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current regulated by speed PI is hard to follow the load fluctuation on time(see,
for example, [1]). A method of low frequency torque compensation is proposed
in[2], but it is a forward-feed compensation, which makes it dicult to accurately
locate the compensation point. In[3], an automatic torque estimating schemes
is proposed, which is based on current feed forward compensation and load
torque estimation. However, it is dicult to accurately estimate the load in
actual system . As far as we know, there is no existing work on applying control
parameter optimization techniques to attack the torque compensation problem
for PMSM systems with periodic-nonlinear load. Therefore, aimed at solving
periodic-nonlinear variations of the load torque under low frequency operations
of the compressor, we present a method in this paper based on control parameter
optimization techniques.
With the increasing development of science and technology, industrial produc-
tion on the energy saving requirements are extremely urgent, the optimization
method has become indispensable to modern theoretical research and industrial
production of energy saving methods(see, for example, [4]). Analytical methods
and numerical methods are used to solve these optimal control problems. For
the analytical method, it includes the variation formulation (see, for example,
[5]) and dynamic programming technique (see, for example, [6]). The algorithms
developed in this paper belongs to the numerical method, including control pa-
rameterization (see, for example, [7]), orthogonal collocation (see, for example,
[8]), iterative dynamic programming (see, for example, [9]) and intelligent op-
timization (see, for example, [10]). The control parameterization has low com-
putationally complexity and does not have instability problems as in intelligent
optimization methods. The control parameterization technique divides the time
interval [0, T] into several subintervals. Then, the control is approximated by
piecewise constant function with possible discontinuities at the partition points,
which are called switching times. So the infinite dimensional complex control
problem can be transformed into finite dimensional optimization problems with
constant control. Based on IPMSM motor mathematical models, we use the
sequential quadratic programming algorithm to find the optimal numerical so-
lution of the actual control of the system state equations, thus obtaining the
optimal control parameters. The rest of the paper is organized as follows: Sec.
II formulates the problem and Sec. III presents the algorithm. Simulations are
given in Sec. IV. Finally, a conclusion is give in Sec .V.
2 Problem Description
Unlike surface mount permanent magnet synchronous motor, the inductance of
d-coordinate (L
d
) of the interior permanent magnet synchronous motor (IPMSM)
is not equal to the q-coordinate (L
q
). By analyzing the mathematical model of
the IPMSM (see, for example, [13]), we obtain the model used in the optimal
control algorithm. The motor stator voltage equations in the d-q rotating coor-
dinate system are as below:
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