SMO改进:
- 滤波器滤波后进行相位补偿
- 增加线性区间,使用饱和函数\(sat(x)\)代替符号函数\(sign(x)\)降低抖振,滑膜增益K
- 将观测到的\(E_α E_β\),作为反馈加入滑膜观测器函数,参与电流计算,降低抖振
改进后的观测方程:
\(\frac{d (\hat{i_α} - i_α)}{dt} = - \frac{R_s}{L} \hat{i_α} - i_α + \frac{1}{L}(U_α - E_α - Z_α)\)
\(\frac{d (\hat{i_β} - i_β)}{dt} = - \frac{R_s}{L} \hat{i_β} - i_β + \frac{1}{L}(U_β - E_β - Z_β)\)
位置提取:
\(\hat{θ} = arctan(-\frac{E_α}{E_β})\)
离散化的方式:
后向欧拉法:
\(\frac{dy(t)}{dt} = \frac{y(k) - y(k-1)}{T_s}\)
前向欧拉法:
\(\frac{dy(t)}{dt} = \frac{y(k+1) - y(k)}{T_s}\)
双线性变换法:
\(\frac{dy(t)}{dt} = \frac{2(y(k) - y(k-1))}{T_s(1 + Z(-1))}\)
利用后向欧拉法:
\(\frac{d (\hat{i_α}(n) - \hat{i_α}(n-1))}{T_s} = (- \frac{R_s}{L})\hat{i_α}(n-1) + \frac{1}{L}(U_α(n-1) - \hat{E_α}(n-1) - Z_α(n-1))\)
\(\frac{d (\hat{i_β}(n) - \hat{i_β}(n-1))}{T_s} = (- \frac{R_s}{L})\hat{i_β}(n-1) + \frac{1}{L}(U_β(n-1) - \hat{E_β}(n-1) - Z_β(n-1))\)
进一步整理离散后的方程:
\(i_α(n) = (1 -T_s\frac{R_s}{L})\hat{i_α}(n-1) + \frac{T_s}{L}(U_α(n-1) - \hat{E_α}(n-1) - Z_α(n-1))\)
\(i_β(n) = (1 -T_s\frac{R_s}{L})\hat{i_β}(n-1) + \frac{T_s}{L}(U_β(n-1) - \hat{E_β}(n-1) - Z_β(n-1))\)
