Adaptive multilayer T-S fuzzy controller for nonlinear siso system optimized by differential evolution algorithm

Science & Technology Development Journal – Engineering and Technology, 2(SI1):SI9-SI21
Open Access Full Text Article Research Article
1Industrial University of Ho Chi Minh
City, Viet Nam
2Faculty of Electrical and Electronics
Engineering, Ho Chi Minh City
University of Technology (HCMUT), 268
Ly Thuong Kiet Street, District 10, Ho
Chi Minh City, Vietnam
3Vietnam National University Ho Chi
Minh City, Linh Trung Ward, Thu Duc
District, Ho Chi Minh City, Vietnam
Correspondence
Ho PhamHuy Anh, Faculty of Electrical
and Electronics Engineering, Ho Chi
Minh City University of Technology
(HCMUT), 268 Ly Thuong Kiet Street,
District 10, Ho Chi Minh City, Vietnam
Vietnam National University Ho Chi Minh
City, Linh Trung Ward, Thu Duc District,
Ho Chi Minh City, Vietnam
Email: hphanh@hcmut.edu.vn
History
 Received: 18-10-2018
 Accepted: 12-12-2018
 Published: xx-12-2019
DOI : 10.32508/stdjet.v3iSI1.717 
Adaptivemultilayer T-S fuzzy controller for nonlinear SISO system
optimized by differential evolution algorithm
Cao Van Kien1, Ho PhamHuy Anh2,3,*
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ABSTRACT
In this paper, the authors propose a novel adaptive multilayer T-S fuzzy controller (AMTFC) with a
optimize soft computing algorithm for a class of robust control uncertain nonlinear SISO systems.
First, a new multilayer T-S fuzzy was created by combined multiple simple T-S fuzzy model with a
sum function in the output. The multi-layer fuzzy model used in nonlinear identification has many
advantages over conventional fuzzy models, but it cannot be created by the writer's experience or
the trial and error method. It can only be created using an optimization algorithm. Then the pa-
rameters of multilayer fuzzy model is optimized by the differential evolution DE algorithm is used
to offline identify the inverse nonlinear system with uncertain parameters. The trained model was
validated by a different dataset from the training dataset for guarantee the convergence of the
training algorithm. Second, for robustly and adaptive purposes, the authors have proposed an ad-
ditional adaptive fuzzy model based on Lyapunov stability theory combined with the optimized
multilayer fuzzy. The adaptive fuzzy based on sliding mode surface is designed to guarantee that
the closed-loop system is asymptotically stable has been proved base on a lyapunov stability the-
ory. Furthermore, simulation tests are perfomed in Matlab/Simulink environment that controling
a water level of coupled tank with uncertain parameters are given to illustrate the effectiveness of
the proposed control scheme. The proposed control algorithm is implemented in simulation with
many different control parameters and it is also compared with the conventional adaptive control
algorithm and inverse controller. The simulation results also shows the superior of proposed con-
troller than an adaptive fuzzy control or inverse controller when using the least mean square error
standard.
Key words: Multilayer T-S Fuzzy, Inverse Controller, Adaptive Control, Differential Evolution,
Lyapunov Theory
INTRODUCTION
Fuzzy logic was first proposed in 1965 by Zadeh1.
There aremany studies developed based on this fuzzy-
based domain, such as Fuzzy type-2, Fuzzy type-n,
neural fuzzy, hierarchical fuzzy to model and con-
trol nonlinear system,2,3. Recently, Takagi–Sugeno
(T–S) fuzzy model can provide a modeling frame for
nonlinear systems. The advantage of T–S fuzzy sys-
tems is that they allow us to use a set of local linear
systemswith correspondingmembership functions to
represent nonlinear systems. The T-S fuzzy model
is widely accepted as a powerful modeling tool and
it’s applications to various kinds of non-linear sys-
tems can be found in 4–9. Based on the T-S fuzzy
model of a plant, papers10–13 introduced a fuzzy con-
trol designmethod for nonlinear systems with a guar-
anteed H2=¥ model reference tracking performance.
However, if the membership functions of the T–S
fuzzy system encounter parametric-uncertainty prob-
lem, the T–S fuzzy system cannot operate efficiently.
Moreover, with a complex system, the more time it
requires for training, the more complex membership
functions that eventual fuzzy rule-table will become.
To achieve a higher precision from the Fuzzy model,
its parameters are required to be optimized and the
fuzzy structure is needed to be changed. Recently,
Type-2 fuzzy sets14–16 have been shown that they
prove better than type-1 ones both on representing
the nonlinear systems and handling the uncertain-
ties. Paper17 presented the problem of fuzzy con-
trol for nonlinear networked control systems with
packet dropouts and parameter uncertainties based
on the interval type-2 fuzzy-model-based approach.
Paper18 introduced an inverse controller based on
a type-2 fuzzy model control. Moreover, many re-
searchers used the optimization algorithms such as
a cuck ...  is superior to inverse fuzzy control methods and
adaptive fuzzy control.
CONCLUSIONS
In this paper, we propose an adaptive inverse multi-
layer fuzzy control coupled tanks system fluid level
regulation. The adaptive inverse multilayer fuzzy
logic controller is created from themultiple T-S Fuzzy
models and adaptive fuzzy model. The simulation
results show that proposed adaptive multilayer fuzzy
logic controller can be efficiently applied for con-
trol nonlinear system. The proposed controller pos-
sesses better control quality and proves strongly ro-
bust due to satisfy Lyapunov stability principle. It
is available for applying a scalable multilayer fuzzy
model to amore complex nonlinear uncertain system.
