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

Project :-

mathematical equations solution for model :-

speed control equation for DC Motor :-

w/vs = Kt/[J*La*s^2 + (J*Ra+B*La)s+(B*Ra+Kb*Kt)]

w/vs = Kt/[(La*s+Ra)(J*s+B)+Kb*Kt]

vs*Kt = w[(La*s+Ra)(J*s+B)+Kb*Kt]

vs*Kt = w(La*s+Ra)(J*s+B)+w*Kb*Kt

vs*Kt/(La*s+Ra)(J*s+B) = w[1+(Kb*Kt)/(L*s+Ra)(J*s+B)]

vs*Kt/(La*s+Ra)(J*s+B) - w(Kb*Kt)/(L*s+Ra)(J*s+B)] = w

(vs*Kt - Kb*Kt*w)/[(La*s+Ra)(J*s+B)] = w

[Kt(vs - Kb*w)]/[(La*s+Ra)(J*s+B)] = w

(vs - Kb*w)[1/(La*s+Ra)]*Kt*[1/(J*s+B)] = w

from above equation we can simulate the speed control of DC motor

here the constants

% This file contains the design parameters to model a DC motor
J = 0.1; % moment of inertia of the rotor in kg-m^2
B = 0.5; % motor vicous friction constant in N-ms
Kb = 0.1; % Back emf constant in V/rad/s
Kt = 0.1; % motor torque constant in N-m/Ampere
Ra = 2; % Armature resistance in ohm
La = 0.5; % Armature inductance in henry

vs = 440 v % Supply voltage

Simulation Model :-

PLOT :-