Energy consumption optimization strategy for linear motors in multi-leaf collimator
MU Xiaofei1,2, LI Bingran1,2, GAO Qiantong1,2, YE Peiqing1,2, ZHANG Hui1,2
1. Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China; 2. Intelligent CNC System Technology Research, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
Abstract：[Objective] Medical linear accelerator is a high-end piece of equipment used in cancer radiotherapy. A key component of this system is the multi-leaf collimator (MLC), which considerably influences the accuracy and efficiency of radiotherapy. This study examines the fast MLC, which employs a two-phase permanent magnet synchronous tubular linear motor (PMSTLM) to directly drive the leaves and enhance the precision of radiation dose distribution. However, factors such as inductance, magnetic chain, and resistance in the PMSTLM are influenced by temperature changes, resulting in parameter changes that affect the current loop's steady-state error. Moreover, drastic fluctuations in current result in increased energy consumption. The heightened energy usage negatively impacts the blade motion accuracy, thus compromising the overall quality of radiotherapy. The objective of this study is to address these challenges by reducing the energy consumption of linear motors used in MLC. [Methods] This study proposes a method for optimizing the energy consumption of linear motors in MLC by improving velocity planning at the instruction level of the control system. To address the issue of kinematic constraints not fully utilizing the motor thrust, a dynamic friction coefficient is introduced to determine the moment boundary of the motor thrust. Based on this boundary, an improved exponential acceleration and deceleration speed planning method is developed. Furthermore, acceleration distance and deceleration characteristic coefficients are introduced as independent variables. The mapping relationship between full-stroke energy consumption, the transition time of the displacement section in the middle of the motor travel, and these coefficients is established. Using this relationship, an optimization model for energy consumption, transition time, and speed planning is formulated. The second-generation non-inferiority sorting genetic algorithm (NSGA-Ⅱ) is employed to perform multi-objective optimization of energy consumption and transition time. The result is utilized as commands for the controller and is validated through experimental testing.[Results] Through the proposed method, this study achieved acceleration and deceleration planning results with constant transition time and relatively low energy consumption for the full stroke. Experimental data indicate that the method reduces energy consumption by 21.5%, compared to trapezoidal acceleration-deceleration planning (TSP) under identical transition time conditions. The proposed method effectively reduces the energy consumption of PMSTLM operation while maintaining the normal functional requirements of the MLC.[Conclusions] The energy consumption optimization method proposed in this paper combines exponential acceleration and deceleration planning, an energy consumption-transition time speed planning model, and the NSGA-Ⅱ algorithm to enhance the performance of MLC. Based on theoretical research and experimental validation, the following conclusions are drawn. The proposed method can optimize the intermediate displacement section corresponding to the transition time by effectively utilizing the velocity peak. This is achieved by choosing appropriate acceleration distances and deceleration characteristic coefficients. Transition time and energy consumption are conflicting optimization objectives. By employing the energy consumption-transition time optimization model, choosing appropriate optimization parameters can considerably reduce energy consumption while ensuring that the transition time meets the performance requirements of the MLC. The experimental results verify the effectiveness of the proposed method. Energy consumption is reduced by 21.5% compared to that of the TSP method.
穆小飞, 李炳燃, 郜乾桐, 叶佩青, 张辉. 基于速度规划的多叶光栅直线电机能耗优化方法[J]. 清华大学学报（自然科学版）, 2025, 65(5): 891-900.
MU Xiaofei, LI Bingran, GAO Qiantong, YE Peiqing, ZHANG Hui. Energy consumption optimization strategy for linear motors in multi-leaf collimator. Journal of Tsinghua University(Science and Technology), 2025, 65(5): 891-900.
