Fuzzy gain scheduling control apply to an RC Hovercraft

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 10, No. 3, June 2020, pp. 2434~2440
ISSN: 2088-8708, DOI: 10.11591/ijece.v10i3.pp2434-2440  2434
Journal homepage: http://ijece.iaescore.com/index.php/IJECE
Fuzzy gain scheduling control apply to an RC Hovercraft
Huu Khoa Tran1
, Pham Duc Lam2
, Tran Thanh Trang3
, Xuan Tien Nguyen4
, Hoang-Nam Nguyen5
1
Industry 4.0 Center, National Taiwan University of Science and Technology, Taiwan
1
Center for Cyber-Physical System Innovation, National Taiwan University of Science and Technology, Taiwan
2
Faculty of Mechanical, Electrical, Electronic and Automotive Engineering, Nguyen Tat Thanh University, Vietnam
3
Faculty of Engineering and Technology, Van Hien University, Vietnam
4
Faculty of Electronics and Telecommunications, Saigon University, Vietnam
5
Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical and
Electronics Engineering, Ton Duc Thang University, Vietnam
Article Info ABSTRACT
Article history:
Received Jun 16, 2019
Revised Nov 27, 2019
Accepted Dec 12, 2019
The Fuzzy Gain Scheduling (FGS) methodology for tuning the Proportional-
Integral-Derivative (PID) traditional controller parameters by scheduling
controlled gains in different phases, is a simple and effective application both
in industries and real-time complex models while assuring the high
achievements over pass decades, is proposed in this article. The Fuzzy logic
rules of the triangular membership functions are exploited on-line to verify
the Gain Scheduling of the Proportional-Integral-Derivative controller gains
in different stages because it can minimize the tracking control error and
utilize the Integral of Time Absolute Error (ITAE) minima criterion of
the controller design process. For that reason, the controller design could
tune the system model in the whole operation time to display the efficiency
in tracking error. It is then implemented in a novel Remote Controlled (RC)
Hovercraft motion models to demonstrate better control performance in
comparison with the PID conventional controller.
Keywords:
Fuzzy gain scheduling
ITAE criterion
PID control
RC Hovercraft
Copyright © 2020 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Hoang-Nam Nguyen,
Modeling Evolutionary Algorithms Simulation and Artificial Intelligence,
Faculty of Electrical and Electronics Engineering, Ton Duc Thang University,
19 Nguyen Huu Tho street, Tan Phong ward, District 7, Ho Chi Minh City, Vietnam.
Email: nguyenhoangnam@tdtu.edu.vn
1. INTRODUCTION
PID controller is one of the most popular controller and is applied in many operation conditions due
to its simple structure and effectiveness [1]. In literature, PID controllers is literally divided into two main
categories. The first is the controller gains, which have been tuned or chosen by traditional ways, are fixed
during the running time and Ziegler-Nichols tuning methodology is the best representative off-line
formula [2]. In this category, the PID controller gain designs are simple and cannot always effective, it is also
mean that different gains give the different system's response. The controller designs in the second category
have a similarity structure, however, its parameters are adapted on-line throughout the operating time.
With the purpose of getting the optimal performance in terms of accuracy, stability and satisfatory response,
the control system must carefully consider the compromise between the settling time and the overshoot.
Thus, the PID parameters design of the new operating conditions have spent lots of time for tuning [1].
Gain scheduling is regarded as an excellent controller design approaches in [2, 3]. It can be
classified as “divide-and-conquer” control procedure type, in which some linear sub-problems are combined
to implement the non-linear design operation [2] and various gains of controllers are utilized in every
regions. The critical point in building a good controller is determining the scheduling variables, which have
suitable priori insight to the process dynamics [3]. State variables, errors and their changing rates are

