Sensorless control of double-sided linear switched reluctance motor based on simplified flux linkage method

Abstract

that a large amount of flux linkage data has to be stored, which will occupy lots of DSP storage space. Taking this shortcoming into account, [10] proposed a simplified flux method. Comparing with the original flux linkage method, the simplified flux method can reduce the amount of stored data and microprocessor's workload. But the simplified flux method can only realize single special position detection. In [2], the double position detection method based on simplified flux has been proposed. However, the above literature do not take the integral flux linkage error in the simplified flux method into account, and the error of the integral flux linkage has an important influence on the accuracy of the position estimation. To solve this problem, a new improved method based on simplified flux linkage method is presented in this paper, which can correct integral flux linkage error. II. MOTOR STRUCTURE Mover Stator A B C A B C A B C A B C 60mm 1 2 3 4 5 6 7 8 Fig.1. 6/4 three phase DLSRM structure. Fig.1 shows the structure of the 6/4 three-phase DLSRM. DLSRM is evolved from SRM. Three-phase 6/4 single linear SRM can be obtained by spreading three-phase 6/4 SRM radially. The mover of linear motor is analogous to rotor of rotary motor. Comparing with the linear switched reluctance motor, the DLSRM can counteract most of the normal force of the mover [3]. In this paper, the distance of the mover moving from one alignment position to the next alignment position is 20mm; the distance of the motor running a cycle, C-A-B-C is 60mm. For example, if the phase C is excited the C salient poles on stator will align with the fourth salient pole and the sixth salient pole on mover. Then the phase A is turned on, and the A salient poles on stator will align with the third salient pole and the fifth salient pole on mover. The mover displacement is 20mm.Then, the phase B is excited, and the mover will move another 20mm. After that, phase C is excited, and the C salient poles on stator will align with the fifth salient pole and the seventh salient pole on mover. The mover displacement is 20mm.The total distance a C-A-B-C is 60mm. III. BASIC PRINCIPLE SIMPLIFICATION AND ALGORITHM OF FLUX LINKAGE METHOD A. Basic Principle of Flux Linkage Method The voltage equation of a phase winding is [10]: dt d ir u    (1) where, u is the voltage of one phase winding, i is the current of one phase winding, r is the resistance of one phase winding. dt d /  is differential of flux linkage. The expression of the flux linkage is deduced from (1) [10] :) 0 () (0       dt ir u t (2) We can see from the (2) that the instantaneous flux linkage can be calculated by integral of difference u and ir. The influence of mutual inductance among phases is ignored in this paper. The relationship between the flux linkage Ψ, the mover position x and the current i can be obtained: ） ， （ i x    (3)) , (i x x   (4) It can be proved that the flux linkage is a single valued function of the current at any fixed position. It can be seen from (3) and (4) [10] that if the flux linkage and current are determined, the position of the mover can be known. The basic idea of flux linkage method is that the different positions have different curves of flux linkage vs current. In order to estimate the mover position, the flux linkage at the demagnetization position should be measured and stored in the controller. The data table which includes flux linkage, current and position is stored in the memory, then the estimated value of the position can be obtained according to the current and the calculated flux linkage in the actual operation. B. Simplified Flux Linkage Method It can be seen from the last section that flux linkage method has three main disadvantages. Firstly, the stored data in the control chip is a three-dimensional table. They take up a lot of DSP memory. Secondly, the query workload of the three-dimensional table is large. The computational complexity requires higher performance control chip which costs more. Thirdly, the three-dimensional data means that the workload of off-line measurement is very large, which reduces the practicability of the flux linkage method. In view of the above problems, [10] proposed a simplified flux linkage method. Because of the same operating principle with SRM, the control of the DLSRM can take the control experience of SRM as the reference. When the motor operates in single phase mode, it is not necessary to know the exact position of the motor, and just need to know whether the mover has reached the position where present phase needs to demagnetize or not [10]. If the demagnetization position is reached, the present phase is demagnetized and the next phase is excited. Because the flux linkage is a monotonous increasing function of the current at a fixed position. When the current is same, the corresponding flux linkage values are different at different positions. Therefore, it just needs to compare the calculated flux linkage value with the stored magnetic flux linkage data. If calculated flux linkage value is bigger than the value of the stored magnetic flux, the mover has reached the demagnetization position. The present phase should be demagnetized and the