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

Modelling of a DC motor

A system is stable if every bounded input yields a bounded output

The location of the poles decides the stability of the system.

Matlab code for the model for the DC motor

clear all

clc

J = 0.01;%Inertia

b = 0.1;%friction

Vb = 0.01; %back emf

Ra = 1;%resistance

La = 0.5; % inductance

Kt = 0.01; % torque constant

% Design of a PID controller

A = [-b/J Kt/J; Vb/La -Ra/La];

B = [0; 1/La]

wn = 6.2832;

fn = 1;

zeta = 1.2; % under damped system.

p1 = -zeta*wn + wn*sqrt(zeta^2-1);

p2 = -zeta*wn - wn*sqrt(zeta^2-1);

P = [p1;p2];

k = place(A,B,P)

kp = k(1)

kd = k(2);

screenshot of matlab script

Simulink model

scope for the model

Here i have used proportional gain,integral gain and derivative gain to control design objectives for settling time, overshoot, and steady-state error .