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

Aim:

To build a Simulink model for speed control of direct current (DC) motor.

Objective:

1. In this project, a Simulink model for the DC motor will be first developed per the schematic shown in Figure 1.
2. Use the Proportional, Integral, and Derivative (PID) control design knowledge gained in the training to design, develop and test a controller to maintain a desired speed for the motor.

Solution:

In this project, a Simulink model for the DC motor will be first developed per the schematic.

ω(s) / Vs(s) =Kt/J La s2 + (J Ra + B La) s+(B Ra + kt km)

Dc motor parameter:

% this file contains the design parameters to model dc motor
J = 0.01 ; % moment of inertia kg-m^2
B = 0.1;   % motor viscous constant N-m-s
km = 0.01; % Back emf constant v/rad/s
kt = 0.01; % motor torque constant N-m/amp
Ra = 1 ; % resistance of armature circuit ohm
La = 0.5 ; % inductance of armature circuit in henries

Dc motor plot:

figure(1)
subplot(321);plot(out.time,out.vs);grid;title('Supply Voltage');
subplot(322);plot(out.time,out.w);grid;title('Speed (rad/s) ');
subplot(323);plot(out.time,out.vb);grid;title('Back EMF (V)');
subplot(324);plot(out.time,out.ia);grid;title('Armature Current(A)');
subplot(325);plot(out.time,out.t);grid;title('Torque N-m');

Plot:

PID Design for Speed control of DC motor:

%Parameter for speed control of dc motor PID
J = 0.01 ; % moment of inertia kg-m^2
B = 0.1;   % motor viscous constant N-m-s
km = 0.01; % Back emf constant v/rad/s
kt = 0.01; % motor torque constant N-m/amp
Ra = 1 ; % resistance of armature circuit ohm
La = 0.5 ; % inductance of armature circuit in henrys

%PID design from DC_motor_PID_design.m
%Load the parameters of DC motor
run Dc_motor_PID_parameter.m;

%PD design
A = [-B/J kt/J; -km/La -Ra/La];
B = [0; 1/La];
%pole placement design
f = 1;
wn = 2*pi*f;
zeta = 0.5;
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);
kp = 38.3133;
kd = -2.85;
ki = 10;

figure(4)
subplot(321);plot(out.time,out.vs);grid;title('Supply Voltage');
subplot(322);plot(out.time,out.w);grid;title('Speed (rad/s) ');
subplot(323);plot(out.time,out.vb);grid;title('Back EMF (V)');
subplot(324);plot(out.time,out.ia);grid;title('Armature Current(A)');
subplot(325);plot(out.time,out.t);grid;title('Torque N-m');
subplot(326);plot(out.time,out.u);grid;title('control -u');
 

Simulink model:

Out put:

Control Design Objectives:

Settling time < 2s

Overshoot < 5%

Steady state error < 1%

Initially assuming Ki=10

To reduce the overshoot, the Kd value is increased to -0.9:

To reduce the overshoot further, the Kp value is decreased:

On further decreasing the Ki value to 3, the desired characteristic is obtained.

We can observe that the settling time <2s, Overshoot<5% and Steady state error <1%

Result:

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