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    Journals >Spacecraft Recovery & Remote Sensing >Volume 45 >Issue 6 >Page 47 > Article
    • Spacecraft Recovery & Remote Sensing
    • Vol. 45, Issue 6, 47 (2024)
    A Speed Anti-disturbance Control Algorithm for Permanent Magnet AC Servo Systems
    Huan LIU1, Zhongyang HAO1, Xiaomin ZHANG1, and Xinhao WANG2
    Author Affiliations
  • 1Beijing Institute of Space Mechanics & Electricity, Beijing 100094, China
  • 2Hefei Polytechnic University, Hefei 230009, China
    • show less
    DOI: 10.3969/j.issn.1009-8518.2024.06.005 Cite this Article
    Huan LIU, Zhongyang HAO, Xiaomin ZHANG, Xinhao WANG. A Speed Anti-disturbance Control Algorithm for Permanent Magnet AC Servo Systems[J]. Spacecraft Recovery & Remote Sensing, 2024, 45(6): 47 Copy Citation Text show less

    Abstract

    The speed controller is an extremely important segment in servo control systems, and its performance is an important factor in measuring the control effect of the entire control system. In practical engineering, there is a large amount of interference in permanent magnet AC servo system, and traditional PID control algorithms are difficult to achieve satisfactory control results. To improve the anti-interference control performance of permanent magnet AC servo systems, this paper designs a speed anti-interference control algorithm based on an extended state observer. Firstly, the extended state observer is designed to accurately estimate interference in real time while realizing demodulation, and feedforward compensation is performed. Then, a non-singular terminal sliding mode controller is designed to achieve high-precision anti-interference speed control. Simulation and experimental results show that the speed control error of this control algorithm is reduced by more than 64% compared to traditional PID controllers. Therefore, the proposed method has better control performance than the traditional PID control methods, and can improve the anti-interference performance and control accuracy of permanent magnet AC servo systems in practical engineering.

    Keywords

    $ \left\{\begin{gathered}\dot{\theta}=\omega \\ \dot{\omega}=\frac{1}{J}\left(\frac{3K_{\text{m}}}{2}i_{\text{q}}-T_{\text{l}}-D\omega-g(t)\right) \\ \end{gathered}\right. $(1)

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    $ \left\{ \begin{gathered} \dot \theta = \omega \\ \dot \omega = f{\text{(}}t{\text{)}} + {b_0}{i_{\text{q}}} \\ \end{gathered} \right. $(2)

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    $ \left\{ \begin{gathered} {{\dot x}_1} = {x_2} \\ {{\dot x}_2} = {x_3} + {b_0}{i_{\text{q}}} \\ {{\dot x}_3} = h(t) \\ \end{gathered} \right. $(3)

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    $ {\boldsymbol{\dot x}} = {\boldsymbol{Ax}} + {\boldsymbol{B}}{i_{\text{q}}} + {\boldsymbol{E}}h(t) $(4)

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    $ \left\{ \begin{gathered} {{\dot{ \hat x}}_1} = {\text{ }}{{\hat x}_2} + {l_1}\varepsilon \\ {{\dot { \hat x}}_2} = {{\hat x}_3} + {b_0}{i_{\text{q}}} + {l_2}\varepsilon \\ {{\dot { \hat x}}_3} = {l_3}\varepsilon \\ \end{gathered} \right. $(5)

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    $ {{\dot {\boldsymbol{z}}}} = {\boldsymbol{A{z}}} + {\boldsymbol{B}}{i_{\text{q}}} + {\boldsymbol{L}}\varepsilon $(6)

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    $ \dot {{ \tilde{ \boldsymbol x}}} = {{{\boldsymbol{ A}}}_{\text{e}}}{{\tilde{ \boldsymbol x}}} + {\boldsymbol{E}}h(t) $(7)

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    $ f(\lambda ) = \left| {{{\boldsymbol{A}}_{\text{e}}} - \lambda {\boldsymbol{I}}} \right| = {\lambda ^3} + {l_1}{\lambda ^2} + {l_2}\lambda + {l_3} $(8)

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    $ {\boldsymbol{P}}{{\boldsymbol{A}}_{\text{e}}} + {\boldsymbol{A}}_{\text{e}}^{\text{T}}{\boldsymbol{P}} = - {\boldsymbol{Q}} $(9)

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    $ {V_0} = {{{\tilde {\boldsymbol {x}}}}^{\text{T}}}{{\boldsymbol{P}\tilde {\boldsymbol{x}}}} > 0 $(10)

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    $ {\dot V_0} = - {{{\tilde {\boldsymbol {x}}}}^{\text{T}}}{\boldsymbol{Q\tilde x}} + 2{{{\tilde {\boldsymbol {x}}}}^{\text{T}}}{\boldsymbol{PE}}h(t) $(11)

