Speed sensorless MPTC of linear induction motors for rail transit based on improved SMO
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摘要: 针对轨道交通直线感应电机(LIM)无速度传感器模型预测控制对速度观测的鲁棒性及模型精度要求较高的问题，提出了一种基于改进滑模观测器(SMO)的模型预测推力控制(MPTC)策略，应用改进滑模观测器提高速度及磁链观测的实时性及鲁棒性，降低对模型精度要求，实现LIM无速度传感器模型预测高性能控制；考虑动态边端效应，建立静止坐标系下LIM动态模型；建立模型预测推力控制离散模型，提出了基于改进SMO的磁链和速度的观测方法，并完成基于改进SMO的直线感应电机无速度传感器模型预测推力控制系统设计；为提高速度及磁链的估计精度，减小滑模抖振，提高收敛速度，设计一种基于连续sigmod函数的开关函数，并采用改进变指数幂次趋近律，平衡系统快速收敛及抖振间的矛盾；对改进SMO的稳定性和动态性能进行分析，搭建硬件在环试验环境验证算法的有效性。试验结果表明：改进SMO观测精度高，在次级电阻、励磁电感突变时，速度观测误差为0.20和0.35 m·s-1，均减小了1.4%；在引入方差为0.01的白噪声扰动时，最大误差为0.2 m·s-1，误差率约为1.8%，观测器收敛速度快，观测结果抖动小，具有较好的抗干扰能力；在多速域工况下，误差为0.075 m·s-1，同样可以满足性能要求，同时基于改进SMO的直线感应电机无速度传感器MPC控制系统稳态误差小，动态响应快，系统鲁棒性能好。Abstract: To address the high robustness of speed observation and model accuracy for speed sensorless model predictive control of linear induction motors (LIM) in rail transit, a model predictive thrust control (MPTC) strategy based on an improved sliding mode observer (SMO) was proposed. Through the improved SMO, the real-time performance and robustness of speed and flux linkage observation were enhanced, and the demand for model accuracy was lowered, thus realizing high performance model predictive control of the speed sensorless of LIM. A LIM dynamic model based on the dynamic end effect was established in the static coordinate system. A discrete model of model predictive thrust control was established. An observation method of flux linkage and speed based on the improved SMO was proposed. Subsequently, a speed sensorless MPTC system for LIM based on the improved SMO was designed. To enhance the estimation precision of speed and flux linkage, minimize sliding mode chattering, and accelerate the convergence speed, a switch function based on the continuous sigmod function was designed. Meanwhile, an improved variable exponential power reaching law was proposed to balance the contradiction between the rapid convergence and chattering of the system. The stability and dynamic performance of the improved SMO were analyzed, and the hardware-in-the-loop environment was built to verify the effectiveness of the algorithm. Experimental results show that the observation accuracy of the improved SMO is high. In the case of abrupt changes in secondary resistance and excitation inductance, the speed observation errors are 0.20 and 0.35 m·s-1, both of which reduce by 1.4%. When the white noise perturbation with a variance of 0.01 is introduced, the maximum error is 0.20 m·s-1, with an error rate of about 1.8%. Characterized by a fast convergence speed and less chattering of observation results, the observer exhibits a better anti-interference ability. Under the multi-speed domain conditions, the error is 0.075 m·s-1, satisfying the performance requirements. The speed sensorless MPC system of LIM based on the improved SMO exhibits small steady state error, fast dynamic response, and good robustness performance.
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图 3 无速度传感器模型预测推力控制系统架构
Figure 3. Architecture of speed sensorless model predictive thrust control system
图 6 传统滑模观测器在Rr突变的速度观测性能
Figure 6. Speed observation performance of conventional sliding mode observer for Rr abrupt changes
图 7 改进滑模观测器在Rr突变的速度观测性能
Figure 7. Speed observation performance of improved sliding mode observer for Rr abrupt changes
图 8 传统滑模观测器在Lm突变的速度观测性能
Figure 8. Speed observation performance of conventional sliding mode observer for Lm abrupt changes
图 9 改进滑模观测器在Lm突变的速度观测性能
Figure 9. Speed observation performance of improved sliding mode observer for Lm abrupt changes
图 10 负载和外部扰动下的速度观测性能
Figure 10. Speed observation performance under load and external disturbances
图 11 负载和外部扰动下的磁链观测性能
Figure 11. Flux linkage observation performance under load and external disturbances
表 1 电机参数
Table 1. Motor parameters
参数 数值 极距/m 0.280 8 初级长度/m 2.476 互感/mH 26.477 初级漏感/mH 6.688 次级漏感/mH 2.091 初级电阻/Ω 0.138 次级电阻/Ω 0.576 额定功率/kw 120 额定速度/(m·s-1) 11.11 
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表 2 速度辨识方案的试验条件
Table 2. Experimental conditions for speed identification schemes
试验 试验名称 试验工况 1 次级电阻Rr变化时的速度辨识性能对比 恒负载1 kN，Rr突变为1.5倍 2 励磁电感Lm变化时的速度辨识性能对比 恒负载1 kN，Lm突变为1.5倍 3 负载和外部扰动下的速度辨识性能对比 变负载(1 kN→2 kN)和采集的电压电流引入白噪声(方差0.01) 4 多速域工况下的观测性能 恒负载1 kN，加、减、匀速
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