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

Simulink model for the DC motor developed per the schematic.

Using the Proportional, Integral, and Derivative (PID) control design knowledge gained in the training to design, developed and tested a controller to maintain a desired speed for the motor.

Figure 1

In Armature Circuit In Field Circuit

Vs= Supply Voltage i_f=Field Current

i_a=Armature Current Lf=Field inductance

Vb=Back EMF V_f =Field excitation

Ra=Armature Voltage

La= Armature Inductance

Applying Kirchhoff’s Voltage Law.

Vs = Ra.ia + La dia/dt + Vb

Back EMF

Vb = Km dθ/dt

t = kti

km=Back EMF

Kt=Torque const.

Angular Velocity=ωθ

Open loop transfer function of motor with speed (ω) & velocity (Vs)

ωs/Vs = kt/JLas²+(J Ra + B La)s + (B Ra + Kt Km)

J = moment of the inertia of the rotor in kg-m^2

B = Motor viscous friction constant in N-m-s

Km = Back EMF in v/rad/s

Kt = Motor Tprque constant in N-m/amp

Ra = Resitance of armature ckt in amps

La = Inductance of the armature ckt in henries

PID CONTROL FOR DC MOTOR

PID Controller

A Proportional Integral Derivative Controller is also called three term controller is loop mechanism in a control manner with feedback.

It is used in industries and in area where it requiring continuously modulated control.

U(t) = Kpe(t) + Ki ʃ e(t)dt + Kd de(t)/dt

U(s) = (K_p + K_i/s + K_Ds) E(s)

U(s)/E(s) = K_P + K_I + K_Ds

Matlab Code

% This file contains the desgin parameters to Model DC Motor

fn=1;

wn=2*pi*fn;

zeta=0.5;

J =0.01; % moment of the inertia of the rotor in kg-m^2

B = 0.1; % Motor viscous friction constant in N-m-s

Km = 0.01; % Back EMF in v/rad/s

Kt = 0.01; % Motor Tprque constant in N-m/amp

Ra = 1.0; % Resitance of armature ckt in amps

La = 0.5; % Inductance of the armature ckt in henries

A=[-B/J Kt/J; -Km/La -Ra/La];

Bm=[0;1/La];

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

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

p =[p1;p2];

K=place(A,Bm,p);

Kp=K(1);

Kd=-0.86;

Ki=12.3;

Simulink Model

Graph