function/solve for variable that is constantly changing/ Question is explained in detail at the end of code

clear all
close all
poles = [-1,-2,-10];
a = poly(poles);
gs = tf(1,a)
% ess (step input) = 0 ; z = 0.147
    
% Finding w_n associated with damping from plot
%% STEP 1 Transient characteristics
z = 0.174;
wn = [0,10];
figure(1)  
rlocus(gs)
sgrid(z,wn) % sgrid to find the point where z is at RL

w_n = 3.98;   % natural frequency from plot

%% Step 2 pole locations
[DPLp,DPLn,re,ima] = Remar_Sebastian_DPL (z , w_n);


%% Step 3 - plotting desire poles
figure(2)
rlocus(gs)
hold on                                    % Keep using the same fig
plot(re,ima/i,'ko','Markersize',5)         % DPL with black marker
plot(re,-1*ima/i,'ko','Markersize',5)      % DPL with black marker

%% Step 4 - plotting 
% p_c = 0;  % Compensator 
z = 0;

%% Step 5 - Lemma #2
% Using a function in this hw now. 
[p_c , theta_pc] = Remar_Sebastian_Lemma2 (ima , re , poles,z)

%% Step #6 Lemma #1
num = [p_c];                                              % Tf numerator of compensator
den = [z];                                                % Tf denominator of compensator

%%%%%%%%%%%%%%%%%%%%%% Here is my question %%%%%%%%%%%%%%%%%%%%
gc = tf(poly(num) , poly(den));                            % Tf compensator
glemma = (1 / (gc*gs))                                      % Transfer function to find K
syms s 
s = DPLp;                                                   % s is equal to positive DPL
k =  abs( s^4 + 13 s^3 + 32 s^2 + 20 s / (s + 0.006991));  % Finding k 

My question is, how can I create a function that does this last part. K is equal to the transfer function glemma,

now I am just displaying glemma in the command window and then writing the transfer function manually. How can I create a function

that takes glemma, DPL, as an input and somehow plug in DLPp into it and solve for k.

I want to achieve this because I am designing PID controllers and I am constantly changing my transfer function, it takes time

to display the glemma and copy paste the num/den and then run program again. I was able to recreate function for everything else

but this step.

thanks!

[SL: moved the actual question out of the code section]

Answer 1

[Maadhav Akula]

Hi Sebastian,

I believe you want to substitute the value of DPLp in place of s in your Transfer Function glemma, right? For that you can use the following function evalfr, or you can also utilise freqresp.

Hope this helps!