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 同济大学学报(自然科学版)  2018, Vol. 46 Issue (11): 1562-1567.  DOI: 10.11908/j.issn.0253-374x.2018.11.014 0

### 引用本文

LIAO Gaohua, WU Jianzhong. Load Control of Vibration Exciter in Two-point Fatigue Test System of Wind Turbine Blade[J]. Journal of Tongji University (Natural Science), 2018, 46(11): 1562-1567. DOI: 10.11908/j.issn.0253-374x.2018.11.014

### 文章历史

1. 同济大学 机械与能源工程学院，上海 201804;
2. 南昌工程学院 江西省精密驱动与控制重点实验室，江西 南昌 330099

Load Control of Vibration Exciter in Two-point Fatigue Test System of Wind Turbine Blade
LIAO Gaohua 1,2, WU Jianzhong 1
1. College of Mechanical Engineering, Tongji University, Shanghai 201804, China;
2. Jiangxi Province Key Laboratory of Precision Drive & Control, Nanchang Institute of Technology, Nanchang 330099, China
Abstract: Based on the electrically driven inertial vibration exciter, a two-point excitation fatigue test system of wind turbine blade was constructed. The virtual master synchronization control algorithm was put forward. The PID algorithm was used to design the error compensator, then the stability of the control algorithm was proved by using Lyapunov function. The control simulation model was established, and the convergence and the robustness of the control algorithm were analyzed by numerical simulation. Finally, the effectiveness of the control algorithm of electromechanical coupling was verified. The results show that the control algorithm can make the exciter follow quickly, the fluctuation of phase difference between the exciters is very small, the blade amplitude is stable, and the stable and effective loading of wind turbine blades is realized.

1 叶片两点疲劳加载试验系统构建

 图 2 振动耦合特性试验分析 Fig.2 Experimental analysis of coupling characteristics of vibration
2 同步控制策略

 图 3 基于虚拟主令偏差耦合的同步控制策略结构 Fig.3 Synthronization control strategy structure based on virtual master deviation coupling

 $\left[ {\begin{array}{*{20}{c}} {{\varepsilon _1}}\\ {{\varepsilon _2}}\\ \vdots \\ {{\varepsilon _{n - 1}}}\\ {{\varepsilon _n}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 2&{ - 1}&0& \cdots &0&0&{ - 1}\\ 1&2&{ - 1}& \cdots &0&0&0\\ \vdots&\vdots&\vdots &{}& \vdots&\vdots&\vdots \\ 0&0&0& \cdots &{ - 1}&2&{ - 1}\\ { - 1}&0&0& \cdots &0&{ - 1}&2 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{e_1}}\\ {{e_2}}\\ \vdots \\ {{e_{n - 1}}}\\ {{e_n}} \end{array}} \right]$ (1)

 $\mathit{\boldsymbol{\varepsilon }} = \mathit{\boldsymbol{Te}}$ (2)

 $\begin{array}{l} {\mathit{\boldsymbol{e}}^2}\mathit{\boldsymbol{Te}} = {\left( {{e_1} - {e_2}} \right)^2} + {\left( {{e_2} - {e_3}} \right)^2} + \cdots + \\ \;\;\;\;\;\;\;\;\;\;{\left( {{e_n} - {e_1}} \right)^2} \ge 0 \end{array}$ (3)

 $\mathit{\boldsymbol{E}} = \left( {\mathit{\boldsymbol{I}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} T}}} \right)\mathit{\boldsymbol{e}}$ (4)

3 同步控制算法及稳定性

 $\left\{ \begin{array}{l} {J_i}{{\ddot \theta }_i} + {B_i}{{\dot \theta }_i} = {T_{{\rm{em}}i}} - {T_{{\rm{L}}i}}\\ {T_{{\rm{em}}i}} = 1.5{p_{\rm{n}}}{\mathit{\Psi }_{\rm{f}}}{i_{\rm{q}}},{T_{{\rm{L}}i}} = \frac{{{P_{\rm{h}}}}}{{2{\rm{ \mathsf{ π} }}}}{F_{{\rm{s}}i}} \end{array} \right.$ (5)
 图 4 伺服控制结构框图 Fig.4 Servo control structure diagram

