analytical.m

Ra = 11.4;
La = 0.1214;
Jm = 0.02215;
Bm = 0.002953;
Kt = 1.28;
Ke = 0.0045;

% Define the transfer function
sys = tf(Kt / (La * Jm), [1, (Ra * Jm + Bm * La) / (La * Jm), (Kt * Ke + Ra * Bm + Kt) / (La * Jm)]);

% Plot the root locus with increased line width
figure;
rlocus(sys);
h = findall(gca, 'type', 'line');
set(h, 'linewidth', 2);

% Compute and plot the poles
ch_eq_coefs = [1, (Ra * Jm + Bm * La) / (La * Jm), (Kt * Ke + Ra * Bm + Kt) / (La * Jm)];
poles = roots(ch_eq_coefs);
T = 1 / max(abs(poles));
ts_2 = 4 * T;
ts_5 = 3 * T;

figure;
plot(real(poles), imag(poles), 'rx', 'LineWidth', 2, 'MarkerSize', 20);
grid on;
xlabel('Real');
ylabel('Imaginary');
title('Poles');

% Ensure all grid lines and axis lines are of width 2
set(gca, 'LineWidth', 2);
set(findall(gcf, 'Type', 'Line'), 'LineWidth', 2);

% Additional calculations
result1 = (Kt * Ke + Ra * Bm) / Kt;
result2 = Kt / (Kt * (Ke + 1) + Ra * Bm);

% Display results
disp('Results:');
disp(['Result 1: ', num2str(result1)]);
disp(['Result 2: ', num2str(result2)]);

tf_eq_bb = [Kt / (La * Jm)];
ch_eq_coefs2 = [1, (Ra * Jm + Bm * La) / (La * Jm), (Kt * Ke + Ra * Bm) / (La * Jm)];

%% Lead Compensator

close all

wd = 80;
z_lead = -90;
p1 = poles(1);
p2 = poles(2);

p_lead = p1 - (wd/(   tan(   -atan((p2-p1)/wd) + atan(wd/(p1 - z_lead))  )));

lead_tf = tf([1, -z_lead], [1, -p_lead]);  % Transfer function: (s - z)/(s - p)

% Combine the existing transfer function with the new zero and pole
lead_sys = series(sys, lead_tf);

% Plot the root locus of the new system
figure;
rlocus(lead_sys);
title('Root Locus Plot for Lead Compensation');
grid on;
atan((p2-p1)/wd) + atan(wd/(p1 - p_lead)) - atan(wd/(p1 - z_lead))


%% Lag Compensator

close all

p_lag = -100;
z_lag = p1 + p_lag - p2;

lag_tf = tf([1, -z_lag], [1, -p_lag]);  % Transfer function: (s - z)/(s - p)

% Combine the existing transfer function with the new zero and pole
lag_sys = series(sys, lag_tf);

% Plot the root locus of the new system with lag compensator
figure;
rlocus(lag_sys);
title('Root Locus Plot for Lag Compensation');
grid on;

%% Lead Lag Compensator

z_lead = -90;
p_lead = -190;
z_lag = -182.9482;
p_lag = -150;

lead_tf = tf([1, -z_lead], [1, -p_lead]);  % Transfer function: (s - z)/(s - p)
lag_tf  = tf([1, -z_lag],  [1, -p_lag]);   % Transfer function: (s - z)/(s - p)

lead_lag_sys = series(sys, lag_tf);
lead_lag_sys = series(lead_lag_sys, lead_tf);

% Plot the root locus of the new system with lead-lag compensator
figure;
rlocus(lead_lag_sys);
title('Root Locus Plot for Lead-Lag Compensation');
grid on;