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本文中结合模糊控制与神经网络,设计的模糊神经网络PID控制器原理图如图 2所示[11-12]。在图 2中,系统处于第k个时刻,xin(k)为系统的输入、yout(k)为输出信号,位置误差e(k)和误差变化率ec(k)作为模糊神经网络控制器的输入变量,而u(k)作为该控制器的输出量。该控制器的特点是:利用模糊神经网络的模糊推理与自主学习能力,自适应整定PID控制器的3个参量Kp,Ki和Kd,直至输出PID控制器的最优控制参量[13-14]。
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模糊神经网络结构主要由输入层、隶属度函数生成层、模糊推理层、归一化层和输出层五部分组成[15-16],其模型如图 3所示。
(1) 输入层:由2个神经元作为输入量,且输入量x1,x2分别为系统的位置误差e(k)和误差变化率ec(k),该层通过函数f1(x)=x直接把输入量传至下一层,其输出为:
$ \left\{ \begin{align} &{{I}_{i}}\left( 1 \right)={{x}_{i}} \\ &{{O}_{i}}\left( 1 \right)={{f}_{i}}\left( {{I}_{i}}\left( 1 \right) \right)={{I}_{i}}\left( 1 \right)={{x}_{i}} \\ \end{align} \right. $
(1) 式中,Ii(1)和Oi(1)分别为第1层的第i个神经元的输入量与输出量。
(2) 隶属度函数生成层:该层将两个输入函数x1与x2均分成7个模糊集,即{Nb,Nm,Ns,Z,Ps,Pm,Pb},分别代表{负大,负中,负小,零,正小,正中,正大}。第i个输入量的第j个模糊集(i=1, 2;j=1, 2,…, 7)记为Aij(xi),将隶属度函数选为高斯函数,且作用函数为f2(x)=x,则可得到隶属度函数Aij(xi)的值为:
$ \left\{ \begin{align} &{{I}_{ij}}\left( 2 \right)={{A}_{ij}}({{x}_{i}})=\exp \left[ -\frac{{{O}_{i}}\left( 1 \right)-{{a}_{ij}}}{{{b}_{ij}}^{2}} \right] \\ &{{O}_{ij}}\left( 2 \right)={{f}_{2}}({{I}_{ij}}\left( 2 \right))={{I}_{ij}}\left( 2 \right)=\exp \left[ -\frac{{{O}_{i}}\left( 1 \right)-{{a}_{ij}}}{{{b}_{ij}}^{2}} \right] \\ &\left( i=1, 2;j=1, 2, \cdots , 7 \right) \\ \end{align} \right., $
(2) 式中,Iij(2)和Oij(2)分别表示第2层的第i个神经元、第j个模糊集的输入量与输出量,aij与bij分别为第i个输入量和第j个隶属度函数对应的均值和标准差。
(3) 模糊推理层:该层借助与第2层的连接对模糊规则进行匹配,实现每个节点间的模糊推理运算,得到每条规则的适应度。且该层的作用函数为f3(x)=x,则:
$ \left\{ \begin{align} &{{I}_{p}}\left( 3 \right)={{A}_{1m}}\cdot {{A}_{2n}} \\ &{{O}_{p}}\left( 3 \right)={{f}_{3}}\left( {{I}_{p}}\left( 3 \right) \right)={{A}_{1m}}\cdot {{A}_{2n}} ~~~,\\ &\ \ \ (m, n=1, 2, \cdots , 7;p=1, 2, \cdots , 49) \\ \end{align} \right. $
(3) 式中,Ip(3)和Op(3)分别为第3层的第p个神经元的输入量与输出量,A1m为第1个输入量的第m个模糊集,A2n为第2个输入量的第n个模糊集。
(4) 归一化层:该层实现对模糊推理层的输出值进行归一化计算,则:
$ {{O}_{p}}\left( 4 \right)=\frac{{{O}_{p}}\left( 3 \right)}{\sum\limits_{p=1}^{49}{{{O}_{p}}\left( 3 \right)}} $
(4) 式中,Op(4)为第4层的第p个神经元的输出量。
(5) 输出层:该层进行反模糊化计算,得到PID控制器的最优控制参量,其输出值为:
$ {{O}_{k}}\left( 5 \right)=\sum\limits_{p=1}^{49}{{{\omega }_{kp}}}{{O}_{p}}\left( 4 \right), (k=1, 2, 3) $
(5) 式中,Ok(5)为第5层的第k个控制参量的输出值,ωkp是归一化层与输出层之间的可调权系数。
本文中PID控制器采用增量式,则其控制输出为:
$ \left\{ \begin{align} &\Delta u\text{ }\left( k \right)={{K}_{\text{p}}}{{x}_{\text{c}}}\left( 1 \right)+{{K}_{\text{i}}}{{x}_{\text{c}}}\left( 2 \right)+{{K}_{\text{d}}}{{x}_{\text{c}}}(3) \\ &u\text{ }\left( k \right)=u\text{ }\left( k-1 \right)+\Delta u\text{ }\left( k \right) \\ &{{x}_{\text{c}}}(1)=e\text{ }\left( k \right) \\ &{{x}_{\text{c}}}(2)=e\text{ }\left( k \right)-e\text{ }\left( k-1 \right) \\ &{{x}_{\text{c}}}\left( 3 \right)=e\text{ }\left( k \right)-2e\text{ }\left( k-1 \right)+e\text{ }(k-2) \\ \end{align} \right. $
