Plotting root locus with variables in transfer function

Question

Sean 2012-11-25

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/54753-plotting-root-locus-with-variables-in-transfer-function

Hi. I've been using matlab to plot root loci for my control systems class but I ran into a problem with a recent assignment. This particular problem asks me to plot the root locus of a system in which the transfer function has a variable gain in addition to numeric terms. I just don't have the matlab experience to figure out how to do this on my own with the help command. It would be greatly appreciated if anyone could help me with this. Thank you.

5 个评论
显示 3更早的评论隐藏 3更早的评论

Sean 2012-11-26

So if I have a diagram like this:

Can I factor out the K2 somehow and use that in the rlocus command as the K portion?

Azzi Abdelmalek 2012-11-26

编辑：Azzi Abdelmalek 2012-11-26

在 MATLAB Online 中打开

Yes we can

 g1=tf(1,[1 2]) % your GH(s) transfer function
 g2=tf([1 1],[1 9]); % your second TF (s+1)/(s+9)
 g=g1*g2;
 rlocus(g)

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Azzi Abdelmalek 2012-11-25

2
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/54753-plotting-root-locus-with-variables-in-transfer-function#answer_66475

编辑：Azzi Abdelmalek 2012-11-25

在 MATLAB Online 中打开

If G(p) is your system transfer function, The transfer function of your system in a closed loop with gain k is Gc(p)=G(p)/(1+k.G(p))

%you are looking for closed loop system poles depending on k vakues

G=tf([1 10],[1 2 1]) % your system in open loop
k=0:0.1:100; % k values
rlocus(G,k);  % your poles in closed loop

%or

rlocus(G);

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

Answer 2

Jonathan Epperl 2012-11-26

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/54753-plotting-root-locus-with-variables-in-transfer-function#answer_66593

在 MATLAB Online 中打开

Yeah, like Azzi is hinting: The regular Root Locus shows you where the solutions of the equation 1+k*G(s) = 0 go as you increase k from 0 to infinity.

Assuming you are interested in the transfer function from left to right here, it is

G_H/(1 + k_2*G_H*(s+1)/(s+9) ),

and so the closed-loop poles are precisely the solutions of 1 + k_2*G_H*(s+1)/(s+9) = 0. You will actually find, that this is the case for any transfer function in your loop, e.g. say from T_d to the controller output etc.

Anyway, you might be confused by the way the closed loop is written, probably you expect the controller in the forward path together with G_H, but you can just use the "normal" root locus techniques here, no trickery needed.

rlocus( series(G_H, tf([1 1],[1 9]) ) )