The Optimization Algorithm of Torque Compensation for PMSM Systems with Periodic-Nonlinear Load - Intelligent Computing for Sustainable Energy and Environment - page 339

subject to the following inequality constraints:

− ≤ x 1 ≤

1 , 1

(18)

0 ≤ x 2 ≤ 3

Set the time interval [0 , 2] (unit: s), the direct axis current i d target equal to 0A,
the i q target value of 2A. Therefore, the objective function (8) can be expressed
as:

g 0 ( u )= 2
0

[( x 1 ( t )) 2 +( x 2 ( t ) 2) 2 ] dt

−

(19)

According to Theorem 1 and (16) and the actual motor parameters given by
Tab.1, we can deduce gradient σ 1 oftheobjectivefunction g 0 ( u )onthecontrol
parameters σ 1 and σ 2 j =1 , 2 , ··· , 20 :

⎧
⎨

= I 158 . 73 λ 1 dt

∂g 0 ( σ q )
∂σ j
1

(20)

= I 84 . 75 λ 2 dt

⎩

∂g 0 ( σ q )
∂σ j
2

Using the obtained model parameters and selected simulation parameters, we
use sequential quadratic programming algorithm to calculate the optimal control
parameters corresponding to U 1 and U 2 . Control curves are shown as Fig.2 and
Fig. 3.

Fig. 2. U 1 Fig. 3. U 2

From Figure 2 and Figure 3, we can observe that U 1 and U 2 are much smaller
than the actual values after optimization Furthermore, during the process of
calculating the optimal control parameters, a new set of state variables are cal-
culated that are shown in Figure 4, Figure 5 and Figure 6. They are closer to
the actual state values, which also verifies the effectiveness of the parametric
approach.