Chin. Phys. B Vol. 24, No. 11 (2015) 110504
Full-order sliding mode control of uncertain chaos in a permanent
magnet synchronous motor based on a fuzzy extended state observer
∗
Chen Qiang(陈 强)
a)†
, Nan Yu-Rong(南余荣)
a)
, Zheng Heng-Huo(郑恒火)
a)
, and Ren Xue-Mei(任雪梅)
b)
a)
College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, China
b)
School of Automation, Beijing Institute of Technology, Beijing 100081, China
(Received 7 April 2015; revised manuscript received 10 June 2015; published online 12 October 2015)
A full-order sliding mode control based on a fuzzy extended state observer is proposed to control the uncertain chaos
in the permanent magnet synchronous motor. Through a simple coordinate transformation, the chaotic PMSM model is
transformed into the Brunovsky canonical form, which is more suitable for the controller design. Based on the fuzzy control
theory, a fuzzy extended state observer is developed to estimate the unknown states and uncertainties, and the restriction
that all the system states should be completely measurable is avoided. Thereafter, a full-order sliding mode controller is
designed to ensure the convergence of all system states without any chattering problem. Comparative simulations show the
effectiveness and superior performance of the proposed control method.
Keywords: permanent magnet synchronous motor, chaotic system, sliding mode control, fuzzy extended state
observer
PACS: 05.45.Gg DOI: 10.1088/1674-1056/24/11/110504
1. Introduction
Due to higher efficiency, larger power density, and lower
manufacturing cost, permanent magnet synchronous motors
(PMSMs) have been widely used in industrial applications.
As described in Refs. [1] and [2], the PMSM systems with
smooth air gap (L
d
= L
q
) and non-smooth air gap (L
d
6= L
q
)
behave in chaotic manners when system parameters fall into a
certain area, respectively. Since the chaotic behavior may de-
stroy the stability of the motor system, how to control and sup-
press chaos in the PMSM system becomes an important task
and many approaches have been proposed in Refs. [3]–[7].
Sliding mode control (SMC) is a kind of robust control
technique, and widely used for systems with uncertainties and
bounded disturbances. As we know, the existence of a switch-
ing function in the controller design will lead to an unavoid-
able chattering phenomenon in the conventional SMC scheme.
Therefore, many efforts have been made for attenuating the
chattering problem, and desirable reduced-order dynamics of
the system can be obtained by choosing appropriate sliding-
mode surfaces.
[8–11]
Recently, a full-order sliding mode con-
trol scheme was presented in Ref. [12] to make the control sig-
nal smooth, and thus the chattering problem is reduced much
in the system response. Unfortunately, all the states in the sys-
tem should be completely known in advance, which may block
its applications in the PMSM control system as some system
states are unmeasurable.
With the advantages in the nonlinear control system,
the observer-based control has been widely used in indus-
trial applications. Compared with most existing observers,
the extended state observer (ESO) is able to estimate the sys-
tem states and model uncertainties simultaneously by viewing
them as an extended state. As a model-free control approach,
the ESO-based control scheme has been applied to a wide va-
riety of plants.
[13–16]
However, the coefficients of ESO usually
need to be determined in advance. Recently, fuzzy logic con-
trol (FLC) is regarded as one of the most commonly used tools
in functional approximation and parameter optimization.
[17]
In
the FLC, a set of linguistic control rules about the concepts of
fuzzy implication are given first, and then fuzzy variables are
adjusted according to expert knowledge and error. It can pro-
vide an effective way for setting and optimizing parameters,
which is an important application in practical control engineer-
ing. Therefore, the use of fuzzy-based optimization to tune the
coefficients of the ESO has the potential ability to improve the
control performance.
Motivated by previous work, a full-order sliding
mode control based on the fuzzy extended state observer
(FSMC+FESO) is proposed in this paper to control chaos in
the permanent magnet synchronous motor (PMSM). An FESO
is designed to estimate the unknown states and uncertainties
of the chaotic PMSM with ESO coefficients being tuned via
fuzzy logic rules, and thus the restriction that all the system
states should be completely measurable is avoided. Then, a
full-order sliding-mode controller based on the FESO is pro-
posed to control all the chaotic states to zero rapidly and
∗
Project supported by the National Natural Science Foundation of China (Grant Nos. 61403343 and 61433003), the Scientific Research Foundation of Education
Department of Zhejiang Province, China (Grant No. Y201329260), and the Natural Science Foundation of Zhejiang University of Technology, China (Grant
No. 1301103053408).
†
Corresponding author. E-mail: sdnjchq@zjut.edu.cn
© 2015 Chinese Physical Society and IOP Publishing Ltd http://iopscience.iop.org/cpb http://cpb.iphy.ac.cn
110504-1