[1] ZHENG R S, ZHANG S W, ZENG H M, et al. Cancer incidence and mortality in China, 2016[J]. Journal of the National Cancer Center, 2022, 2(1):1-9. [2] BRAY F, LAVERSANNE M, WEIDERPASS E, et al. The ever-increasing importance of cancer as a leading cause of premature death worldwide[J]. Cancer, 2021, 127(16):3029-3030. [3] 陈刘利,吕军,朱志强,等.医用动态多叶光栅技术的发展概述[J].医疗装备, 2023, 36(1):156-161.CHEN L L, LV J, ZHU Z Q, et al. A summary of technical development of medical dynamic multi-leaf collimator[J]. Medical Equipment, 2023, 36(1):156-161.(in Chinese) [4] LI F, YE P Q, ZHANG H. Performance evaluation of a high-speed multileaf collimator in real-time IMRT delivery to moving targets[J]. Medical Physics, 2016, 43(3):1401-1410. [5] ZHANG X, YE P Q, ZHANG H. Development and performance evaluation of a high-speed multi-leaf collimator[J]. Journal of Applied Clinical Medical Physics, 2017, 18(1):96-106. [6] 张春雷.快速成野光栅伺服系统位置检测及轨迹规划研究[D].北京:清华大学, 2022. ZHANG C L. Research on position detection and trajectory planning for high-speed multi-leaf collimator[D]. Beijing:Tsinghua University, 2022.(in Chinese) [7] 张鲁宏.直线电机驱动多叶光栅位置的冗余检测技术研究[D].北京:清华大学, 2023. ZHANG L H. Research on redundant detection technology for the position of fast multi-leaf collimator driven by linear motors[D]. Beijing:Tsinghua University, 2023.(in Chinese) [8] LU D B, OUYANG M G, GU J, et al. Optimal velocity control for a battery electric vehicle driven by permanent magnet synchronous motors[J]. Mathematical Problems in Engineering, 2014, 2014(1):193960. [9] CHAKRABORTY D, VAZ W, NANDI A K. Optimal driving during electric vehicle acceleration using evolutionary algorithms[J]. Applied Soft Computing, 2015, 34:217-235. [10] VAZ W S, NANDI A K, KOYLU U O. A multiobjective approach to find optimal electric-vehicle acceleration:Simultaneous minimization of acceleration duration and energy consumption[J]. IEEE Transactions on Vehicular Technology, 2016, 65(6):4633-4644. [11] LI L F, LIU Q. Acceleration curve optimization for electric vehicle based on energy consumption and battery life[J]. Energy, 2019, 169:1039-1053. [12] HUANG X Z, WANG Z, ZHANG Y W, et al. Temperature rise calculation and velocity planning of permanent magnet linear synchronous motor under trapezoidal speed[J]. CES Transactions on Electrical Machines and Systems, 2022, 6(3):225-234. [13] SUN W S, SI H Q, QIU J X, et al. Research on efficiency of permanent-magnet synchronous motor based on adaptive algorithm of fuzzy control[J]. Sustainability, 2024, 16(3):1253. [14] 邓国发.基于损耗模型观测器的永磁同步电机效率优化控制[D].长沙:湖南大学, 2020. DENG G F. Study on efficiency optimization control of PMSM based on loss model observer[D]. Changsha:Hunan University, 2020.(in Chinese) [15] YANG H Y, HUANG X Y, SHEN Q D, et al. A loss minimization control method for IPMSM drive system based on improved gradient descent algorithm[J]. IEICE Electronics Express, 2022, 19(7):20220069. [16] NAVRAPESCU V, POPESCU M, KISCK D O, et al. Modelling of iron losses in salient pole permanent magnet synchronous motors[C]//Proceedings of the 2007 7th Internatonal Conference on Power Electronics. Daegu, Korea (South):IEEE, 2007:352-357. [17] SENJYU T, SHIMABUKURO T, UEZATO K. Vector control of synchronous permanent magnet motors including stator iron loss[C]//Proceedings of 1995 International Conference on Power Electronics and Drive Systems. Singapore:IEEE, 1995:309-314. [18] ZHANG C M, GUO Q B, LI L Y, et al. System efficiency improvement for electric vehicles adopting a permanent magnet synchronous motor direct drive system[J]. Energies, 2017, 10(12):2030. [19] ALZAYED M, CHAOUI H, FARAJPOUR Y. Dynamic direct voltage MTPA current sensorless drives for interior PMSM-based electric vehicles[J]. IEEE Transactions on Vehicular Technology, 2023, 72(3):3175-3185. [20] LI K, WANG Y. Maximum torque per ampere (MTPA) control for IPMSM drives based on a variable-equivalent-parameter MTPA control law[J]. IEEE Transactions on Power Electronics, 2019, 34(7):7092-7102. [21] LI C X, ZHANG W J, GAO J, et al. Permanent magnet flux linkage analysis and maximum torque per ampere (MTPA) control of high saturation IPMSM[J]. Energies, 2023, 16(12):4717. [22] ZANG B Q, CHEN Y G. Multiobjective optimization and multiphysics design of a 5 MW high-speed IPMSM used in FESS based on NSGA-Ⅱ[J]. IEEE Transactions on Energy Conversion, 2023, 38(2):813-824. [23] KALAIVANI L, SUBBURAJ P, IRUTHAYARAJAN M W. Speed control of switched reluctance motor with torque ripple reduction using non-dominated sorting genetic algorithm (NSGA-Ⅱ)[J]. International Journal of Electrical Power&Energy Systems, 2013, 53:69-77. [24] YU Y Q, PAN Y, CHEN Q P, et al. Cogging torque minimization of surface-mounted permanent magnet synchronous motor based on RSM and NSGA-Ⅱ[J]. Actuators, 2022, 11(12):379. [25] GUAZZELLI P R U, DE ANDRADE PEREIRA W C, DE OLIVEIRA C M R, et al. Weighting factors optimization of predictive torque control of induction motor by multiobjective genetic algorithm[J]. IEEE Transactions on Power Electronics, 2019, 34(7):6628-6638. [26] ZHANG X G, CAO Y H, ZHANG C G, et al. Model predictive control for PMSM based on the elimination of current prediction errors[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2024, 12(3):2651-2660.
2025, Vol. 65 
