حل تمرین:

Dorf book page 284 (13th Ed)-(figure AP4.4)

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%DC Motor System with feedback

clc; clear; close all;

% Define system parameters
Ra=1; % Armature resistance
La=1; % Armature inductance
J=2; % Moment of inertia

K=1; %power amplifier constant (You must find value of K from Root Locus technique(sisotool))

Km=10; % Motor constant
Kb=0.1; % Back EMF constant
Kt=1.2; % Sensor constant

% Define the transfer functions for different parts of the system
num_G1=[1]; den_G1=[1 0]; G1=tf(num_G1,den_G1); % Transfer function for the Integrator
num_G2=[K]; den_G2=[1]; G2=tf(num_G2,den_G2); % Transfer function for Power Amplifier
G3=series(G1,G2); %Combined transfer function for the integrator and power amplifier

num_G4=[Km]; den_G4=[Ra J]; G4=tf(num_G4,den_G4); % Transfer function for the motor
num_G5=[Kb]; den_G5=[1]; G5=tf(num_G5,den_G5); % Transfer function for the back EMF
G6=feedback(G4,G5); %Feedback loop combining the motor and back EMF

G7=series(G3,G6);%Overall system transfer function (integrator, power amplifier, motor, and back EMF)

num_G8=[Kt]; den_G8=[1]; G8=tf(num_G8,den_G8); % Transfer function for Sensor
G9=feedback(G7,G8) %Feedback loop combining the overall system and the sensor

%sisotool(G9)

% Example: Step input for V(s)
% Define the time range for the simulation
t0=0 ; tfinal=10; n=1000; t=linspace(t0,tfinal,n);

V_step = 10; % Set the desired control voltage

% Simulate the response
[y, t] = step(G9 * V_step, t);

% Plot the motor speed
figure;
plot(t, y);
xlabel('Time (seconds)');
ylabel('Motor Speed (w)');
title('Motor Speed Response');