control

Fig. 2.

[STEP 1] Create an initial database.
The database is constructed by the following
information vector:
� (𝑗), 𝑲(𝑗)] (𝑗 = 1,2, ⋯ , 𝑁)
𝝓(𝑗) ≔ [𝝓(8)� (𝑗) ≔ [𝑟(𝑡 + 1), 𝑟(𝑡), 𝑦(𝑡), ⋯ , 𝑦�𝑡 − 𝑛𝑦 + 1�,
𝝓𝑤(𝑡 − 1), ⋯ , 𝑤(𝑡 − 𝑛𝑤 )](9)(10)
𝑲(𝑗) ≔ [𝐾𝑃 (𝑡), 𝐾𝐼 (𝑡), 𝐾𝐷 (𝑡)],where 𝑁 denotes the number of data.
[STEP 2] Calculate distance and select neighbors’ data.
� (𝑡) and 𝝓� (𝑗) isThe distance between query 𝝓calculated by using the following L1–norm:

Leg model: two vertical joint manipulators.

𝜏1(𝑚 𝑙 + 𝑚02 𝐿1 )𝐶(𝜃1 ) + 𝑚02 𝑙2 𝐶(𝜃1 + 𝜃2 )+� 1 1
� 𝑔 = �𝜏 �,
𝑚02 𝑙2 𝐶(𝜃1 + 𝜃2 )2(1)

� (𝑡), 𝝓� (𝑗)� =𝑑 �𝝓where 𝐶(𝜃) and 𝑚02 denote 𝐶(𝜃) = 𝑐𝑐𝑐𝑐 and𝑚02 = 𝑚0 + 𝑚2 , respectively.
In addition, Kansei signal y(𝑡) in Fig. 1 is expressedas the following equation based on Weber-Fechner law3:
1𝑦(𝑡) =(2)1 + log�1 + 𝑒𝜃 (𝑡)�(3)𝑒𝜃 (𝑡) = 𝑟𝜃 1 (𝑡) − 𝜃1 (𝑡),where 𝑟𝜃1 (𝑡) is reference signal of 𝜃1 (𝑡).

𝑛𝑦 +𝑛𝑤 +1

�
𝑙=1

�

� 𝑙 (𝑗)� 𝑙 (𝑡) − 𝝓𝝓� . (11)� 𝑙 (𝑚)� 𝑙 (𝑚) − min𝝓max𝝓

(𝑗 = 1,2, , ⋯ , 𝑁)
� 𝑙 (𝑗) denotes the 𝑙th element of query 𝝓� (𝑗).
𝝓�
max𝝓𝑙 (𝑚) is a maximum value of the 𝑙th element in� 𝑙 (𝑚) is a minimum value
database. In contrast, min𝝓of the 𝑙th element. In addition, the number of neighbors’
data 𝑘 are selected, which data are based on smallest
distance value 𝑑.
[STEP 3] Calculate control parameters.
Control parameters are calculated by using thefollowing Linearly Weighted Average (LWA):

4. Design of a data-driven controller in outerloop as primary controller

𝑘𝑘

𝑖=1

𝑖=1𝑲(t) = � 𝑤𝑖 𝑲(𝑖) , � 𝑤𝑖 = 1,

4.1. Control law of a primary PID controller
The primary controller in Fig. 1 is designed as adata-driven controller1 because the Kansei is nonlinear
in equation (2). The primary controller is defined asfollows:
𝛥𝛥(𝑡) = 𝐾𝐼 𝜀(𝑡) − 𝐾𝑃 𝛥𝛥(𝑡) − 𝐾𝐷 𝛥2 𝑦(𝑡) (4)𝜀(𝑡) ≔ 𝑟(𝑡) − 𝑦(𝑡),(5)where 𝐾𝑃 , 𝐾𝐼 and 𝐾𝐷 are proportional gain, integral
gain and derivative gain, respectively. 𝛥 denotes adifference operator. Note that the controller of AFO in(12)

where 𝑤𝑖 is the weight parameter corresponding to the� (𝑖)𝑖 th information vector 𝝓in the selectedneighbors’ data. It is calculated by the following
equation:
1/(1 + 𝑑𝑖 ).
(13)
𝑤𝑖 = 𝑘∑𝑖=1{1/(1 + 𝑑𝑖 )}The off-line learning method is described in next
section.