(6) 式中,e(k)为系统期望值与实际值的差值,Kp=O1(5),Ki=O2(5),Kd=O3(5)。
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模糊神经网络学习算法的参量主要是将权值、隶属度函数的均值aij与隶属度函数的标准差bij连接起来。若系统处于第k个时刻,xin(k)为系统的期望输出值,yout(k)为实际输出值,则可定义误差函数为:
$ E\left( k \right)=\frac{1}{2}{{[{{x}_{\text{in}}}(k)-{{y}_{\text{out}}}(k)]}^{2}} $
(7) 所以,模糊神经网络的最优权值与参量的表达式为:
$ \begin{gathered} \left\{ \begin{gathered} {a_{ij}}\left( {{k_0} + 1} \right) = {a_{ij}}\left( {{k_0}} \right) - \eta \frac{{\partial E}}{{\partial {a_{ij}}}} + \hfill \\ \;\;\;\alpha \left[ {{a_{ij}}\left( {{k_0}} \right) - {a_{ij}}\left( {{k_0} - 1} \right)} \right] \hfill \\ {b_{ij}}\left( {{k_0} + 1} \right) = {b_{ij}}\left( {{k_0}} \right) - \eta \frac{{\partial E}}{{\partial {b_{ij}}}} + \hfill \\ \;\;\alpha \left[ {{b_{ij}}\left( {{k_0}} \right) - {b_{ij}}\left( {{k_0} - 1} \right)} \right] \hfill \\ {\omega _{kp}}\left( {{k_0} + 1} \right) = {\omega _{kp}}\left( {{k_0}} \right) - \eta \frac{{\partial E}}{{\partial {\omega _{kp}}}} + \hfill \\ \;\;\alpha \left[ {{\omega _{kp}}\left( {{k_0}} \right) - {\omega _{kp}}\left( {{k_0} - 1} \right)} \right], \hfill \\ \end{gathered} \right. \hfill \\ (i = 1,2;j = 1,2, \cdots ,7; \hfill \\ {k_0} = 1,2,3;p = 1,2, \cdots ,49) \hfill \\ \end{gathered} $
(8) 式中,k0为神经网络迭代步数;η为学习速率;α为网络学习动量因子。
机载激光通信的模糊神经网络PID视轴稳定控制
PID control of optical axis stabilization for airborne laser communication based on fuzzy neural network
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摘要: 机载激光通信的视轴稳定是建立激光通信链路的前提。为了有效地克服载体扰动与参量改变对粗跟踪系统视轴稳定的不利影响,设计了一种基于模糊神经网络的比例-积分-微分(PID)控制方法。该方法结合模糊理论的非线性控制能力与神经网络的自主学习能力,实现了对PID参量的实时在线调整。结果表明,与传统PID控制方法相比,模糊神经网络PID控制方法提高了系统的动态响应速度,减小了系统超调量,当载体受到扰动与参量改变时,具有较强的自适应性和鲁棒性。
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关键词:
- 光通信 /
- 机载激光通信 /
- 模糊神经网络 /
- 视轴稳定 /
- 比例-积分-微分控制
Abstract: For airborne laser communication, optical axis stabilization is the premise to establish laser communication link. In order to overcome the negative effect of carrier disturbance and parameters change on optical axis stabilization of coarse tracking system effectively, a proportion-integral-derivative(PID) control algorithm based on fuzzy neural network was designed. The algorithm combines the nonlinear controllability of fuzzy theory with self-learning ability of the neural network, and can achieve the real-time online adjustment of PID parameters. The simulation experiment results show that compared with the traditional PID control method, the fuzzy neural network PID control method can improve dynamic response speed and reduce the overshoot of a system and that the system has strong adaptability and robustness when the carrier is disturbed and the parameters change. -
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