《1 引言》

1 引言

《2 无轴承永磁同步电机悬浮机理》

2 无轴承永磁同步电机悬浮机理

《2.1转子悬浮机理》

2.1转子悬浮机理

《图1》

《2.2数学模型》

2.2数学模型

$\left\{\begin{array}{l}i{}_{\text{a}\text{p}}=-Ι{}_{\text{q}}\phantom{\rule{0.25em}{0ex}}\mathrm{sin}\phantom{\rule{0.25em}{0ex}}2\omega t+Ι{}_{\text{p}}\phantom{\rule{0.25em}{0ex}}\mathrm{cos}\phantom{\rule{0.25em}{0ex}}2\omega t\\ i{}_{\text{b}\text{p}}=-Ι{}_{\text{q}}\phantom{\rule{0.25em}{0ex}}\mathrm{cos}\phantom{\rule{0.25em}{0ex}}2\omega t+Ι{}_{\text{p}}\phantom{\rule{0.25em}{0ex}}\mathrm{sin}\phantom{\rule{0.25em}{0ex}}2\omega t\end{array}\text{ }\text{ }\text{ }\left(1\right)$

$\left\{\begin{array}{l}i{}_{\text{a}\text{p}}=Ι{}_{\text{a}\text{b}\text{p}}\mathrm{cos}\left(2\omega t+\theta {}_{1}\right)\\ i{}_{\text{b}\text{p}}=Ι{}_{\text{a}\text{b}\text{p}}\mathrm{sin}\left(2\omega t+\theta {}_{1}\right)\end{array}\text{ }\text{ }\text{ }\left(2\right)$

$\left\{\begin{array}{l}U{}_{\text{a}}=2\omega L{}_{4}Ι{}_{\text{a}\text{b}\text{p}}\\ U{}_{\text{b}}=2\omega L{}_{4}Ι{}_{\text{a}\text{b}\text{p}}\end{array}\text{ }\text{ }\text{ }\left(3\right)$

$\left(\begin{array}{l}\Psi {}_{\text{a}\text{p}}\\ \Psi {}_{\text{b}\text{p}}\\ \Psi {}_{x}\\ \Psi {}_{y}\end{array}\right)=\left(\begin{array}{cccc}L{}_{4}& 0& -{Μ}^{\prime }x& {Μ}^{\prime }y\\ 0& L{}_{4}& {Μ}^{\prime }y& {Μ}^{\prime }x\\ -{Μ}^{\prime }x& {Μ}^{\prime }y& L{}_{2}& 0\\ {Μ}^{\prime }y& {Μ}^{\prime }x& 0& L{}_{2}\end{array}\right)\left(\begin{array}{l}i{}_{\text{a}\text{p}}\\ i{}_{\text{b}\text{p}}\\ i{}_{x}\\ i{}_{y}\end{array}\right)\text{ }\text{ }\text{ }\left(4\right)$

${Μ}^{\prime }=\frac{\mu {}_{0}\text{π}n{}_{2}n{}_{4}l}{8}\cdot \frac{r-\left(l{}_{\text{p}}+l{}_{\text{g}}\right)}{\left(l{}_{\text{p}}+l{}_{\text{g}}\right){}^{2}}\text{ }\text{ }\text{ }\left(5\right)$

$\begin{array}{l}W{}_{\text{m}}=\frac{1}{2}\left(i{}_{\text{a}\text{p}}\text{ }i{}_{\text{b}\text{p}}\text{ }i{}_{x}\text{ }i{}_{y}\right)\cdot \\ \left(\begin{array}{cccc}L{}_{4}& 0& -{Μ}^{\prime }x& {Μ}^{\prime }y\\ 0& L{}_{4}& {Μ}^{\prime }y& {Μ}^{\prime }x\\ -{Μ}^{\prime }x& {Μ}^{\prime }y& L{}_{2}& 0\\ {Μ}^{\prime }y& {Μ}^{\prime }x& 0& L{}_{2}\end{array}\right)\left(\begin{array}{l}i{}_{\text{a}\text{p}}\\ i{}_{\text{b}\text{p}}\\ i{}_{x}\\ i{}_{y}\end{array}\right)\text{ }\text{ }\text{ }\left(6\right)\end{array}$

$\left(\begin{array}{l}F{}_{x}\\ F{}_{y}\end{array}\right)=\left(\begin{array}{l}\frac{\partial W{}_{\text{m}}}{\partial x}\\ \frac{\partial W{}_{\text{m}}}{\partial y}\end{array}\right)\text{ }\text{ }\text{ }\left(7\right)$

$\begin{array}{l}\left(\begin{array}{l}F{}_{x}\\ F{}_{y}\end{array}\right)={Μ}^{\prime }Ι{}_{\text{a}\text{b}\text{p}}\cdot \\ \left(\begin{array}{cc}-\mathrm{cos}\left(2\omega t+\theta {}_{1}\right)& \mathrm{sin}\left(2\omega t+\theta {}_{1}\right)\\ \mathrm{sin}\left(2\omega t+\theta {}_{1}\right)& \mathrm{cos}\left(2\omega t+\theta {}_{1}\right)\end{array}\right)\left(\begin{array}{l}i{}_{x}\\ i{}_{y}\end{array}\right)\text{ }\text{ }\text{ }\left(8\right)\end{array}$

