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网站推广东莞,福州网站建设专业定制,响应式网站 图片尺寸奇数,绵阳seo通过i_α和i_β估计反电势e_α和e_β一、龙博格观测器简介二、状态变量推导三、实现过程四、仿真一、龙博格观测器简介 龙博格观测器#xff0c;一种典型的全维状态观测器#xff0c;依赖系统的输出状态与搭建的状态误差收敛状态对状态进行观测 假设一个系统为#xff1a;…通过i_α和i_β估计反电势e_α和e_β一、龙博格观测器简介二、状态变量推导三、实现过程四、仿真一、龙博格观测器简介龙博格观测器一种典型的全维状态观测器依赖系统的输出状态与搭建的状态误差收敛状态对状态进行观测假设一个系统为{ x ˙ A x B u y C x \left\{ \begin{aligned} \dot{x} A x B u \\ y C x \end{aligned} \right.{x˙y​AxBuCx​根据框图格式构建观测器如下K为增益{ x ^ ˙ A x ^ B u K ( y − y ^ ) y ^ C x ^ \left\{ \begin{aligned} \dot{\hat{x}} A \hat{x} B uK(y-\hat{y}) \\ \hat{y} C \hat{x} \end{aligned} \right.{x^˙y^​​Ax^BuK(y−y^​)Cx^​进一步即状态x的观测值为x ^ ˙ ( A − K C ) x ^ B u K y 式 1 \ \dot{\hat{x}} (A-KC) \hat{x} B uKy \ 式1x^˙(A−KC)x^BuKy式1进一步离散化后状态x为x ^ ( k 1 ) [ ( A − K C ) x ^ ( k ) B u ( k ) K y ( k ) ] ∗ T s x ^ ( k ) \ {\hat{x}(k1)}[ (A-KC) \hat{x}(k) B u(k)Ky (k) ]*T_s\hat{x}(k)\x^(k1)[(A−KC)x^(k)Bu(k)Ky(k)]∗Ts​x^(k)在PMSM控制中我们通过对输出状态i a \ i_aia​和i β \ i_βiβ​的追踪实现对反电动势e a \ e_aea​与e a \ e_aea​的观测进而通过PLL可以提取PMSM的转子信息二、状态变量推导表贴式PMSM两相静止坐标系下电压方程{ u α R s i α L s d i α d t e α u β R s i β L s d i β d t e β \left\{ \begin{aligned} u_{\alpha} R_s i_{\alpha} L_s \frac{di_{\alpha}}{dt} e_{\alpha} \\ u_{\beta} R_s i_{\beta} L_s \frac{di_{\beta}}{dt} e_{\beta} \end{aligned} \right.⎩⎨⎧​uα​uβ​​Rs​iα​Ls​dtdiα​​eα​Rs​iβ​Ls​dtdiβ​​eβ​​其中反电动势为{ e α − ω r ψ f sin ⁡ ( θ r ) e β ω r ψ f cos ⁡ ( θ r ) \left\{ \begin{aligned} e_{\alpha} -\omega_{r} \psi_{f} \sin \left( \theta_{r} \right) \\ e_{\beta} \omega_{r} \psi_{f} \cos \left( \theta_{r} \right) \end{aligned} \right.{eα​−ωr​ψf​sin(θr​)eβ​ωr​ψf​cos(θr​)​其中ω r \ \omega_{r}ωr​为电角度、θ r \ \theta_{r}θr​为转子位置、ψ f \ \psi_{f}ψf​为永磁体磁链由假设近似ω r ˙ 0 \ \dot{ \omega_{r} }0ωr​˙​0d θ r d t ω r \ \frac{d\theta_r}{dt} \omega_rdtdθr​​ωr​从电压方程解出电流导数和反电势导数d i α d t 1 L s ( u α − R s i α − e α ) \frac{di_{\alpha}}{dt} \frac{1}{L_s}(u_{\alpha} - R_s i_{\alpha} - e_{\alpha})dtdiα​​Ls​1​(uα​−Rs​iα​−eα​)d i β d t 1 L s ( u β − R s i β − e β ) \frac{di_{\beta}}{dt} \frac{1}{L_s}(u_{\beta} - R_s i_{\beta} - e_{\beta})dtdiβ​​Ls​1​(uβ​−Rs​iβ​−eβ​)d e α d t d d t ( − ω r ψ f sin ⁡ ( θ r ) ) − ω r d d t ( ψ f sin ⁡ ( θ r ) ) ≈ − ω r e β \frac{de_{\alpha}}{dt} \frac{d}{dt} \Bigl(-\omega_{r} \psi_{f} \sin(\theta_{r}) \Bigr) -\omega_{r} \frac{d}{dt} \Bigl( \psi_{f} \sin(\theta_{r}) \Bigr) \approx -\omega_{r} e_{\beta}dtdeα​​dtd​(−ωr​ψf​sin(θr​))−ωr​dtd​(ψf​sin(θr​))≈−ωr​eβ​d e β d t d d t ( ω r ψ f cos ⁡ ( θ r ) ) ω r d d t ( ψ f cos ⁡ ( θ r ) ) ≈ ω r e α \frac{de_{\beta}}{dt} \frac{d}{dt} \Bigl( \omega_{r} \psi_{f} \cos(\theta_{r}) \Bigr) \omega_{r} \frac{d}{dt} \Bigl( \psi_{f} \cos(\theta_{r}) \Bigr) \approx \omega_{r} e_{\alpha}dtdeβ​​dtd​(ωr​ψf​cos(θr​))ωr​dtd​(ψf​cos(θr​))≈ωr​eα​故而状态空间方程构建如下状态空间方程为d d t [ i α i β e α e β ] [ − R s L s 0 − 1 L s 0 0 − R s L s 0 − 1 L s 0 0 0 − ω r 0 0 ω r 0 ] [ i α i β e α e β ] [ 1 L s 0 0 1 L s 0 0 0 0 ] [ u α u β 0 0 ] \frac{d}{d t}\left[\begin{array}{c} i_{\alpha} \\ i_{\beta} \\ e_{\alpha} \\ e_{\beta} \end{array}\right] \left[\begin{array}{cccc} -\frac{R_{s}}{L_{s}} 0 -\frac{1}{L_{s}} 0 \\ 0 -\frac{R_{s}}{L_{s}} 0 -\frac{1}{L_{s}} \\ 0 0 0 -\omega_{r} \\ 0 0 \omega_{r} 0 \end{array}\right] \left[\begin{array}{c} i_{\alpha} \\ i_{\beta} \\ e_{\alpha} \\ e_{\beta} \end{array}\right] \left[\begin{array}{cc} \frac{1}{L_{s}} 0 \\ 0 \frac{1}{L_{s}} \\ 0 0 \\ 0 0 \end{array}\right] \left[\begin{array}{c} u_{\alpha} \\ u_{\beta} \\ 0 \\ 0 \end{array}\right]dtd​​iα​iβ​eα​eβ​​​​−Ls​Rs​​000​0−Ls​Rs​​00​−Ls​1​00ωr​​0−Ls​1​−ωr​0​​​iα​iβ​eα​eβ​​​​Ls​1​000​0Ls​1​00​​​uα​uβ​00​​输出方程为[ i α i β ] [ 1 0 0 0 0 1 0 0 ] [ i α i β e α e β ] \left[\begin{array}{l} i_{\alpha} \\ i_{\beta} \end{array}\right] \left[\begin{array}{llll} 1 0 0 0 \\ 0 1 0 0 \end{array}\right] \left[\begin{array}{l} i_{\alpha} \\ i_{\beta} \\ e_{\alpha} \\ e_{\beta} \end{array}\right][iα​iβ​​][10​01​00​00​]​iα​iβ​eα​eβ​​​三、实现过程仿照一、中对上面给出的状态方程设计Lunberger观测器如下d d t [ i ^ α i ^ β e ^ α e ^ β ] A [ i ^ α i ^ β e ^ α e ^ β ] B [ u α u β 0 0 ] K ( [ i α i β 0 0 ] − [ i ^ α i ^ β 0 0 ] ) ( 式 2 ) \frac{d}{d t}\left[\begin{array}{c} \hat{i}_{\alpha} \\ \hat{i}_{\beta} \\ \hat{e}_{\alpha} \\ \hat{e}_{\beta} \end{array}\right] \mathbf{A}\left[\begin{array}{c} \hat{i}_{\alpha} \\ \hat{i}_{\beta} \\ \hat{e}_{\alpha} \\ \hat{e}_{\beta} \end{array}\right] \mathbf{B}\left[\begin{array}{c} u_{\alpha} \\ u_{\beta} \\ 0 \\ 0 \end{array}\right] \mathbf{K}\left( \left[\begin{array}{c} i_{\alpha} \\ i_{\beta}\\0 \\0 \end{array}\right] - \left[\begin{array}{c} \hat{i}_{\alpha} \\ \hat{i}_{\beta} \\0 \\0 \end{array}\right] \right)(式2)dtd​​i^α​i^β​e^α​e^β​​​A​i^α​i^β​e^α​e^β​​​B​uα​uβ​00​​K​​iα​iβ​00​​−​i^α​i^β​00​​​(式2)其中系数矩阵A、B、C为A [ − R s L s 0 − 1 L s 0 0 − R s L s 0 − 1 L s 0 0 0 − ω r 0 0 ω r 0 ] \mathbf{A}\left[\begin{array}{cccc} -\frac{R_{s}}{L_{s}} 0 -\frac{1}{L_{s}} 0 \\ 0 -\frac{R_{s}}{L_{s}} 0 -\frac{1}{L_{s}} \\ 0 0 0 -\omega_{r} \\ 0 0 \omega_{r} 0 \end{array}\right]A​−Ls​Rs​​000​0−Ls​Rs​​00​−Ls​1​00ωr​​0−Ls​1​−ωr​0​​B [ 1 L s 0 0 1 L s 0 0 0 0 ] , C [ 1 0 0 0 0 1 0 0 ] \mathbf{B}\left[\begin{array}{cc} \frac{1}{L_{s}} 0 \\ 0 \frac{1}{L_{s}} \\ 0 0 \\ 0 0 \end{array}\right],\quad \mathbf{C}\left[\begin{array}{cccc} 1 0 0 0 \\ 0 1 0 0 \end{array}\right]B​Ls​1​000​0Ls​1​00​​,C[10​01​00​00​]增益矩阵为K [ K 1 0 0 0 0 K 1 0 0 K 2 0 0 0 0 K 2 0 0 ] \mathbf{K} \left[ \begin{array}{cc} K_1 0 0 0\\ 0 K_1 0 0\\ K_2 0 0 0\\ 0 K_2 0 0\\ \end{array} \right]K​K1​0K2​0​0K1​0K2​​0000​0000​​其中K1是对电流的观测增益K2是对反电动势的观测增益状态变量输入矩阵输出矩阵分别为x [ i α i β e α e α ] , u [ u α u β 0 0 ] , y [ i α i β 0 0 ] \mathbf{x}\left[\begin{array}{c} i_{\alpha} \\ i_{\beta} \\ e_{\alpha} \\ e_{\alpha} \end{array}\right] ,\mathbf{u}\left[\begin{array}{c} u_{\alpha} \\ u_{\beta} \\ 0 \\ 0 \end{array}\right] ,\mathbf{y}\left[\begin{array}{c} i_{\alpha} \\ i_{\beta} \\ 0 \\ 0 \end{array}\right]x​iα​iβ​eα​eα​​​,u​uα​uβ​00​​,y​iα​iβ​00​​对(式2)离散化后得到反电动势的龙博格观测器为i ^ α ( k 1 ) i ^ α ( k ) T [ − R s L s i ^ α ( k ) − 1 L s e ^ α ( k ) 1 L s u α ( k ) K 1 ( i α ( k ) − i ^ α ( k ) ) ] i ^ β ( k 1 ) i ^ β ( k ) T [ − R s L s i ^ β ( k ) − 1 L s e ^ β ( k ) 1 L s u β ( k ) K 1 ( i β ( k ) − i ^ β ( k ) ) ] e ^ α ( k 1 ) e ^ α ( k ) T [ − ω ^ e e ^ β ( k ) K 2 ( i α ( k ) − i ^ α ( k ) ) ] e ^ β ( k 1 ) e ^ β ( k ) T [ ω ^ e e ^ α ( k ) K 2 ( i β ( k ) − i ^ β ( k ) ) ] \begin{aligned} \hat{i}_{\alpha}(k1) \hat{i}_{\alpha}(k) T\bigg[-\frac{R_s}{L_s}\hat{i}_{\alpha}(k) - \frac{1}{L_s}\hat{e}_{\alpha}(k) \frac{1}{L_s}u_{\alpha}(k) K_1\big(i_{\alpha}(k) - \hat{i}_{\alpha}(k)\big)\bigg] \\ \hat{i}_{\beta}(k1) \hat{i}_{\beta}(k) T\bigg[-\frac{R_s}{L_s}\hat{i}_{\beta}(k) - \frac{1}{L_s}\hat{e}_{\beta}(k) \frac{1}{L_s}u_{\beta}(k) K_1\big(i_{\beta}(k) - \hat{i}_{\beta}(k)\big)\bigg] \\ \hat{e}_{\alpha}(k1) \hat{e}_{\alpha}(k) T\bigg[-\hat{\omega}_e \hat{e}_{\beta}(k) K_2\big(i_{\alpha}(k) - \hat{i}_{\alpha}(k)\big)\bigg] \\ \hat{e}_{\beta}(k1) \hat{e}_{\beta}(k) T\bigg[\,\hat{\omega}_e \hat{e}_{\alpha}(k) K_2\big(i_{\beta}(k) - \hat{i}_{\beta}(k)\big)\bigg] \end{aligned}i^α​(k1)i^β​(k1)e^α​(k1)e^β​(k1)​i^α​(k)T[−Ls​Rs​​i^α​(k)−Ls​1​e^α​(k)Ls​1​uα​(k)K1​(iα​(k)−i^α​(k))]i^β​(k)T[−Ls​Rs​​i^β​(k)−Ls​1​e^β​(k)Ls​1​uβ​(k)K1​(iβ​(k)−i^β​(k))]e^α​(k)T[−ω^e​e^β​(k)K2​(iα​(k)−i^α​(k))]e^β​(k)T[ω^e​e^α​(k)K2​(iβ​(k)−i^β​(k))]​T为采样时间四、仿真simulink搭建仿真验证如下选取合适增益后运行用示波器查看i_α和hat(i_α)波形发现观测收敛如下反电动势为