MATLAB transfer function information

transfer.m

%% Transfer function information
% This script takes either polynomial coefficients for the numerator and denominator 
% OR zero and pole locations (factorized roots) + gain
% OR characteristic equation (undamped natural frequency and damping ratio)
% of a system with a second order complex pole
% of the transfer function of a system, and then returns:
% 1. A graph of system's impulse response.
% 2. A graph of the system's step response.
% 3. The pole-zero diagram of the system.
% 4. The factorized transfer function printed with LaTeX.
% 5. The transfer function printed with LaTeX.
% 6. The partial fraction decomposition of the transfer function printed
% with LaTeX.
% 7. The time-domain equation (impulse response) of the system printed with
% LaTeX.
% 8. Bode diagrams.

%% Configuration Parameters
mode = 2; % 0 = polynomial coefficients, 1 = factorized roots, 2 = complex conjugate pair
time_multiplier = 2; % Increase to make the impulse response show a longer timespan
digits(6);   % maximum number of digits for the program to disply

% Polynomial coefficients (i.e. [1, 2, 0] will yield s^2 + 2s; [1 0 0 0] will yield s^3)
num = [10 -10 0];    % Enter coefficients for TF zeros here
den = [1 4 17/4];    % Enter coefficients for TF poles here

% Factorized roots (i.e. [1 0] will yield (s-1)s)
zeros = [1 0]';                    % Enter roots of TF zeros 
poles = [-2+0.5j -2-0.5j]';        % Enter roots of TF poles 
gain  = 10;                        % Enter DC gain 

% Complex conjugate pair char. equation (omega^2/(s^2 + 2*zeta*omega*s + omega^2))
omega = 0.4;                    
zeta = 0.2;

%% Program
syms s
if mode == 0
    zeros = roots(num);
    poles = roots(den);
elseif mode == 1
    [num, den] = zp2tf(zeros, poles, gain);
else % mode == 2
    num = [omega^2];
    den = [1 2*zeta*omega omega^2];
end
H = tf(num,den);
num_sym = poly2sym(num,s);
den_sym = poly2sym(den,s);
h = ilaplace(num_sym/den_sym);
t=0:0.1:32*time_multiplier;

factored_num = '';
for n=factor(num_sym,"FactorMode","complex")
    factored_num = strcat(factored_num,'(',string(n),')');
end

factored_den = '';
for d=factor(den_sym,"FactorMode","complex")
    factored_den = strcat(factored_den,'(',string(d),')');
end

factored = strcat('$H(s)=','\frac{', factored_num, '}{', factored_den, '}$');

figure(1)
clf();
subplot(2,3,1)
hold on
impulse(H, t);
grid on
hold off

subplot(2,3,4)
hold on
step(H, t);
grid on
hold off

subplot(2,3,3)
hold on
zplane(num,den)
grid on
hold off

subplot(2,3,2)
hold on
title("Transfer Function")
text(-0.25, 0.75, factored , 'Interpreter', 'latex', 'FontSize', 16)
text(-0.25, 0.5, ['= $' latex(num_sym/den_sym) '$ = $' latex(partfrac(num_sym/den_sym, s)) '$'], 'Interpreter', 'latex', 'FontSize', 22);
axis off;
hold off

subplot(2,3,5)
hold on
title("Impulse Response")
text(-0.25, 0.5, ['h(t) = $' latex(h) '$'], 'Interpreter', 'latex', 'FontSize', 16);
axis off;
hold off

subplot(2,3,6)
hold on
bode(H)
grid on
hold off