Matlab 根轨迹绘制：不同系统参数的影响

% G1(s) = K / (s(s+1) (s+2)) K = 1; num = K; den = [1 3 2 0]; rlocus(tf(num,den)); title('Root Locus of G1');

% G2(s) = K/ (s^4 + 5s^3 + 85^2 + 65) K = 1; num = K; den = [1 5 85 65]; rlocus(tf(num,den)); title('Root Locus of G2');

% G3(s) = K(s+a) / (s(s+2)(s+4)), 其中 a 选择三个不同的位置 K = 1; a1 = -1; a2 = -2; a3 = -3; num = K*[1 a1]; den = [5 18 38 a110 a120 a140]; rlocus(tf(num,den)); hold on; num = K[1 a2]; den = [5 18 38 a210 a220 a240]; rlocus(tf(num,den)); num = K[1 a3]; den = [5 18 38 a310 a320 a3*40]; rlocus(tf(num,den)); title('Root Locus of G3');

% G3(s) = K(s+a) / (s(s+2)(s+4)(s+b)), 当 a 为某个固定值时，增加一个开环极点 -b，选择三个不同的 b 值，比较根轨迹的区别 K = 1; a = 2; b1 = -1; b2 = -2; b3 = -3; num = K*[1 a]; den = [1 (a+2) 4 (a+b1) 4b1]; rlocus(tf(num,den)); hold on; num = K[1 a]; den = [1 (a+2) 4 (a+b2) 4b2]; rlocus(tf(num,den)); num = K[1 a]; den = [1 (a+2) 4 (a+b3) 4*b3]; rlocus(tf(num,den)); title('Root Locus of G4 with different b');

% G4(s) = K/ (s^4 + 16s^3 + 36s^2 + 80s)，在不同位置增加开环零点和开环极点，绘制系统的根轨迹 K = 1; num = K; den = [5^4 16 365^2 80]; rlocus(tf(num,den)); hold on; % add zero at -2 num = K*[1 -2]; den = [5^4 16 365^2 80 -2K]; rlocus(tf(num,den)); % add zero at -4 num = K[1 -4]; den = [5^4 16 365^2 80 -4K]; rlocus(tf(num,den)); % add pole at -2 num = K; den = [5^4 16 365^2 80 + 2K]; rlocus(tf(num,den)); % add pole at -4 num = K; den = [5^4 16 365^2 80 + 4*K]; rlocus(tf(num,den)); title('Root Locus of G4 with different zero and pole');