Project - Speed Control of a Direct Current (DC) motor
here we took the refernce or input as the step and we set it to step 1 and initial value to zero final value to 240 and from we supply the voltage and as we move next it is pid controller and this makes the output more efficent and the steady state error will continue on the base line and here we can control the dc speed control we can see how much is the overshoot setttling time and the steady state error .adding sum block to it the transfer function and the parameters are the armature resistance and armature inducatnce and we can take the output aramature current and the gain block is added and toruqe constant the output is the torque and another transfer function is taken parameters are the moment of inertia of the rotor j and the motor viscous friction constant b and the output gives us the speed (w) .
to build the simulink model we use the electrical circuit and mechancial circuit
the transfer function of angular velocity w(s) to the input voltage v(s)
Ga(s) = w(s)/v(s) = Kt/[(Ls+R)(Js+B)+Kt*Kb]
for the above given schematic block it contains the 2 parts the electrical and mechancial circuit and both combined we get the mathematical equation for the electical circuit the end part will be of the torque and it measures withrespect to armature current and the mechancial circuit it measures through speed (w).
the equations are
I(s)= V(s)-Kbs*teta(s)/Ls+R electrical circuit. w(s)=Kt*I(S)/Js+B mechancial circuit
the matlab script for the modeling and control design parameters
%this file contains the parameters that help to build the simulink blocks
J=0.01; %moment of inertia of the motor in kg-m^2
B = 0.1;%motor viscus friction constant in N-m-srun
Km = 0.01; �ck EMF constant in N-m/amp
Kt=0.01; %moto
% r Torque constant n-m/amp
Ra = 1.0;% risistance of armature circuit in ohm
La =0.5; %inductans of armature circuit in henries
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% parameters of spring mass system
m=100.0;
k=3944.0;
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% consider the damping
zeta=0.5; %underdamped condition
fn=1.0; %frequency in hz
wn=2*pi*fn; %frequency in rad/sec
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%respectivly placement of poles
p1=-zeta*wn+wn*sqrt(zeta^2-1);
p2=-zeta*wn-wn*sqrt(zeta^2-1);
P = [p1;p2];
%matrices
A =[-B/J Kt/J;-Km/La -Ra/La];
B1 =[0; 1/La];
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%pole placements
K=place(A,B1,P);
K1=38.3133 ;
K2= -2.8584;
as we observe the armature circuit the stator will faclitate cutting down the resistance we have huge resistance in series in armature circuit as we cutting down the resistance move will the current driven into armature circuit armature is the winding of an electric machine which carries altenating currrent .when the both the armature and the field winding are excited by a ds supply current flows through the winding and a magnetic flux proportional to the current is produced when the flux from the field interact with the flux from the armature it results in motion of the rotor .
backemf V(b)=Km*w;
torque = armature current *Kt;
torque related to the rotational force of an electric motor while the speed refers to the rate that the motor can rotate this means that torque is assoaciated with the rotational force while speed relates to the rate of rotation which can be calculated by examing the rpm or revolution per minute .
control law of design and test here we need the parameters like
% consider the damping
zeta=0.5; %underdamped condition
fn=1.0; %frequency in hz
wn=2*pi*fn; %frequency in rad/sec
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%respectivly placement of poles
p1=-zeta*wn+wn*sqrt(zeta^2-1);
p2=-zeta*wn-wn*sqrt(zeta^2-1);
P = [p1;p2];
%matrices
A =[-B/J Kt/J;-Km/La -Ra/La];
B1 =[0; 1/La];
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%pole placements
K=place(A,B1,P);
stability of the dynamic system
as the pole placements value the stability willbe depend and as we take zeta more than 1 it goes unstable and the wave form efficiency will be depended on the ki value as per kp and kd values the ki value should be added as we use place command to find the pole placements and as they are in the range then the speed of the dc motor will be in the control or else it shows the unstable and ifinte value and the simulation of model denpend on the pole placement .as we test the ki value for the set of paremeters of the kp and kd the ki value is around 35 then the scope it shows it has the overshoot and undershoot and it goes to the steady state and then goes to the referenece line and becomes stable .
as we observe the waveform we see that it starts from 1sec as we given step time as the 1 as the settling time it takes 2sec of the time to settle down as we can observe in the scope
as we see the scope the steady state error it doesnt have to many oscillations and it reaches steady state error within 1% and flow through the base line steadly and constant
as we see the scope the highest peak is the overshoot and lowest peak is the under shoot and for each oscillation the overshoot is less than5%.