control systems lab report

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matlab_codes.docx

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% Lab 2

%% Experiment 1 a

clear all;

clc;

close all;

numg = 10*poly([-7]);

deng = poly([0 -4 -8 -12]);

G = tf(numg,deng);

numh = poly([-10]);

denh = poly([-5 -15 -20]);

H = tf(numh,denh);

Ge = feedback(G,(H-1));

disp('Checking Stability:')

Ge = tf(Ge)

T = feedback(Ge,1);

disp('Step Input of 30u(t)')

Kp = dcgain(Ge)

ess = 30/(1+Kp);

Zeros = zero(Ge);

Poles = pole(Ge);

disp('Ramp Input of 30tu(t)')

numsGe = 10*poly([Zeros]);

numsGe = conv([1 0],numsGe);

densGe = poly([Poles]);

sG = tf(numsGe,densGe);

sG = minreal(sG);

Kv = dcgain(sG)

ess = 30/Kv

disp('Parabolic Input of 30t^2(t)')

nums2Ge = 10*poly([Zeros]);

nums2Ge = conv([1 0 0],numsGe);

dens2Ge = poly([Poles]);

s2G = tf(nums2Ge,dens2Ge);

s2G = minreal(s2G);

Ka = dcgain(s2G)

ess = 30/Ka

%% Experiment 1b

clear all;

clc;

close all;

numG1 = poly([-7]);

denG1 = poly([0 -4 -8 -12]);

G1 = tf(numG1,denG1); % Creating the transfer function G1

numG2 = 5*poly([-9 -13]); % Numerator of Ge

denG2 = poly([-10 -32 -64]); % Denominator of Ge

G2 = tf(numG2,denG2); % Creating the transfer function

G2 = feedback(G2,10); %Checking Stability

Ge1 = G1*G2 %Multiplying the transfer function by the feedback

numH = 1; % Numerator of h

denH = poly([-3]); % Denominator of h

H = tf(numH,denH); % Creating the transfer function H

Ge = feedback(Ge1,H) %Checking Stability

Zeros = zero(Ge) % finding the roots of the numerator

Poles = pole(Ge) % finding the roots of the denominator

disp('Step input of 30u(t)'); %display step Input of 30tu(t)

Kp = dcgain(Ge) %Dc gain of function Ge

ess = 30/(1+Kp) %Steady state error formula

disp('Ramp input of 30tu(t)'); %display ramp input 30tu(t)

numsGe = 5*poly([Zeros]); %Numerator of Ge

numsGe = conv([1 0],numsGe); %New Numerator of Ge

densGe = poly([Poles]); %Denominator of Ge

sG = tf(numsGe,densGe); %Transfer function of numerator and denominator Ge

sG = minreal(sG); % pole cancelation of the poles outside the range

Kv = dcgain(sG) %Dc gain of function Ge

ess = 30/Kv %Steady state error formula for Kv

disp('Parabolic Input of 30t^2(t)') %Displays Parabolic input of 30t^2(t)

nums2Ge = 5*poly([Zeros]);

nums2Ge = conv([1 0 0],numsGe);

dens2Ge = poly([Poles]);

s2G = tf(nums2Ge,dens2Ge);

s2G = minreal(s2G);

Ka = dcgain(s2G)

ess = 30/Ka

%% Experiment 2A)a

clc; %Clear Screen

close all; %Close all the opened programs within matlab

clear all; %Clears all values

Kp=2; %Setting variable Kp to 2

Km=19.513; %Setting variable Km to 19.513

Ko=0.796; %Setting variable Kp to 0.796

t=0.1; %Setting variable Kp to 0.1

var = 10*Kp*Km*Ko; %Setting variable var to multiply 10*Kp*Km*Ko

num = var; %Setting variable num to var

den = [1,10,var]; %Setting variable Kp to 1 10 and variable var

G = tf(num,den) %Transfer function num divided by den

s = tf([1 0],1); %Transfer function of values shown

'Step' %For step function

Kp = dcgain(G) %Setting variable Kp to the gain G (feedback)

estep = 1/(1+Kp) %Applying the step function formula for error

'Ramp' %For step function

Kv = dcgain(s*G) %Setting variable Kv to the gain G times s

eramp = 1/Kv %Applying the ramp function formula for error

'Parabolic' %For step function

Ka = dcgain((s^2)*G) %Setting variable Ka to the gain G times s^2

epara = 1/Ka %Applying the parabolic function formula for error

if ((Kp~=0) && (Kp~=inf)) %If Kp does not=0, and kp is not infinite

fprintf('System type 0 \n'); %Displays “system type 0”

elseif ((Kv~=0) && (Kv~=inf)) %If Kv does not=0, and kv is not infinite

fprintf('system type 1 \n'); %Displays “system type 1”

else %Or else move to next line

fprintf('System type 2 \n'); %Displays “system type 2”

end

%% Experiment 2B