 $\mathit{\boldsymbol{J}}\left( \mathit{\boldsymbol{\theta }} \right)\mathit{\boldsymbol{\ddot \theta }} + \mathit{\boldsymbol{B}}\left( {\mathit{\boldsymbol{\theta }},\mathit{\boldsymbol{\dot \theta }}} \right)\mathit{\boldsymbol{\dot \theta }} = {\mathit{\boldsymbol{T}}_\tau }$ (6)

 $\mathit{\boldsymbol{\dot e}}\left( t \right) = \mathit{\boldsymbol{\dot \theta }},\mathit{\boldsymbol{\dot \varepsilon }}\left( t \right) = \left( {\mathit{\boldsymbol{I}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} T}}} \right)\mathit{\boldsymbol{\dot \theta }}$ (7)

 ${\mathit{\boldsymbol{T}}_\tau } = {\mathit{\boldsymbol{K}}_{\rm{p}}}\mathit{\boldsymbol{E}} + {\mathit{\boldsymbol{K}}_{\rm{d}}}\mathit{\boldsymbol{\dot E}} + {\left( {\mathit{\boldsymbol{I}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} T'}}} \right)^{ - 1}}{\mathit{\boldsymbol{K}}_{\rm{e}}}\mathit{\boldsymbol{\dot e}}$ (8)

 $\begin{array}{l} \mathit{\boldsymbol{J}}\left( \mathit{\boldsymbol{\theta }} \right)\mathit{\boldsymbol{\ddot \theta }} + \mathit{\boldsymbol{B}}\left( {\mathit{\boldsymbol{\theta }},\mathit{\boldsymbol{\dot \theta }}} \right)\mathit{\boldsymbol{\dot \theta }} = {\mathit{\boldsymbol{K}}_{\rm{p}}}\mathit{\boldsymbol{E}} + {\mathit{\boldsymbol{K}}_{\rm{d}}}\mathit{\boldsymbol{\dot E + }}\\ \;\;\;\;\;\;\;\;\;\;{\left( {\mathit{\boldsymbol{I}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} T'}}} \right)^{ - 1}}{\mathit{\boldsymbol{K}}_{\rm{e}}}\mathit{\boldsymbol{\dot e}} \end{array}$ (9)

 $V = \frac{1}{2}\left( {\left( {\mathit{\boldsymbol{\dot e'J}}\left( \mathit{\boldsymbol{\theta }} \right)\mathit{\boldsymbol{\dot e}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} \dot e'T'J}}\left( \mathit{\boldsymbol{\theta }} \right)\mathit{\boldsymbol{\dot e}}} \right) + \mathit{\boldsymbol{E'}}{\mathit{\boldsymbol{K}}_{\rm{p}}}\mathit{\boldsymbol{E}}} \right)$ (10)

 $\begin{array}{*{20}{c}} {\dot V = \mathit{\boldsymbol{\dot e'}}\left( {\mathit{\boldsymbol{I}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} T'}}} \right)\mathit{\boldsymbol{J}}\left( \mathit{\boldsymbol{\theta }} \right)\mathit{\boldsymbol{\ddot e + }}\frac{1}{2}\mathit{\boldsymbol{\dot e'}}\left( {\mathit{\boldsymbol{I}} + } \right.}\\ {\left. {\mathit{\boldsymbol{ \boldsymbol{\varLambda} T'}}} \right)\mathit{\boldsymbol{\dot J}}\left( \mathit{\boldsymbol{\theta }} \right)\mathit{\boldsymbol{\dot e}} + \mathit{\boldsymbol{E'}}{\mathit{\boldsymbol{K}}_{\rm{p}}}\mathit{\boldsymbol{\dot E}}} \end{array}$ (11)

 $\begin{array}{l} \mathit{\boldsymbol{\dot e'}}\left( {\mathit{\boldsymbol{I}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} T'}}} \right)\mathit{\boldsymbol{J}}\left( \mathit{\boldsymbol{\theta }} \right)\mathit{\boldsymbol{\ddot e}} + \mathit{\boldsymbol{\dot e'}}\left( {\mathit{\boldsymbol{I}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} T'}}} \right)\mathit{\boldsymbol{B}}\left( {\mathit{\boldsymbol{\theta }},\mathit{\boldsymbol{\dot \theta }}} \right)\mathit{\boldsymbol{\dot e}} = \\ \;\;\;\;\;\;\; - \left( {\mathit{\boldsymbol{\dot E'}}{\mathit{\boldsymbol{K}}_{\rm{p}}}\mathit{\boldsymbol{E}} + \mathit{\boldsymbol{\dot E'}}{\mathit{\boldsymbol{K}}_{\rm{d}}}\mathit{\boldsymbol{\dot E}} + \mathit{\boldsymbol{\dot e'}}{\mathit{\boldsymbol{K}}_{\rm{e}}}\mathit{\boldsymbol{\dot e}}} \right) \end{array}$ (12)

