In a case where it is unsuitable, all experiments will have to be repeated; (ii) RSM is supposed to be a continuous optimization method, since RSM is similar to gradient-based approaches. Hence, unlike other optimizations, RSM is not suitable for discrete optimization; (iii) RSM may find a local optimum, as opposed to other optimizations that search for a global one [16]. On the other hand particle swarm optimization (PSO) doesn’t readjust the initial search domain of the parameters [17]. PSO approaches are proposed for continuous and discrete optimization problems [18]. PSO is a member of the wide category of swarm intelligence methods for solving global optimization problems [19]. Compared with the design optimization of inductive sensor using genetic algorithms [20], PSO has no overlapping and mutation calculations with much simpler implementation.

In this paper, most parameters of the sensor are discussed, but understanding the parameters’ effect on the nonlinearity error is a critical step in designing an effective sensor. Key parameters are chosen on the basis of their influence on the nonlinearity error. The finite element method and particle swarm optimization (PSO) are combined to design the sensor to achieve the minimum nonlinearity error.This paper is organized as follows: in Section 2, the principle of the inductive angle sensor is described. In Section 3, key parameters for the design are selected and the sensor is optimized using PSO-FEM. The results are measured and discussed in Section 4. Finally, our conclusions about the sensor design is drawn in Section 5.

2.?Principle of the Inductive Angle SensorThe proposed inductive angle sensor consists of a stator and a rotor, as illustrated in Figure 1. The stator has two receiving coils and Dacomitinib one excitation coil, and the separation angle between the receiving coil 1 and 2 is 30��. The receiving coil comprises six loops with the same geometric shape. Adjacent loops are wound in the opposition direction. The stator layout has two advantages. The induced voltages in two receiving coils will be periodic when the rotor rotates. The induced voltages in two receiving coils are zero from the excitation coil because adjacent loops are symmetrical and wound in the opposition direction. However, the number of turns in two receiving coils is limited by the number of printed circuit board (PCB) layers.

The multi-layer PCB layout will increase the cost burden. The number of turns in two receiving coils is a compromise between the performance and cost of the sensor.Figure 1.View of inductive angle sensor.A sine-wave voltage is applied to the excitation coil which generates an alternating magnetic field BE. The alternating magnetic field BE induces an eddy current in the rotor, and the current creates an alternating magnetic field BR that opposes the alternating magnetic field BE.