15

Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 1 (June 2017) 14–17___________________________________________________________________________________________________________

4.3. Fictitious Reference Iterative Tuning: FRITFig. 3 shows a block diagram of the FRIT4. FRIT is ascheme to calculate control parameters directly fromclosed-loop data which are input 𝑤0 (𝑡), output 𝑦0 (𝑡).
𝑤0 (𝑡) is given by the following equation:(14)
𝛥𝑤0 (𝑡) = 𝐾𝐼 𝑒0 (𝑡) − 𝐾𝑃 𝛥𝑦0 (𝑡) − 𝐾𝐷 𝛥2 𝑦0 (𝑡),where 𝑒0 (𝑡) = 𝑟̃ (𝑡) − 𝑦0 (𝑡). 𝑟̃ (𝑡) is derived asfollows:𝑟̃ (𝑡) = [𝛥𝑤0 (𝑡) + 𝐾𝑃 𝛥𝑦0 (𝑡)+𝐾𝐼 𝑦0 (𝑡) + 𝐾𝐷 𝛥2 𝑦0 (𝑡)]/𝐾𝐼 . (15)
In addition, the user-specified reference model isexpressed by the following equation:𝑧 −1 𝑃(1)𝑦�𝑚 (𝑡) =𝑟̃ (𝑡),(16)𝑃(𝑧 −1 )where 𝑦�𝑚 (𝑡) is reference model output and 𝑃(𝑧 −1 ) is
the user-specified polynomial.

Fig. 4. Walking trajectories by using fixed PID controller as
primary controller.

4.4. Off-line learning method in Data-Driven
Control scheme by using FRIT
In this section, an off-line learning method is describedby using FRIT. Firstly, the number of neighbors’ data 𝑘
is selected and 𝑲𝑜𝑜𝑜 (𝑡) is calculated by equation (12)by using closed-loop data 𝑤0 (𝑡) and 𝑦0 (𝑡). Next, thefollowing steepest descent method is utilized to modify
the control parameters:𝜕𝜕(𝑡 + 1)(17)𝑲𝑛𝑛𝑛 (𝑡) = 𝑲𝑜𝑜𝑜 (𝑡) − 𝜼𝜕𝑲(𝑡)𝜼 = [𝜂𝑃 , 𝜂𝐼 , 𝜂𝐷 ],where 𝜼 denotes the learning ratio and 𝐽(𝑡) isdefined as the following error criterion:
1(18)𝐽(𝑡) ≔ 𝜖(𝑡)22(19)𝜖(𝑡) ≔ 𝑦0 (𝑡) − 𝑦�𝑚 (𝑡).
The each partial differential of equation (17) are
expanded as follows:𝜕𝜕(𝑡 + 1)
𝜕𝜕(𝑡 + 1) 𝜕𝑦�𝑚 (𝑡 + 1) 𝜕𝑟̃ (𝑡)⎫=𝜕𝐾𝑃 (𝑡)𝜕𝑦�𝑚 (𝑡 + 1) 𝜕𝑟̃ (𝑡) 𝜕𝐾𝑃 (𝑡) ⎪𝜖(𝑡 + 1)𝑃(1)𝛥𝑦0 (𝑡)⎪=⎪𝐾𝐼𝑜𝑜𝑜 (𝑡)𝜕𝜕(𝑡 + 1)
𝜕𝜕(𝑡 + 1) 𝜕𝑦�𝑚 (𝑡 + 1) 𝜕𝑟̃ (𝑡) ⎪=⎪𝜕𝐾𝐼 (𝑡)𝜕𝑦�𝑚 (𝑡 + 1) 𝜕𝑟̃ (𝑡) 𝜕𝐾𝐼 (𝑡), (20)𝜖(𝑡 + 1)𝑃(1)𝛤(𝑡)⎬=⎪𝐾𝐼𝑜𝑜𝑜 (𝑡)2𝜕𝜕(𝑡 + 1)
𝜕𝜕(𝑡 + 1) 𝜕𝑦�𝑚 (𝑡 + 1) 𝜕𝑟̃ (𝑡) ⎪=⎪𝜕𝐾𝐷 (𝑡)𝜕𝑦�𝑚 (𝑡 + 1) 𝜕𝑟̃ (𝑡) 𝜕𝐾𝐷 (𝑡)⎪2 (𝑡)𝜖(𝑡 + 1)𝑃(1)𝛥 𝑦0⎪=
𝐾𝐼𝑜𝑜𝑜 (𝑡)⎭Where 𝛤(𝑡) is given by the following equation:

Fig. 5. Trajectories of Kansei signal 𝑦(t) and ankle angle
𝜃1 (t) corresponding to Fig. 4.