Thus, these results also ensure that proposed multi-
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Science & Technology Development Journal – Engineering and Technology, 2(SI1):SI9-SI21
Figure 7: Validation result
Figure 8: Comparison results of algorithms with alpha=10, K=5
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Science & Technology Development Journal – Engineering and Technology, 2(SI1):SI9-SI21
Figure 9: Comparison results of algorithms with alpha=2, K=5
Figure 10: Comparative results of algorithms with alpha=0.3, K=5
Table 2: COMPARATIVE PERFORMANCE OF THREE CONTROLLERS
Method LMSE
Inverse Fuzzy Control (IFC) 6.322 6.322
Adaptive Fuzzy Control (AFC) 4.229 4.675
Proposed Inverse Fuzzy Control with Adaptive Fuzzy (IFC+AFC) 2.648 2.8
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layer fuzzy controller can be used to successfully con-
trol of uncertain nonlinear complex system in near fu-
ture study.
ABBREVIATION
SISO: Single Input – Single Output
MISO: Multi Input – Single Output
MIMO: Multi Input – Multi Output
DE: Differential Evolution
GA: Genetic Algorithm
PSO: Particle Swarm Optimization
T-S Fuzzy: Takagi-Sugeno Fuzzy
CONFLICT OF INTEREST
Theauthors declare that there is no conflict of interest.
AUTHOR CONTRIBUTIONS
CaoVanKien: Designed and performed experiments,
analysed data and co-wrote the paper.
Ho Pham Huy Anh: Supervised the research and co-
wrote the paper.
ACKNOWLEDGEMENT
This research is funded by Vietnam National Univer-
sity of Ho Chi Minh City (VNU-HCM) under grant
number B2020-20-04. We acknowledge the support
of time and facilities from Ho Chi Minh City Uni-
versity of Technology (HCMUT), VNU-HCM for this
study.
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Open Access Full Text Article Bài Nghiên cứu
1Trường Đại học Công nghiệp Tp.HCM,
Việt Nam
2Trường Đại học Bách Khoa,
ĐHQG-HCM, Việt Nam
3Trường Đại học Công nghiệp Tp.HCM,
Việt Nam
Liên hệ
Hồ PhạmHuy Ánh, Trường Đại học Bách
Khoa, ĐHQG-HCM, Việt Nam
Email: hphanh@hcmut.edu.vn
Lịch sử
 Ngày nhận: 18-10-2018
 Ngày chấp nhận: 12-12-2018
 Ngày đăng: 31-12-2019
DOI : 10.32508/stdjet.v3iSI1.717
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the Creative Commons Attribution 4.0
International license.
Điều khiểnmờ nhiều lớp thích nghi áp dụng chomô hình phi
tuyến SISO tối ưu với giải thuật tiến hóa vi sai
Cao Văn Kiên1, Hồ PhạmHuy Ánh2,*, Nguyễn Ngọc Sơn3
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TÓM TẮT
Bài báo đề xuất giải thuật điều khiển mờ nhiều lớp thích nghi (AMTFC) kết hợp giải thuật tính toán
mềm tối ưu áp dụng cho điều khiển hệ phi tuyến SISO có các tham số không chắc chắn. Đầu tiên,
mô hình mờ nhiều lớp được tạo ra bằng cách ghép nhiều mô hình mờ đơn giản với ngõ ra là một
hàm tổng. Mô hình fuzzy nhiều lớp dùng trong nhận dạng hệ phi tuyến có nhiều đặc điểm vượt
trội hơn so với mô hình mờ thông thường, tuy nhiên nó không thể tạo ra bằng kinh nghiệm của
người viết hay phương pháp thử sai nên chỉ có thể kết hợp với một giải thuật tối ưu. Các tham số
của mô hình mờ nhiều lớp ngược sau đó được nhận dạng với giải thuật tiến hóa vi sai (DE) nâng
cao để nhận dạngmô hình ngược của hệ phi tuyến với các tham số không chắc chắn. Kết quả mô
hình ngược được đánh giá trênmột tập dữ liệu khác so với tập dữ liệu huấn luyện để đảm bảo tính
hội tụ của mô hình nhận dạng. Tiếp theo, để tăng tính ổn định và sự thích nghi của giải thuật điều
khiển, tác giả đã có những đề xuất thêm vàomộtmô hìnhmờ thích nghi được xây dựng dựa vào lý
thuyết ổn định Lyapunov kết hợp với mô hình điều khiển ngược trước đó. Mô hình mờ thích nghi
dựa vào mặt trượt được thiết kế để đảm bảo hệ kín ổn định tiệm cận đã được các tác giả chứng
minh thành công theo lý thuyết ổn định Lyapunov. Thêm nữa, kết quả mô phỏng điều khiển mực
nướcmô hình bồn nước đôi với nhiều tham số điều khiển khác nhau và chất lượng điều khiển theo
tiêu chuẩn tổng bình phương sai số đã chứng minh sự hiệu quả của giải thuật đề xuất so với các
giải thuật điều khiển thích nghi truyền thống hoặc giải thuật điều khiển ngược.
Từ khoá: Mô hình mờ nhiều lớp, điều khiển ngược, điều khiển thích nghi, giải thuật tiến hóa vi
sai, ổn định Lyapunov
Trích dẫn bài báo này: Văn Kiên C, Huy Ánh H P, Ngọc Sơn N. Điều khiển mờ nhiều lớp thích nghi áp
dụng cho mô hình phi tuyến SISO tối ưu với giải thuật tiến hóa vi sai. Sci. Tech. Dev. J. - Eng. Tech.;
2(SI1):SI9-SI21.
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