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    $ \begin{split} {{\dot V}_0} \leqslant &- {\lambda _{\min }}({\boldsymbol{Q}}){\left\| {{{\tilde {\boldsymbol {x}}}}} \right\|^2} + 2\left\| {{{\tilde {\boldsymbol {x}}}}} \right\| \cdot \left\| {\boldsymbol{P}} \right\| \cdot \left\| {\boldsymbol{E}} \right\| \cdot \left| {h(t)} \right| \\ \leqslant& - {\lambda _{\min }}({\boldsymbol{Q}}){\left\| {{{\tilde {\boldsymbol {x}}}}} \right\|^2} + 2\left\| {{{\tilde {\boldsymbol {x}}}}} \right\| \cdot \left\| {\boldsymbol{P}} \right\|\delta \\ \end{split} $(12)

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    $\left\{\begin{split}&\dot{\tilde{\theta}}=\dot{\theta}_\mathrm{d}-\dot{\hat{\theta}}=\omega_\mathrm{d}-\hat{x}_2-l_1\tilde{x}_1=\tilde{\omega}-l_1\tilde{x}_1\\&\dot{\tilde{\omega}}=\dot{\omega}_\mathrm{d}-\dot{\hat{\omega}}=\dot{\omega}_\mathrm{d}-b_0i_\mathrm{q}-\hat{x}_3-l_2\tilde{x}_1=\dot{\omega}_\mathrm{d}-J^{-1}T_\mathrm{e}^*-\hat{f}(t)-l_2\tilde{x}_1\end{split}\right.$(13)

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    $ s = \tilde \theta + \lambda {\tilde \omega ^{{p \mathord{\left/ {\vphantom {p q}} \right. } n}}} $(14)

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    $ {V_1} = \frac{1}{2}J{s^2} + {V_0} $(15)

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    $ {{\dot V}_1} =Js\dot s + {{\dot V}_0} = s\left\{ {J\tilde \omega - J{l_1}{{\tilde x}_1} + \frac{{\lambda p}}{n}{{\tilde \omega }^{{p \mathord{\left/ {\vphantom {p q}} \right. } n} - 1}}\left[ {J{{\dot \omega }_{\text{d}}} - T_{\text{e}}^{\text{*}} - J\hat f{\text{(}}t{\text{)}} - J{l_2}{{\tilde x}_1}} \right]} \right\} + {{\dot V}_0} $(16)

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    $ T_{\text{e}}^{\text{*}} = J{\dot \omega _{\text{d}}} - J\hat f{\text{(}}t{\text{)}} + \frac{n}{{\lambda p}}J{\tilde \omega ^{{{2 - p} \mathord{\left/ {\vphantom {{2 - p} n}} \right. } n}}} + ks + {\delta _0}{\mathrm{sign}}(s) $(17)

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    $ {\dot V_1} = - \frac{{\lambda pk}}{n}{\tilde \omega ^{{p \mathord{\left/ {\vphantom {p n}} \right. } n} - 1}}{s^2} - \left[ {\frac{{\lambda p}}{n}{{\tilde \omega }^{{p \mathord{\left/ {\vphantom {p n}} \right. } n} - 1}}J{l_2} + J{l_1}} \right]s{\tilde x_1} - \frac{{\lambda p}}{n}{\tilde \omega ^{{p \mathord{\left/ {\vphantom {p n}} \right. } n} - 1}}{\delta _0}\left| s \right| + {\dot V_0} $(18)

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    $ {\dot V_1} \leqslant - \frac{{\lambda pk}}{n}{\tilde \omega ^{{p \mathord{\left/ {\vphantom {p n}} \right. } n} - 1}}{s^2} + \left[ {\left(\frac{{\lambda p}}{n}{{\tilde \omega }^{{p \mathord{\left/ {\vphantom {p n}} \right. } n} - 1}}J{l_2} + J{l_1}\right)\left| {{{\tilde x}_1}} \right| - \frac{{\lambda p}}{n}{{\tilde \omega }^{{p \mathord{\left/ {\vphantom {p n}} \right. } n} - 1}}{\delta _0}} \right]\left| s \right| + {\dot V_0} $(19)

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    $ \dot{V}_1\leqslant-\frac{\lambda pk}{n}\tilde{\omega}^{p\mathord{\left/\vphantom{pn}\right.}n-1}s^2-\lambda_{\min}(\boldsymbol{Q}) \left\| \tilde{\boldsymbol{x}} \right\| ^2+2 \left\| \tilde{\boldsymbol{x}} \right\| \cdot \left\| \boldsymbol{P} \right\| \delta $(20)

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    $ \begin{gathered}\dot{V}_1\leqslant-\gamma \left\| \boldsymbol{z} \right\| ^2+2 \left\| \boldsymbol{\tilde{x}} \right\| \cdot \left\| \boldsymbol{P} \right\| \delta \\ \begin{array}{*{20}{c}}\end{array}\leqslant-\gamma \left\| \boldsymbol{z} \right\| ^2+2 \left\| \boldsymbol{z} \right\| \cdot \left\| \boldsymbol{P} \right\| \delta \\ \end{gathered} $(21)

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    Huan LIU, Zhongyang HAO, Xiaomin ZHANG, Xinhao WANG. A Speed Anti-disturbance Control Algorithm for Permanent Magnet AC Servo Systems[J]. Spacecraft Recovery & Remote Sensing, 2024, 45(6): 47
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