 $\begin{array}{l} \dot V = \mathit{\boldsymbol{\dot e'}}\left( {\mathit{\boldsymbol{I}} + \mathit{\boldsymbol{ \boldsymbol{\varLambda} T'}}} \right)\left( {\frac{1}{2}\mathit{\boldsymbol{\dot J}}\left( \mathit{\boldsymbol{\theta }} \right) - \mathit{\boldsymbol{B}}\left( {\mathit{\boldsymbol{\theta }},\mathit{\boldsymbol{\dot \theta }}} \right)} \right)\mathit{\boldsymbol{\dot e}} - \mathit{\boldsymbol{\dot E'}}{\mathit{\boldsymbol{K}}_{\rm{d}}}\mathit{\boldsymbol{\dot E}} - \\ \;\;\;\;\;\;\frac{1}{2}\mathit{\boldsymbol{\dot e'}}{\mathit{\boldsymbol{K}}_{\rm{e}}}\mathit{\boldsymbol{\dot e}} = \mathit{\boldsymbol{\dot e'}}\left( {\mathit{\boldsymbol{ \boldsymbol{\varLambda} T'}}\left( {\frac{1}{2}\mathit{\boldsymbol{\dot J}}\left( \mathit{\boldsymbol{\theta }} \right) - \mathit{\boldsymbol{B}}\left( {\mathit{\boldsymbol{\theta }},\mathit{\boldsymbol{\dot \theta }}} \right)} \right) - {\mathit{\boldsymbol{K}}_{\rm{e}}}} \right)\mathit{\boldsymbol{\dot e}} - \\ \;\;\;\;\;\;\mathit{\boldsymbol{\dot E'}}{\mathit{\boldsymbol{K}}_{\rm{d}}}\mathit{\boldsymbol{\dot E}} \le \mathit{\boldsymbol{\dot e'}}\left( {\left\| {\mathit{\boldsymbol{ \boldsymbol{\varLambda} T'}}\left( {\frac{1}{2}\mathit{\boldsymbol{\dot J}}\left( \mathit{\boldsymbol{\theta }} \right) - \mathit{\boldsymbol{B}}\left( {\mathit{\boldsymbol{\theta }},\mathit{\boldsymbol{\dot \theta }}} \right)} \right)} \right\|} \right. - \\ \;\;\;\;\;\;\left. {{\lambda _{\min }}\left\{ {{\mathit{\boldsymbol{K}}_{\rm{e}}}} \right\}} \right)\mathit{\boldsymbol{\dot e}} - \mathit{\boldsymbol{\dot E'}}{\mathit{\boldsymbol{K}}_{\rm{d}}}\mathit{\boldsymbol{\dot E}} \end{array}$ (13)

4 同步控制算法仿真分析

 图 5 PID控制器的跟踪误差 Fig.5 Tracking error control of PID

 图 6 同步控制算法仿真模型 Fig.6 Simulation model of synchronous control algorithm

5 试验及分析

 图 9 叶片振幅变化曲线 Fig.9 Amplitude variation curve of the blade

 图 10 频率改变及受扰后控制曲线 Fig.10 Control curve after frequency change and disturbance
6 结论

(1) 基于电驱动惯性式激振装置，配置叶片加载试验系统参数，构建了兆瓦级风电叶片两点疲劳加载试验系统.振动试验结果表明，激振器之间具有较强的力与能量传递，耦合同步传动是机电耦合的结果，相位差会有趋于零或某个固定角度的趋势.

(2) 风电叶片加载过程中耦合效应影响2台激振器的同步性，因此提出了虚拟主令同步控制算法.以PID算法设计误差补偿器，对同步控制算法的稳定收敛性进行了分析，并数值仿真验证同步控制算法的有效性.本文提出的同步控制算法为一种无模型的耦合控制，实施简单.

(3) 同步控制算法的性能测试结果表明，2台激振器均能快速跟随并保持，耦合作用的固有相位差减小，加载时叶片振幅稳定，误差在设定范围内.