位置式PID算法 { e r r o r ( k ) = r i n ( k ) − y o u t ( k ) x ( 1 ) = e r r o r ( k ) x ( 2 ) = x ( 2 ) + T s ∗ e r r o r ( k ) x ( 3 ) = e r r o r ( k ) − e r r o r ( k − 1 ) p i d = [ K p   K i   K d ] u ( k ) = p i d ∗ x \begin{cases}error(k)=rin(k)-yout(k) \\x(1)=error(k) \\x(2)=x(2)+Ts*error(k)\\x(3)=error(k)-error(k-1)\\pid = [K_p \:K_i\:K_d]\\u(k)=pid*x\end{cases} ⎩⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎧​error(k)=rin(k)−yout(k)x(1)=error(k)x(2)=x(2)+Ts∗error(k)x(3)=error(k)−error(k−1)pid=[Kp​Ki​Kd​]u(k)=pid∗x​ u ( k ) u(k) u(k)为控制量相当于状态量x与pid参数的线性组合，为了动态调整pid参数构建一个单神经元网络，性能指标函数取 J = ∑ ( r i n ( k ) − y o u t ( k ) ) 2 / 2 J=\sum(rin(k)-yout(k))^2/2 J=∑(rin(k)−yout(k))2/2;根据梯度下降法调整pid参数，即 Δ K p = − η ∂ J ∂ K p \Delta K_p=-\eta\frac{\partial J}{\partial K_p} ΔKp​=−η∂Kp​∂J​,这个怎么求偏导？ Δ K p = − η ∂ J ∂ K p = − η ∂ J ∂ y o u t ∂ y o u t ∂ Δ u ∂ Δ u ∂ K p = η . e o r r o r ( k ) . x ( 1 ) . ∂ y o u t ∂ Δ u \Delta K_p=-\eta\frac{\partial J}{\partial K_p}=-\eta\frac{\partial J}{\partial yout}\frac{\partial yout}{\partial \Delta u}\frac{\partial \Delta u}{\partial K_p}=\eta .eorror(k).x(1).\frac{\partial yout}{\partial \Delta u} ΔKp​=−η∂Kp​∂J​=−η∂yout∂J​∂Δu∂yout​∂Kp​∂Δu​=η.eorror(k).x(1).∂Δu∂yout​,利用RBF网络的逼近能力，识别系统的Jacobian阵，即 ∂ y o u t ∂ Δ u \frac{\partial yout}{\partial \Delta u} ∂Δu∂yout​。