基于改进粒子群优化算法的永磁球形电机驱动策略研究

Improved Particle Swarm Optimization Algorithm Based Driving Strategy Research for Permanent Magnet Spherical Motor

永磁球形电机(PMSpM)是一种结构紧凑、可多自由运动的单关节传动装置。该文提出一种适用于PMSpM驱动策略优化的改进粒子群优化(IPSO)算法,该算法可实时计算PMSpM期望转矩所对应的线圈驱动电流。首先,通过圆环函数建立PMSpM转矩解析模型,并构建转矩Map图;然后,在确定种群数量后为标准粒子群优化(PSO)算法引入自适应动态惯性权重和自适应学习因子,将所提IPSO算法与PSO算法进行仿真对比,仿真结果表明,在同样的精度下采用IPSO算法计算驱动电流比采用PSO算法有更快的计算速度;最后,通过PMSpM控制试验进一步证明了该仿真结论的正确性。

A permanent magnet spherical motor(PMSpM) is a compact transmission apparatus that is capable of motion in multiple degrees of freedom. To achieve the close loop control of the PMSpM, the driving current of the stator coils needs to be calculated, and the analytic torque model needs to be built in advance.However, if the geometry of the permanent magnet(PM) is a non-circumferential symmetric one, the pseudoinverse matrix technique is not applicable. Thus, the research on the fast driving strategy of the universal reverse torque model is an essential prerequisite for the PMSpM close-loop control.This paper takes the PMSpM with the stepped cylindrical PM as the research object. Firstly, this paper proposes new analytical torque models using the toroidal expansion method. To avoid repeating integrations in magnetic and torque analytic calculation, this paper builds torque maps by moving one 1A energized electromagnetic coil on the overall spherical surface of the airgap along the azimuth angle direction and polar angle direction. Secondly, the classical particle swarm optimization algorithm(PSO) is introduced to build the reverse torque model. The current of the stator electromagnetic coils is considered as the particle swarm, and the desired torques are set as optimization targets. Thus, we can use the reverse torque model to calculate the driving current of the stator electromagnetic coils from the torque maps. Thirdly, this paper proposes an improved particle swarm optimization(IPSO) algorithm for the PMSpM driving strategy optimization, which can be used for calculating the real-time driving current for the desired torques of the PMSpM. After the determination of the population size of the PSO algorithm, the adaptive dynamic inertia weight and adaptive learning factors are introduced for IPSO.Simulation results on the IPSO algorithm optimization show that the improvement of the classical PSO algorithm is significantly effective. A typical population size can generate convergence before 250 iterations. The larger the population size, the more concentrated the convergence curves. A bigger population size illustrates the robustness of the PSO algorithm, but it also needs more convergence time. Thus, to balance the current calculation algorithm convergence rate, this paper adopts popsize =30. With the same convergence precision, the PSO algorithm with improved adaptive dynamic inertia weight can get greater calculation efficiency, and the convergence can be completed only around 50 iterations instead of 200 iterations which adopts the traditional inertia weight solution.The convergence rate for the electromagnetic coil current calculation is significantly boosted. In addition,introducing adaptive learning factors can also boost the convergence rate by 20%. Finally, after introducing the adaptive dynamic inertia weight and the adaptive learning factors, the mean one-loop driving current calculation time can be reduced from 710.5ms to 128.2ms.The following conclusions can be drawn from the simulation analysis:① The driving current calculation speed of the PSO algorithm with adaptive dynamic inertia weight is 5.5 times faster than the classical PSO algorithm;② The comparison result between the classical PSO algorithm and IPSO algorithm indicates that IPSO has a better convergence rate than PSO on the premise of ensuring the accuracy of convergence.③ The PMSpM control experimental result shows that the proposed IPSO algorithm is effective in the PMSpM driving strategy,and the PMSpM driving current calculation speed of the proposed IPSO algorithm is significantly faster than using the classical PSO algorithm. In addition, the proposed IPSO algorithm is also applicable for the driving current calculation of other complex special motors.