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to parameter variations, external disturbance rejection and fast dynamic response[1]-
[4]. Consequently, SMC has been widely and successfully applied into the position and
velocity control of PMSM. However, SMC has its own disadvantage, i.e., chattering phe-
nomenon, which originated from the interaction between parasitic dynamics and high-
frequency switching control. In order to avoid the phenomenon, several control methods
were proposed to improve the sliding mode control, such as the saturation function or
the sigmoid function instead of the Bang-Bang control[12], low-pass filter[13], hybrid
SMC [14] and second order sliding mode control(SOSMC)[4]etc. But the methods bring
some new problems. For example, the low-pass filter causes the phase lag, and hybrid
SMC increases the computation load. Comparatively, SOSMC can not only eliminate
the chattering but also preserve the main advantages of the SMC, i.e., robustness and
precision of the SMC.
In this paper, a novel second order sliding mode control algorithm is proposed to
accomplish velocity control of the PMSM owing to its system requirement of the fast
response, robustness and good track performance and so on. The integral manifold is
utilized to avoid the acceleration information required in control system. The control
performance can be improved because of diminishing the differentiator to attain the ac-
celeration information compared with others second order sliding mode control, which
amplifies the noise signals. Meanwhile, the second order sliding mode control law is de-
signed by the Lyapunov function approach and effectively eliminates the system chat-
tering phenomenon. In addition, an anti-windup control method is used to address the
windup phenomenon of the PMSM control system. The computer simulation results are
presented to verify the feasibility of the method.
2
The Field-Oriented PMSM Control Scheme
In the stationary (
d
q
) reference frame, the mathematics mode of permanent-magnet
synchronous motor is shown as below:
−
⎧
⎨
⎩
i
d
=
R
L
i
d
+
p
n
ω
i
q
+
u
L
−
p
n
ψ
f
L
ω
+
u
L
i
q
=
R
L
i
q
−
−
p
n
ω
i
d
−
(1)
=
p
n
ψ
f
J
T
J
B
ω
˙
i
q
−
J
ω
−
˙
θ
=
ω
where
i
d
,
i
q
and
u
d
,
u
q
are current and voltage (volt) of motor
d
axis and
q
axis re-
spectively;
R
s
is stator resistance of motor (ohm);
L
is self inductance of motor stator
(H);
ψ
f
is permanent magnet flux of motor (voltsec/rad);
T
L
is motor torque (Nm);
p
n
is pole-pairs of motor;
J
and
B
are the viscous friction coefficient and inertia constant
of the motor;
are angular velocity (rad/sec) and rotor position of motor (rad).
The system is designed for the double close-loop control system to regulate the speed
of motor by the field oriented control technology so that it obtains high performance.
ω
and
θ
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