control systemcontrol theory
I have the following block diagram, and I want to find the transfer function \$\frac{\hat{\theta}}{\hat{T}}\$. I am not sure how to do this, I've got the rules of connection in a series or parallel, but I am stuck.
I started with the entrance of \$T\$ but got stuck, can someone please provide me some help?
OK, I got it. To obtain the necessary transfer function in Evan's form, one has to assume \$ \phi_c = 0 \$. Then, the block diagram in question can be converted into:
So \$ P(s) = \Large \frac{p}{\alpha} = \frac{G(s)H(s)}{1 + \frac{k_p}{s} G(s)H(s)}\$.
A not-at-all elegant way to do it is:
zeta=[...]; %your zeta values
wn = ... % calculate your wn values according to your zeta values
figure;
hold('on');
for idx = 1:length(zeta)
% sys = tf([wn(idx)],[1 2*wn(idx)*zeta(idx) wn(idx)^2]); %system's transfer function
% EDIT : numerator corrected
sys = tf([wn(idx)^2],[1 2*wn(idx)*zeta(idx) wn(idx)^2]); %system's transfer function
step(alpharef*sys);
end
Best Answer
This kind of block diagram doesn't have anything to do with the rules for parallel and series connections of impedances. It just represents a bunch of complex algebraic equations. Each of the rectangular boxes just produces an output variable by multiplying its input by a constant, given by the text in the box.
For example,
\$ V_m = \gamma(I_{ref}-I_m)\$ comes from the first box at the upper left.
\$ I_m = \dfrac{1}{Ls+R}(V_m - E_{emf})\$ comes from the next box to the right.
You can keep making equations like this for each variable in the diagram. At that point you should have a complete set of equations that you can reduce to get a relationship between \$\Omega\$ and T.
To do this for a complex system like yours, you may want to polish up your skills in a symbolic math package like Maple or Mathematica.