步進馬達伺服控制演算法優化;Optimization of servo control algorithm for stepping motor

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题名:	步進馬達伺服控制演算法優化;Optimization of servo control algorithm for stepping motor
作者:	郭偉晟;KUO, WEI-CHENG
贡献者:	光機電工程研究所
关键词:	步進馬達驅動;定點數運算;多項式內插法;stepper motor drive;fixed-point number operation;multinomial interpolation,
日期:	2023-07-24
上传时间:	2024-09-19 15:45:36 (UTC+8)
出版者:	國立中央大學
摘要:	本研究以步進馬達伺服控制為基礎，簡化軟體演算法並將演算法由浮點數(Floating Point)轉換為定點(Fixed Point)運算，而提升比原始系統更高的控制頻率。此外研究還使用二次多項式的拉格朗日插值法，計算近似於正弦波與餘弦波數值。由於弦波具有對稱的特性，插值法只需要紀錄四分之一個弦波函數點，這可以減少微控制器單元( Microcontroller Unit , MCU)記憶體的空間使用量。然而在二次多項式的拉格朗日插值法的運算過程中，需要使用到除法，這樣的操作使得計算時間變長。為了克服這個問題，將弦波的0至360度等分為256份，且讓函數點以二的次方作為計算點，因此可以使用位元操作（bitwise）來取代除法，成功地縮短了程式的運行時間。控制方面利用積分單元(Integral, I) 激磁角回饋以及比例單元與積分單元(Proportional-Integral, PI)電流回饋，雙迴路系統控制，而I激磁角回饋控制，是受到齒槽轉矩影響，定子與轉子之間會形成偏向誤差，因此為了消除偏向誤差，驅動器需提反方向的扭矩來抵消齒槽扭矩。PI電流回饋是為了降低電流，且依照不同負載情形調整所需的電流，可以減少功耗。 ;This study is based on step motor servo control. We simplified the software algorithm and transformed it from floating-point to fixed-point operations, which has successfully increased the control frequency beyond that of the original system. Additionally, the research employs the quadratic polynomial Lagrange interpolation method to approximate sine and cosine wave calculations. Because sinusoidal waves exhibit symmetrical characteristics, the interpolation method only needs to record one quarter of the wave′s data points, reducing memory usage in the Microcontroller Unit (MCU). However, the calculation process of the quadratic polynomial Lagrange interpolation method requires division, leading to an extended computation time. To address this issue, we divided the full range of the wave (0 to 360 degrees) into 256 parts, with function points representing powers of two. This allowed us to replace division with bitwise operations, significantly reducing program execution time. In terms of control, we utilized integral (I) for excitation angle feedback and proportional-integral (PI) for current feedback in a dual-loop control system. The I excitation angle feedback is affected by the cogging torque, causing an offset error between the stator and rotor. To eliminate this offset error, the driver needs to provide a counter-torque to offset the cogging torque. PI current feedback is utilized to minimize current, adjusting the required current according to different load conditions and thereby reducing power consumption.
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