Project - Speed Control of a Direct Current (DC) motor

%dc motor parameters

J=0.02; %moment of inertia of rotor

B=0.05; %motor viscous friction

Km=0.1; %back emf

Kt=0.1;%motor torque constant

Ra=2;%resistance of armature

La=0.5; %inductance of armature

%the motor equations

theta_dot_dot= kt*i-B*theta_dot/J;

i_dot=V-Km*theta_dot-Ra*i/La;

%these two equations govern modeling of DC motor

%the reference speed in rpm

S_ref=1500;

%PID parametes after tuning

Kp=1.388

ki=3.173

kd=0.059

% step 1: the ref speed is compared with measured speed

%step 2: the error (ref speed-measured speed) is given to the input of PID controller

%step3: the output of PID controller is given as voltage input to DC motor and output is given as theta_dot

the above figure shows dc motor subsystem

the above figure shows the system model

the above picture is outut before tuning of pid controller

after tuning of PID the grapha and time domain parameters are shown

from above block we can clearly see the peak overshoot is <5% and settling time <2sec as per design specifications asked in the question