变频空调压缩机在低频运行时存在着较大的电流谐波。当采用普通重复控制器时,由于采样频率与电流谐波基频的比值不一定为整数,使得重复控制器内模与电流谐波基频存在偏差,导致普通重复控制器电流谐波抑制能力下降。针对该问题,采用基于固定采样频率的分数阶重复控制策略。首先,采用Lagrange插值定理去逼近分数延时环节;其次,采用FIR滤波器替代低通滤波器减小相位引起的误差；最后,针对分数阶重复控制器的相位滞后特性,分别进行低、中、高频段相位补偿。试验结果表明,提出的控制策略能够有效地抑制变频空调压缩机低频运行时的电流谐波。

There existed large current harmonics when the variable frequency air conditioner ran in the low frequency. When using the common repetitive control (RC), since the ratio of the sampling frequency to the fundamental frequency of current harmonics may be not an integer, there was deviation between the internal mode of repetitive control and the fundamental frequency of the current harmonics, and thus the suppression effects of the repetitive controller would be degraded drastically. Aiming at this problem, a fractionalorder RC (FORC) strategy at fixed sampling frequency was proposed. Firstly, Lagrange interpolation theory was used to approximate the fractional delay item; secondly, FIR filter was used to eliminate the error caused by low pass filter (LPF); finally, aiming at the phase lag of the FORC, phase compensation was made in all frequency bands to confirm the stability of the closed loop. The experiment results showed that the proposed strategy could effectively suppress the current harmonics of the variable frequency air conditioner running at the low frequency.

国家自然科学基金青年基金项目(61503141)；江西省教育厅科技项目(GJJ161268,GJJ171151)