$\begin{array}{l}\left\{\begin{array}{l}i{}_{\text{a}\text{p}}\approx Ι{}_{\text{p}}\phantom{\rule{0.25em}{0ex}}\mathrm{cos}\phantom{\rule{0.25em}{0ex}}2\omega t\\ i{}_{\text{b}\text{p}}\approx Ι{}_{\text{p}}\phantom{\rule{0.25em}{0ex}}\mathrm{sin}\phantom{\rule{0.25em}{0ex}}2\omega t\end{array}\text{ }\text{ }\text{ }\left(9\right)\\ \left(\begin{array}{l}F{}_{x}\\ F{}_{y}\end{array}\right)={Μ}^{\prime }Ι{}_{\text{p}}\left(\begin{array}{cc}-\mathrm{cos}\phantom{\rule{0.25em}{0ex}}2\omega t& \mathrm{sin}\phantom{\rule{0.25em}{0ex}}2\omega t\\ \mathrm{sin}\phantom{\rule{0.25em}{0ex}}2\omega t& \mathrm{cos}\phantom{\rule{0.25em}{0ex}}2\omega t\end{array}\right)\left(\begin{array}{l}i{}_{x}\\ i{}_{y}\end{array}\right)\text{ }\text{ }\text{ }\left(10\right)\end{array}$

$\left(\begin{array}{l}i{}_{x}\\ i{}_{y}\end{array}\right)=\frac{1}{{Μ}^{\prime }Ι{}_{\text{p}}}\left(\begin{array}{cc}-\mathrm{cos}\phantom{\rule{0.25em}{0ex}}2\omega t& \mathrm{sin}\phantom{\rule{0.25em}{0ex}}2\omega t\\ \mathrm{sin}\phantom{\rule{0.25em}{0ex}}2\omega t& \mathrm{cos}\phantom{\rule{0.25em}{0ex}}2\omega t\end{array}\right)\left(\begin{array}{l}F{}_{x}\\ F{}_{y}\end{array}\right)\text{ }\text{ }\text{ }\left(11\right)$

$\left\{\begin{array}{l}\Psi {}_{\text{d}}=L{}_{\text{d}}i{}_{\text{d}}+\Psi {}_{\text{r}}\\ \Psi {}_{\text{q}}=L{}_{\text{q}}i{}_{\text{q}}\end{array}\text{ }\text{ }\text{ }\left(12\right)$

$\left\{\begin{array}{l}u{}_{\text{d}}=p\Psi {}_{\text{d}}-\omega \Psi {}_{\text{q}}+r{}_{1}i{}_{\text{d}}\\ u{}_{\text{q}}=p\Psi {}_{\text{q}}+\omega \Psi {}_{\text{d}}+r{}_{1}i{}_{\text{q}}\end{array}\text{ }\text{ }\text{ }\left(13\right)$

$Τ{}_{\text{e}\text{m}}=p{}_{1}\left(\Psi {}_{\text{d}}i{}_{\text{q}}-\Psi {}_{\text{q}}i{}_{\text{d}}\right)=\frac{J}{p{}_{1}}\cdot \frac{\text{d}\omega }{\text{d}t}+Τ{}_{\text{L}}\text{ }\text{ }\text{ }\left(14\right)$

$\left\{\begin{array}{l}\Psi {}_{\text{d}}=\Psi {}_{\text{r}}\\ \Psi {}_{\text{q}}=L{}_{\text{q}}i{}_{\text{q}}\\ u{}_{\text{d}}=-\omega \Psi {}_{\text{q}}=-\omega L{}_{\text{q}}i{}_{\text{q}}\\ u{}_{q}=\omega \Psi {}_{r}+r{}_{1}i{}_{q}+L{}_{q}pi{}_{q}\\ Τ{}_{\text{e}\text{m}}=p{}_{1}\Psi {}_{\text{r}}i{}_{\text{q}}\end{array}\text{ }\text{ }\text{ }\left(15\right)$

《图2》

《3 数字控制系统构成》

3 数字控制系统构成

《3.1控制系统硬件》

3.1控制系统硬件

DSP控制器采用TMS320LF2407 [9,10], 它是TMS320C2000平台下的一种定点DSP芯片, 广泛应用于电机的数字控制领域。速度传感器为光电编码盘, 产生频率可变、固定相差为90°的两路脉冲, 转子每转1圈输出一个脉冲信号, 根据脉冲数和频率来计算转子机械位置和转速。为了提高xy方向位移的测量精度, 在每个方向安装2个位移传感器进行差动测量。图3为DSP控制器结构框图。

《图3》

《3.2控制系统软件》

3.2控制系统软件

《图4》

《图5》

《4 实验结果》

4 实验结果

《5 结论》

5 结论

《图6》