Int J Elec & Comp Eng ISSN: 2088-8708 
Fuzzy gain scheduling control apply to an RC hovercraft (Huu Khoa Tran)
2435
commonlu used variables [4-7]. Designers can determine the regions by magnitudes of scheduling
variables or establish the regions by local linearization of dynamic model in the neigbor of some special
operating points [2, 3].
In this work, we intend to create a simple and effective control sytem for quick positioning utilizing
PID controller‘s characteristics. For fast convergence of the controlled system, we set gains to have large
magnitude as scheduling variables are high. Similarly, for system to be settling with less fluctuation, we keep
the gains have low magnitude when scheduling parameters are low. This scheme practically works in
tracking. Unfortunately, this conventional approach can not satisfy the fast-rising response requirement in the
beginning phase since both the time derivative and its error are too low to obtain acceptable large control
output. Therefore, time delay is not very different with traditional PID controller. Actually, the setpoints in
each movement could be the most suitable scheduling variable that satisfies our goal. Orelind et al. [8]
first designed optimal PID gain schedule for the hydro-generators system. In [9], Beaven et al. use
the gain scheduling of setpoints in high-speed independent 2-phase drive. Situm et al. [10] applied this
method to servo pneumatic position control. Later, Dounis et.al. [11] and Vijaya Chandrakala et.al. [12]
exploited adaptive fuzzy gain scheduling to the energy systems. Next, Kankgasabai and Jaya [13] and
Ahmad et. al. [14] then control the PID gains with this technique for MIMO process control. Currently,
Yao and Lakerveld employ this method to microfluidic devices [15]. Yilmaz et.al. also exploit
the gain-scheduling PID controllers for Z-source inverter [16].
In our research, we proposed to apply fuzzy gain scheduling technology for designing a motion
controller. Firstly, we created a PID controller that has large magnitudes of proportional and integral gains
and low magnitude of derivative gain in the motion initialization period. Later, the fuzzy gain scheduling
technique is applied to slowly increase the derivative gain as well as reduce the proportional and integral
gains until another setpoint is met. The first setpoint is then chosen at the ending part of the trapezoid curve
of constant speed region. By this way, the speed could be kept constant as less fluctuation as possible in
the unchanged speed region. We aim to build a moving system to come to the target location and obtain
settling state in a short period. The key technique in proposed approach is the fuzzy logic-based technique of
gain scheduling. After finding the suitable regions for implementing gain scheduling. The suitable controller
gains are determined to achieve our goal. The Hovercraft motion model [17-22] is utilized to demonstrate
the effectiveness of this novel method. It is then compared with the traditional PID auto-tuning control.
This work is presented as follows: In section 2, the development of fuzzy gain scheduling scheme
for dynamic reset of PID controllers is proposed. In section 3, we present how to configure the RC
Hovercraft model. In section 4, we present the simulation results of the proposed controller system
performance. Finally, conclusions are discussed in section 5.
2. RESEARCH METHOD
2.1. PID controller
In literature, discrete-time PID controller is usually defined as:
   
   1
( )P D
1
e n e nn
u n K e n K T e i KI S i TS
 
  

(1)
where, u(n) is known as the control signal and e(n) represents the error input. Ts is the sampling period.
Moreover, the proportional, integral and derivative gains are represented by KP, KI and KD, respectively.
These gains can be tuned to output various responses of a specific process.
2.2. Fuzzy gain scheduling
In many schemes of gain scheduling design process, suitable regions for the variable need to be
determined [7]. The T-curve (trapezoidal velocity curve) as shown in Figure 1, which has three parts:
acceleration t 𝜖 [0, t1], constant speed t 𝜖 [t1, t2], and deceleration t 𝜖 [t2, t3], is chosen to find out the regions.
In the deceleration phase [t2, t3], we apply fuzzy logic technique (inference rule) to change these parameters
linearly and continuously. The two membership functions μ1 and μ2 are demonstared in Figure 2. The Fuzzy
logic inference rules are expressed as followings:
If p<p1, then μ1=1 and μ2=0.
If 21 ppp  , then μ1= 2
2 1
p p
p p


and μ2= 1
2 1
p p
p p


.
If p > p2, then μ1=0 and μ2=1.

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 10, No. 3, June 2020 : 2434 - 2440
2436
Figure 1. Trapezoidal velocity/position curve Figure 2. Membership functions vs set points
The desired positions of the moving model, which based on the above fuzzy logic rules,
are employed to evaluate the response performances. The proposed Fuzzy-PID control system block diagram,
which included two fuzzy logic membership functions, is demonstrated as shown in Figure 3. Specifically,
weighting μi of the i-th membership function depends on the current command position p=yd(t).
We choose μ1=1, andμ2=0 in phase I of initial PID gains. In phase II, 2
1
2 1
p p
p p




, and 1
2
2 1
p p
p p




are chosen
as the blended gains. The second set of initial gains in phase III are μ1 = 0, and μ2=1. The PID gains can be
calculated in any time point and the subscripts 1 and 2 of the PID gains represent the membership function
I and II in (2).
.
.
.
K KiP Pii
K KiI Iii
K KiD Dii











(2)
The standard criterion ITAE [23-25], which are multiply by time at each sampling data and express as
. ( ) .
0
ITAE t e t dt

  , is chosen as the eye to show the less error for both controller design methods Ziegler-
Nichols and Fuzzy Gain Scheduling, which applied to the RC Hovercraft motion models.
Figure 3. The fuzzy gain scheduling-PID controller diagram
3. RC HOVERCRAFT CONFIGURATION MODEL
A hovercraft, also known as an air cushion vehicle (ACV), consists of rotors and a cushion.
The hovercraft can float and cruise smoothly on various surfacec such as rough land, water, sand beach,
as well as the ice [17-22] due to the inside air pressure of the cushion. The lift propeller provides the internal
cushion pressure for operating a long period of time. A hovercraft turning typically is done by directing
the thrust air flow through rotor duct fan and steering by a tilt servo motor placed at the rear. The subsequent
momentum generated is used to maneuver the craft. Though many modern technologies are utilized,

