Our DC MOTOR SYSTEM:
Motor torque (Km is Armure Constant) T(t) = kmi(t) EMK Force (kb is Emf constant) Vemf=ktw(t) Friction against motor movement Tf(s) = kf*w(t)
Jdiff(w)=Kmi(t)-kfw(t) diff(w)=km/ji(t)-kf/j*w(t)
Vo =Ldiff(i(t))-Ri(t)+kbw(t) diff(i(t) =-R/Li(t)-kb/Lw(t)+1/LVa(t)
then our system will be
PID result of our system:
You can see our matlab code in DcMotorModeling.m