Project - Speed Control of a Direct Current (DC) motor
In this project, a Simulink model for the DC motor will be first developed per the schematic shown in Figure 1.
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.
Ans.
Mathematical modeling from the first principles
J = Moment of inertia of rotor
Bv = Damping constant
Ra = Armature Resistance
La = Armature Inductance
Vb = Back emf constant
Kt = Motor torque constant
vs = supply voltage
Motor torque T =
Vs = supply voltage
Motor torque T = kt *1
Back EMF Vb = Kb*w = Kb * d(theta)/dt
Modeling an Electrical Engineering system
As per kirchoff's
closed loop law,
La * d(I)/dt + Ra*l = Vs - Kb *d(theta)/dt.......(a)
As per newton's law
dA2(theta)/dta2 + Bv * d(theta)/dt
= Kt*l.......(b)
\(s) = V(s) - Kb *s*theta(s) / La*s +Ra......... (c)
w(s) = Kt *I(s) /
j*S + BV. .......(d)
substituting I(s) value in
equation (d) and simplyfying the
same
w(s)/v(s) = kt /
[(La*s+Ra) (J*s+Bv)+Kt*Kb)] is
transfer function for the DC Motor.
It can be modelled with more
detail like taking the flux linkage
factor, friction at bearings etc. but
this is basic transfer function to
familiarize with the model here.
Simulink based modeling
Key Highlights:
Mathematical modeling from the first principles
Modeling an Electrical Engineering system
Simulink based modeling
Control law design and test
Stability of a dynamic system
Deliverables:
Matlab script to define modeling and control design parameters
Simulink model to simulate and verify the design
Your Answers
e Simulink based modeling....
script file
%DC Motor Parameters
J=0.01; % unit :- kg*mA2, Name =
Rotor motor of inertia
Bv=0.1; % unit :- Nms, Name = Motor
viscous friction constant
Kb=0.01; % unit :- V/radians/s,
Name = Back EMF Constant
Kt=0.01; % unit :- Nm/Ampere,
Name = Motor torque constant
Ra=1; %unit :- ohm, Name =
Armature resistance
La=0.5; %unit = Henry, Name =
Armature Inductance
A = [-Bv/J Kt/J;-Kb/La -Ra/Lal;
B = [0;1/La];
question
In this project, a Simulink model for
the DC motor will be first developed
per the schematic shown in Figure
1.
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.
Key Highlights:
Mathematical modeling from
the first principles
Kp=K(2);
Kd=K(1);
Ki=1400;
%non linearized controlling method
%Kp = wnA2; % Kp value will be as
per praportionate gain
%Kd = 2*zeta*wn; % Kd value will be
as per derivative gain
%Ki = 1400; % Ki will be tuned
manually here
Control law design and test
The control design tested on
different kp, kd and ki values , after
proper tuning it observed that at ki
1400 value the system behaved
properly and overshoot, rise time