𝛤(𝑡) = −Δ𝑤0 (𝑡) − {𝐾𝑃𝑜𝑜𝑜 (𝑡) + 𝐾𝐷𝑜𝑜𝑜 (𝑡)}𝑦0 (𝑡)+{𝐾𝑃𝑜𝑜𝑜 (𝑡) + 2𝐾𝐷𝑜𝑜𝑜 (𝑡)}𝑦0 (𝑡 − 1)𝑜𝑜𝑜 (𝑡)𝑦 (𝑡− 2).
(21)−𝐾𝐷0Hence, equation (17) and (20) show that control
parameters can be learned off-line by using closed-loop
data.
5. Numerical Example
In this section, the effectiveness of the proposed
scheme is verified. The physical parameters5,6 in Fig. 2
are set as follows: 𝐼1 = 0.44[kg ⋅ m2 ], 𝐼2 = 0.72[kg ⋅m2 ], 𝑚1 = 3.26[kg], 𝑚2 = 7.00[kg], 𝐿1 = 0.42[m],𝐿2 = 0.42[m] , 𝑙1 = 0.24[m] , 𝑙2 = 0.24[m] ,𝑔 = 0.98[m/s 2 ], 𝜼 = [104 , 10−3 , 104 ].
Fig. 4 shows the walking trajectories corresponding toFig. 2 by using a fixed PID controller instead of a
primary controller. The dotted red line denotes thereference walking trajectory of brain. Walking support

16

Journal of Robotics, Networking and Artificial Life, Vol. 4, No. 1 (June 2017) 14–17___________________________________________________________________________________________________________does not worked well in Fig. 4 because the blue solidline does not follow the red reference signal. Therefore,
the Kansei signal 𝑦(𝑡) is not kept around 1 in Fig. 5.
Moreover, a fixed PID controller cannot estimate thereference signal well because 𝑤(𝑡) does not follow𝑟𝜃1 (𝑡).
6. Conclusion
In contrast, the walking trajectories of Fig. 6 by using
the proposed scheme is better than Fig. 7. The
effectiveness of the proposed scheme is shown bykeeping approximately 𝑦(𝑡) = 1 in Fig. 7. The
estimated reference signal 𝑤(t) follows 𝑟𝜃 (t) using adata-driven controller, and PID gains in Fig. 8 areadjusted effectively.
In this paper, the field of welfare equipment has been
focused and the scheme based on the data-orientedKansei feedback has been proposed to support each
person adaptively. In the proposed scheme, reference
signal of a brain was estimated by using a data-driven
controller and it supports walking well. The proposed
scheme has been verified by numerical example. In thefuture, experimental result will be considered.
This work was supported by JSPS KAKENHI Grant
Number 16K14285.

Fig. 6. Walking trajectories by using the proposed scheme.

References
1. T. Yamamoto and K. Takao and T. Yamada, “Design of a
Data-Driven PID Controller”, IEEE Trans on control
systems Technology, 17(1) (2009) 29–39.
2. S. Yamamoto, "Development of Ankle Foot Orthosis for
Hemiplegic Patients Based on Gait Analysis (inJapanese)", The Journal of Japanese Physical Therapy
Association, Vol.39, No.4, pp.240-244 (2012)
3. G. T. Fechner, “Elements of Psychophysics”, New York:holt, Rinehart and Winston (1966)
4. S. Soma, O. Kaneko and T.Fujii, “A New Approach toParameter Tuning of Controllers by Using One-Shot
Experimental Data: A Proposal of Fictitious Reference
Iterative Tuning (in Japanese)”, Trans. of the Institute ofsystems, Control and Information Engineers, 17(2)(2004) 528–536.
5. W. T. Dempster: ``Space Requirements of the Seated
Operator'', WADC(1955)
6. I. P. Herman: “Physics of the Human Body: Biologicaland Medical Physics, Biomedical Engineering”,
Springer-Verlag GmbH & CO. KG(2007)

Fig. 7. Trajectories of Kansei signal 𝑦(t) and ankle angle
𝜃1 (t) corresponding to Fig. 6.

Fig. 8. Trajectories of PID gains corresponding to Fig. 6.

17