Problem with defining a transfer function for Bode plot in MATLAB

Question

I am trying to tune a PID controller using Matlab(not Simulink because I am learning/uni coursework). 1. Summarize the problem:

• 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

2.Describe what I've tried

• 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

Problem

Full_Code: https://drive.google.com/file/d/1sWUnvvye_RBXGL8-nWq___3F5UDmDOoG/view?usp=sharing

Minimum reproducible code example:

clearvars;clc;clearAllMemoizedCaches;clear

syms s w 

%--------------TF of the aircraft

G(s)= (160*(s+2.5)*(s+0.7))/((s^2+5*s+40)*(s^2+0.03*s+0.06));

k= 8;  % selected k value range 4<k<8

Max_PA=asind((k-1)/(k+1)); % computes max phase advance

Centre_dB= 20*log10(sqrt(k)); % computing centre gain in dB

Poi= -120-Max_PA  % looking for Point of interest(Poi)

tf_int= subs(G(s),1j*w); %intermediate transfer function

eqn= atan2d(imag(tf_int),real(tf_int))==Poi; % solve for w at Poi


% computing crossover freq(wc)

wc= vpasolve(eqn,w); % find exactly the wc at Poi

GR=20*log10(abs(subs(tf_int,w,wc))); % find the gain at at wc

Kpa= 10^((GR-Centre_dB)/20);

ti= 1/(sqrt(k)*wc); % computing Kpa and ti

num1= [Kpa*k*ti,Kpa];

den2= [ti,1];

PA= tf(num1,den2) %PA tf defined

Answer 1

Yo are trying to input non-numerical (symbolic numers) values into tf , which only accepts numerical arrays. You can convert them to that with double()

PA= tf(double(num1),double(den2)) %PA tf defined