How to plot bode plot with a transfer functions which are calculated?

I am trying to tune a PID controller using Matlab(not Simulink because I am learning/uni coursework).

Problem I need help with

• So, I have a transfer function of a system for which there are phase margin requirement that needs to met
• In order to find the phase advance part of the PID I need to solve a bunch of equations to plot a bode plot using the variables calculated
• https://i.stack.imgur.com/w0LiC.png

I've done this so far

-I tried to replace the tf([num],[den]) with real numbers but that is not feasible as it defeats the purpose of doing this, I want Matlab to calculate the GR and frequency and substitute that into the tf

Answer 1

[Biral Pradhan]

I understand, you want to calculate the transfer function by substituting intermediate variables calculated with GR and frequency. I went through your live code file, and noticed the use of symbolic variables in tf( ) command. This is not supported. Instead, I recommend creating your ratios symbolic as shown below.

PA = ((Kpa*k*ti)*s + Kpa)/(ti*s + 1);
PI = (taui*s + 1)/(taui*s);

Now, in order to create the bode plots, you need numeric transfer functions. Kindly refer to the below link to obtain the required numeric transfer functions from your symbolic expressions.

https://www.mathworks.com/matlabcentral/fileexchange/10816-mimo-toolbox/content/Mimotools/sym2tf.m