Sliding mode periodic adaptive learning control method for medium-speed maglev trains
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摘要: 为了提高中速磁悬浮列车的运行控制性能，考虑到中速磁悬浮列车沿固定线路往返运行时的周期特性，提出了一种基于滑模周期自适应学习的中速磁悬浮列车运行控制算法，对应的滑模周期自适应控制器由等效比例积分微分(PID)和速度前馈控制部分、磁阻力与空气阻力补偿部分以及坡道阻力滑模周期自适应补偿部分组成；采用粒子群优化算法辨识了运行控制器的参数，采用滑模周期自适应学习控制器学习上一周期内的列车运行信息，实时估计并补偿列车运行过程中的坡道阻力，消除坡道阻力对列车运行性能的影响；利用全长5 076 m的中速磁悬浮列车半实物仿真试验线进行了数值仿真，并将设计的滑模周期自适应控制器与PID控制器进行仿真对比。仿真结果显示：滑模周期自适应控制器和PID控制器作用下的列车最大位置跟踪误差分别为0.004和0.007 m，最大速度跟踪误差分别为0.007和0.036 m·s-1；经过4个迭代周期后，滑模周期自适应控制器已准确地估计了给定的坡道阻力；在控制系统受到扰动的情况下，滑模周期自适应控制器与PID控制器作用下的位置与速度跟踪曲线均有波动，相比于PID控制器，滑模周期自适应控制器控制下的跟踪曲线波动更小。可见，相比于传统的PID控制算法，提出的滑模周期自适应学习控制方法可以提高中速磁悬浮列车的运行控制性能。Abstract: In order to improve the operation control performance of the medium-speed maglev train, the periodic characteristic of the train running along a fixed line was considered, and an operation control algorithm based on the sliding mode periodic adaptive learning control (SMPALC) method for the train was proposed. The corresponding sliding mode periodic adaptive controller was composed of the equivalent proportional-integral-differential (PID) and speed feedforward control part, the magnetic resistance and air resistance compensation part, and the ramp resistance sliding mode periodic adaptive compensation part. The operation controller parameters were tuned through the particle swarm optimization (PSO) algorithm. The sliding mode periodic adaptive controller was used to learn the train operation information in the previous period, the ramp resistance during train operation in real time was estimated and compensated, and the influence of ramp resistance on the train operation performance was eliminated. The semi-physical simulation test line of a medium-speed maglev train with a total route length of 5 076 m was numerically simulated, and the designed sliding mode periodic adaptive controller was compared with the PID controller through the simulation. Simulation results show that the maximum position tracking errors under the sliding mode periodic adaptive controller and PID controller are 0.004 and 0.007 m, respectively, and the maximum speed tracking errors are 0.007 and 0.036 m·s-1, respectively. After four iterative periods, the sliding mode periodic adaptive controller has accurately estimated the given ramp resistance. When the control system is disturbed, the position and speed tracking curves under the sliding mode periodic adaptive controller and PID controller both fluctuate. However, compared with those under the PID controller, the tracking curves under the sliding mode periodic adaptive controller have a smaller fluctuation. Therefore, the proposed SMPALC method can improve the operation control performance of medium-speed maglev trains.
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图 4 PID与SMPALC控制器速度跟踪曲线
Figure 4. Speed tracking curves with PID and SMPALC controllers
图 5 PID与SMPALC控制器速度跟踪误差
Figure 5. Speed tracking errors with PID and SMPALC controllers
图 6 PID与SMPALC控制器位置跟踪误差
Figure 6. Position tracking errors with PID and SMPALC controllers
图 7 SMPALC控制器估计的坡道阻力与实际的坡道阻力
Figure 7. Estimated ramp resistances with SMPALC controller and actual ramp resistances
图 8 SMPALC控制器坡道阻力估计误差
Figure 8. Ramp resistance estimation errors with SMPALC controller
图 9 噪声干扰下PID与SMPALC控制器位置跟踪误差
Figure 9. Position tracking errors with PID and SMPALC controllers under noise interference
图 10 噪声干扰下PID与SMPALC控制器速度跟踪误差
Figure 10. Speed tracking errors with PID and SMPALC controllers under noise interference
图 11 SMPALC控制器滑模面变化曲线
Figure 11. Variation curve of sliding mode surface with SMPALC controller
图 12 SMPALC控制器滑模面导数变化曲线
Figure 12. Variation curve of derivative of sliding mode surface with SMPALC controller
表 1 中速磁悬浮列车基本参数
Table 1. Basic parameters of medium-speed maglev train
参数 数值 列车编组数 2 单节车厢满载总质量/kg 23 000 列车质量/kg 46 000 最大速度/(km·h-1) 194.4 最大加速度/(m·s-2) 0.9 
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表 2 试验线基本参数
Table 2. Basic parameters of test line
参数 数值 线路长度/m 5 076 坡道长度/m 500 坡道坡度千分数系数/‰ 15 弯道长度/m 400 弯道曲线半径/m 2 000
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表 3 PSO算法参数
Table 3. Parameters of PSO algorithm
参数 数值 群体规模 20 惯性权重ω 0.5 加速常数c1 2 加速常数c2 2 迭代次数 60
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表 4 SMPALC控制器参数
Table 4. Parameters of SMPALC controller
参数 数值 ε1 0.000 1 ε2 380.1 Ki 8.13×109 K 3.459×10-5
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