358 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 66, NO. 1, JANUARY 2019
Discrete-Time Direct Model Reference Adaptive
Control Application in a High-Precision Inertially
Stabilized Platform
Deng Ke , Shuang Cong , Senior Member, IEEE, Dejie Kong, and Honghai Shen
Abstract—This paper studies the practical use of
discrete-time direct adaptive control in a high-precision
inertially stabilized platform’s turbulence isolation system
for the purpose of enhancing isolation performance. Under
low-frequency and low-velocity environments, the velocity-
stabilized loop of the platform shows severe nonlinear char-
acteristic; therefore, its isolation performance is limited. In
previous research, we constructed a nonlinear model of the
velocity-stabilized loop by using an improved Stribeck fric-
tion model, and also designed a feed-forward compensation
strategy. Both have obtained outstanding performance dur-
ing practical experiments. However, errors still exist as dis-
turbance of the unmodeled part and environmental change
causes the system’s parameter to vary. To solve this, a
novel discrete-time direct model reference adaptive con-
trol based on nonlinear friction compensation is introduced
to the original proportional-integral control system. An im-
proved projection algorithm and a recursive least-square al-
gorithm with fading memory are respectively used to design
the adaptive law. By using a turbulence observer to provide
a reference signal, both types of controls are applied to the
carrier turbulence isolation system. Results of the practical
experiments prove that model reference adaptive control
can further enhance the system’s isolation ability.
Index Terms—Adaptive control, inertially stabilized
platform (ISP), model reference adaptive control, nonlinear
friction, turbulence isolation.
Manuscript received September 24, 2017; revised January 25, 2018
and March 7, 2018; accepted April 6, 2018. Date of publication April 27,
2018; date of current version August 31, 2018. This work was supported
in part by the Projects of Ultra-Precision Control System Joint Laboratory
of USTC under Grant KD1012210167 and in part by the National Natural
Science Foundation of China under Grant 61573330. (Corresponding
author: Shuang Cong.)
D. Ke is with the State Key Laboratory of Air Traffic Management
System and Technology, Nanjing 210001, China (e-mail: dengke@
mail.ustc.edu.cn). (e-mail:,dengke@mail.ustc.edu.cn).
S. Cong is with the , Department of AutomationUniversity of Sci-
ence and Technology of China, Hefei 230027, China (e-mail: scong@
ustc.edu.cn). (e-mail:,scong@ustc.edu.cn).
D. Kong is with the , Department of Optoelectronic Engineer-
ingChangchun University of Science and Technology, Changchun
130022, China (e-mail: kongdejie78@126.com). (e-mail:, kongde-
jie78@126.com).
H. Shen is with the , Key Laboratory of Aviation Optical Imaging
and MeasurementChangchun Institute of Optics, Fine Mechanics and
Physics,, Chinese Academy of Sciences, Changchun 130022, China
(e-mail: shenhh@ciomp.ac.cn). (e-mail:,shenhh@ciomp.ac.cn).
Digital Object Identifier 10.1109/TIE.2018.2831181
I. INTRODUCTION
I
NERTIALLY stabilized platform (ISP) is the core device
used in navigation, guidance, and measurement applications.
It is used to isolate carrier turbulence and stabilize the optical
equipment, so the equipment can keep its orientation or main-
tain line-of-sight [1]. It has a wide range of use in both civil and
military applications [2], [3] such as aircraft, ships, and electron
telescopes. Furthermore, high-precision ISP is one of the most
important components in the present day sophisticated military
equipment. The stabilization accuracy of the optical axis is one
of the key performance indexes of ISP, and it directly impacts
its tolerance toward carrier turbulence. This is currently reduced
to microradian magnitude (μrad). ISP is a complicated control
system, and it is affected by various disturbances, for example,
nonlinear frictions, gyrodrift, and mechanical resonance. Under
the assumption that the hardware of ISP is fixed, the key to fur-
ther improve accuracy lies within analyzing errors and how they
affect the system, and then designing a strategy to compensate
them. Accurate modeling of the platform is the most effective
method to analyze the errors.
ISP requires high stabilization precision and quick real-time
feedback [4], especially because the optical equipment it carries
already faces the problem of time lapse during identification
and analysis of the t arget. Due to its high practical usage, a
linear controller with a simple design and structure, such as
proportional-integral-differential (PID) compensator, is widely
used on ISP. However, its ability to further increase stabilization
precision faces two limitations. First, under low-frequency and
low-velocity environment, nonlinear friction causes the qual-
ity of the control system to significantly decrease [5]. Sec-
ond, when environment change occurs, it is unable to overcome
the control error that is brought by parameter variations of the
system.
For the first limitation, nonlinear modeling and friction com-
pensation are effective methods to rectify it. Currently, friction
compensation is a necessary process in high-precision control
system [6], and it has been split into model-based and model-
free. The key to model-based friction compensation is to select
the proper friction model and to identify important parameters
[7]. Various types of friction models [8] are currently being stud-
ied, and are split into static friction model and dynamic friction
model. The static friction models, i.e., Stribeck model [8], have
a simple and practical structure, but they face problems such
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