getfod.m

Pid自整定程序 输入 num: 控制对象传函分子向量 den 控制对象传函分母向量 time：仿真时间 interval：仿真时间间隔

%==========================================================
%求解模型的拟合参数
%输入：传递函数控制对象G
%输出：被控广义对象（G(s) = k*exp(-sL)/(1+sT)）参数K L T
%采用的算法; 拟Newton算法
%=========================================================
function [K,L,T] = getfod(G)
K = dcgain( G );
if nargin == 1
    [Kc,Pm,wc,wcp] = margin(G);
    ikey = 0;
    L = 1.6*pi/(3*wc);
    T = 0.5*Kc*K*L;
    if finite(Kc),
        x0=[L;T];
        while ikey == 0
             ww1 = wc*x0(1); ww2 = wc*x0(2);
             FF = [K*Kc*(cos(ww1) - ww2*sin(ww1)) + 1 + ww2^2;
                  sin(ww1) + ww2*cos(ww1)];
              J = [-K*Kc*wc*sin(ww1) - K*Kc*wc*ww2*cos(ww1),...
                  -K*Kc*wc*sin(ww1) + 2*wc*ww2;
                  wc*cos(ww1) - wc*ww2*sin(ww1),wc*cos(ww1)];
              x1 = x0 -inv(J)*FF;
              if norm(x1-x0) < 1e-8,
                  ikey = 1;
              else
                  x0 = x1;
              end,
         end,
    elseif nargin == 2
        [n1,d1] = tfderv(G.num{1}, G.den{1});
        [n2,d2] =  tfderv(Gn1,d1);
        K1 = dcgain(n1,d1);
        K2 = dcgain(n2,d2);
        Tar = -K1/K;
        T = sqrt(K2/K - Tar^2);
        L = Tar - T;
    end
end

function [e,f] = tfderv(b,a)
f = conv(a,a);
e1 = conv( (length(b)-1 : -1 : 1).*b(1:legth(b)-1),a );
e2 = conv( (length(a)-1 : -1 : 1).*a(1:legth(a)-1),b );
maxL = max(length(e1),length(e2));
e = [ zeros(1,maxL - length(e1)) e1] - [zeros(1,maxL - length(e2)) e2];
end
end