A Novel Second Order Sliding Mode Control Algorithm for Velocity Control Permanent Magnet Synchronous Motor - Intelligent Computing for Sustainable Energy and Environment - page 215

Moreover, the method of the i d = 0 vector control is utilized in order to simplify the
control motor system.
The control system is regarded as linear system, and the overall configuration of
the speed vector control of PMSM is shown in Fig.1, which consists of a PMSM, an
SVPWM voltage source inverter, a power source rectifier, automatic current regula-
tor(ACR) of the motor, an encoder used to detect speed and position , and a speed
controller(SMC) based on the second order sliding mode control technology. The speed
controller will be described in detail in the next section.

Fig. 1. The structure of a vector control system based on SMC

3 The SOSMC

Here, a novel second order sliding mode control algorithm is proposed to accomplish
the speed control of PMSM. The chattering phenomenon can be avoided so as to im-
prove the motor performance when compared to the conventional PID control.
The speed controller of the PMSM is designed to attain the highly precise speed
track with reference speed and be robust to the disturbance of the load. Assume that the
signal of the reference speed is ω ∗ , and it is sufficient smooth and has almost second

order derivative everywhere. So define the error state equation as follows:

ω ∗ − ω

e ω = (2)

ω ∗ is the reference speed of the motor, and

where is the actual speed of the motor.

The motor speed error equation is obtained from (1) as follows:

ω

p n ψ f
J

i q + B + T L

J

e ω = ˙

˙

= ˙

ω ∗− ω ω ∗−

J ω

(3)

= p n ψ f
J

= T J = J where α , β and δ , so the speed error equation(3) can be rewritten as:

e ω = ˙

˙

= ˙ ω ∗− ω ω ∗− α i q + βω + δ (4)