A paint industry in Oman for its operation, a central load controller with a sec

Question

A paint industry in Oman for its operation, a central load controller with a second/any higher order model is to be designed. The control systems should be equipped with a motor constant and a suitable amplifier gain to balance the operation. The controller should be designed to operate with unity feedback H(s)=1. The system is expected to perform on unit step/ramp input. Obtain the response for such system if the amplifier gain is varying within the rage of 20 to 55, using MATLAB script supplemented with mathematical evaluation.

The system is also expected to be dealt in noisy environments. In such a case, if a disturbance is acting on the system with a unit step phase, determine the steady state error component for the system for the same amplifier gains. Also critically analyze the impact of disturbance on the system to ensure the stability and obtain the responses in MATLAB script/simulation supplemented with mathematical evaluation.

Detailed explanation of the theoretical/Mathematical approach on problem solving for the specified task with its evaluation of results.

Screen shots of MATLAB script along with the responses must be attached for the simulations.

Explanation / Answer

Force and torque control of motor

function out = inductionvarRr()
Vl1=input('Enter the Suppy Voltage (line to line) RMS value: ');
P=input('Enter the number of poles: ');
Rs=input('Stator Resistance: ');
Rr1=input('Enter the first Rotor Resistance: ');
Rr2=input('Enter the second Rotor Resistance: ');
Rr3=input('Enter the third Rotor Resistance: ');
Rr4=input('Enter the fourth Rotor Resistance: ');
Rr5=input('Enter the fifth Rotor Resistance: ');
Xs=input('Stator Leakage Reactance @ 50 Hz frequecny: ');
Xr=input('Rotor Leakage Reactance @ 50 Hz frequecny: ');
Ls=Xs/(2*pi*50);
Lr=Xr/(2*pi*50);
Wsync1=4*pi*50/P;
Tmf2=zeros(Wsync1*500+1,1);
Tmf3=zeros(Wsync1*500+1,1);
Tmf4=zeros(Wsync1*500+1,1);
Tmf5=zeros(Wsync1*500+1,1);
Tmf1=zeros(Wsync1*500+1,1);
m=1;
for Wrotor1=0:0.002:Wsync1

Tmf1(m)=(3*(((Vl1^2)*Rr1/((Wsync1-Wrotor1)/Wsync1))/((Rs+Rr1/((Wsync1-
Wrotor1)/Wsync1))^2+(2*pi*50*Ls+2*pi*50*Lr)^2))/Wsync1); %star connected
m=m+1;
end
m=1;
for Wrotor1=0:0.002:Wsync1

Tmf2(m)=(3*(((Vl1^2)*Rr2/((Wsync1-Wrotor1)/Wsync1))/((Rs+Rr2/((Wsync1-
Wrotor1)/Wsync1))^2+(2*pi*50*Ls+2*pi*50*Lr)^2))/Wsync1);
m=m+1;
end
m=1;
for Wrotor1=0:0.002:Wsync1

Tmf3(m)=(3*(((Vl1^2)*Rr3/((Wsync1-Wrotor1)/Wsync1))/((Rs+Rr3/((Wsync1-
Wrotor1)/Wsync1))^2+(2*pi*50*Ls+2*pi*50*Lr)^2))/Wsync1);
m=m+1;
end

Speed control of motor
m=1;
for Wrotor1=0:0.002:Wsync1

Tmf4(m)=(3*(((Vl1^2)*Rr4/((Wsync1-Wrotor1)/Wsync1))/((Rs+Rr4/((Wsync1-
Wrotor1)/Wsync1))^2+(2*pi*50*Ls+2*pi*50*Lr)^2))/Wsync1);
m=m+1;
end
m=1;
for Wrotor1=0:0.002:Wsync1

Tmf5(m)=(3*(((Vl1^2)*Rr5/((Wsync1-Wrotor1)/Wsync1))/((Rs+Rr5/((Wsync1-
Wrotor1)/Wsync1))^2+(2*pi*50*Ls+2*pi*50*Lr)^2))/Wsync1);
m=m+1;
end
plot(Tmf1);
hold on;
plot(Tmf2);
plot(Tmf3);
plot(Tmf4);
plot(Tmf5);
hold off;
ylabel('Torque(N-m)');
xlabel('Rotor Speed(Rad/s)');
end

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