0
1t 2t 3t
m

2
p1
p
1
0

2437
the hovercraft requires an advanced maneuvering system to achieve optimized performance. Hence, this
paper presents an agile autonomous hovercraft model. It has a single tilt servo motor, which is equipped on
the fin tail. The rotor duct fan is settled along the y-axis and the propeller is attached along the z-axis,
as shown in Figure 4.
Figure 4. The Hovercraft configuration model
The dynamic of the Hovercraft model is derived from [19-21] and the vehicle is demonstrated
utilizing right-hand coordinate system. Additionalyy, positive x-axis shows the lateral, namely sway motion
or surge position. Positive y-axis goes along to the hovercraft body, namely surge motion or sway position.
Besides, positive z-axis is oriented downwards. The Hovercraft’s kinematics can be expressed as:
cos sin
cos sin
x u v
y v u
r
 
 

 
 




 (3)
where ris called as angular velocity, u and v are linear velocities in surge direction and
sway direction, respectively. Using (1), the kinetic and potential energy are derived to define
the Lagrange L=T-V and by applying Euler-Lagrange formulation:
( ) ( , )
0
F
M q q C q q q  
 
 
 
  (4)
where F  represents the control force along the surge direction,   is the torque moment in yaw
action. The torque control depends on F and is at right angle to the center line of the hovercraft propeller.
4. RESULTS AND ANALYSIS
The simulation parameters of the Hovercraft are derived from [19-21] and denoted shortly with
the mass m = 2.1 kg and the inertia moment I = 0.000257. Based on the Hovercraft model, the PID gains are
chosen in [0, 20] range. The proposed control performances in Figures 5, 6, and 7 are displayed in each
channel: surge position x, sway position y and yaw angle, respectively. We then use Matlab to implement
the model. The numerical simulation results have proved that the proposed controllers show significant
stability and robust performance response. The proposed Fuzzy Gain Scheduling for PID controller
simulation have all received results have the maximum response time, without overshoot and less error,
are just after the first second at all. The optimal gains issue is considering in the future work.

 ISSN: 2088-8708
2438
(a) (b)
Figure 5. (a) Fuzzy gain scheduling tuning pid gains, (b) surge control
(a) (b)
Figure 6. (a) fuzzy gain scheduling tuning PID gains, (b) sway control
(a) (b)
Figure 7. (a) fuzzy gain scheduling tuning PID gains, (b) Steering-yaw control
5. CONCLUSION
In this article, the Fuzzy Gain Scheduling is extensively to verify the conventional PID control
parameters. The scheme has been tested on the motion models of the RC Hovercraft and the reasonable
results are obtained. Thus, the operation time is prominently decreased and the goal of fast positioning is
achieved. This method, although is simple but effective in the most control systems. It would be helpful to
promote control system.

2439
ACKNOWLEDGEMENTS
This work was financially supported by the “Center for Cyber-physical System Innovation” from
The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project
by the Ministry of Education (MOE) in Taiwan.
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 ISSN: 2088-8708
2440
BIOGRAPHIES OF AUTHORS
HUU KHOA, TRAN received Ph.D. degrees in the area of Mechatronics Technology from
the Southern Taiwan University of Science and Technology (STUST), Tainan, Taiwan in 2015.
He is currently an Assistant Professor at National Taiwan University of Science and Technology
(NTUST), Taipei, Taiwan. He has over 15 research papers. His research interests include Artificial
Intelligence, Autonomous Robot (UAV, AGV), Decision and Control, Optimization Algorithms, Big
Data and Internet of Things.
Duc-Lam Pham graduated his Master Degree in Mechatronics Engineering from Ho Chi Minh
University of Transport in 2014. He is currently working as Head of Department of Mechatronics
Engineering, Nguyen Tat Thanh University (Vietnam). His research interests include automatic
control, mechatronics engineering, medical engineering and artificial intelligence.
Tran Thanh Trang was born in Vietnam in 1979. He received the B.E and M.E degrees in electronics
engineering from Ho Chi Minh city University of Technology, National University Ho Chi Minh city,
Vietnam, in 2001 and 2004, respectively, and the Ph.D degree in electronics engineering from
Yeungnam University, South Korea in 2012. His research interests is display engineering, photovoltaic
systems, optoelectronics and automatic control system.
Nguyen Xuan Tien received a Bachelor of Physics - Specialization in Nuclear Electronics from Dalat
University in 1988, received a Master's Degree in Mechatronics Engineering from HUTECH
University of Technology, Ho Chi Minh City in 2014. Currently, he is pursuing the Ph.D.
degree and is a lecturer at Faculty of Electronics and Telecommunications, Saigon University.
His research fields including Automation Control, Robotics and Mechatronics systems and
applications.
Hoang-Nam Nguyen graduated his Ph.D degree in Mechanical Engineering from National Chiao
Tung University (Taiwan) in 2017. He is currently working as Lecturer of Faculty of Electrical and
Electronics Engineering, Ton Duc Thang University (Vietnam). His research interests include image
processing, computer vision, computational mechanics, automatic control and artificial intelligence.

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