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| Improved Particle Swarm Optimization Algorithm Based Driving Strategy Research for Permanent Magnet Spherical Motor |
| Zhou Sili1,2, Li Guoli2,3, Wang Qunjing2,4, Zheng Changbao2,3, Wen Yan2,5 |
1. School of Computer Science and Technology Anhui University Hefei 230601 China;
2. National Engineering Laboratory of Energy-Saving Motor & Control Technology Anhui University Hefei 230601 China;
3. School of Electrical Engineering and Automation Anhui University Hefei 230601 China;
4. Anhui Collaborative Innovation Center of Industrial Energy-Saving and Power Quality Control Anhui University Hefei 230601 China;
5. School of Internet Anhui University Hefei 230601 China |
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Abstract 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 pseudo-inverse 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.
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Received: 14 June 2021
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2023, Vol. 38 
