lab 3 nust control
TRANSCRIPT
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
LAB # 3(A)
System Response
OBJECT:
To study the System response for different order systems, natural frequency and damping ratio, Peak response, settling time, Rise time, steady state, using MATLAB commands and LTI Viewer.
THEORY:
Generally we have two types of responses, Steady State Response and Transient response such as rise time, peak time, maximum overshoot, settling time etc.
n=[1 1];
d=[2 4 6];
S1=tf(n,d)
size(S1) %no. of inputs and outputs.
pole(S1) % no.of poles .
pzmap(S1) %pole/zero map.
K=dcgain(S1)
zpk(S1) % zero /pole/gain .
damp (S1) % damping coefficients.
[wn,z] = damp(S1) % naturalfrequency
step(S1) % assinging input for analysis
Transfer function:
s + 1
---------------
2 s^2 + 4 s + 6
Transfer function with 1 outputs and 1 inputs.
ans =
-1.0000 + 1.4142i
-1.0000 - 1.4142i
K=
0.1667
Zero/pole/gain:
0.5 (s+1)
--------------
(s^2 + 2s + 3)
Eigenvalue Damping Freq. (rad/s)
-1.00e+000 + 1.41e+000i 5.77e-001 1.73e+000
-1.00e+000 - 1.41e+000i 5.77e-001 1.73e+000
wn =
1.7321
1.7321
z =
0.5774
0.5774
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
zeta= [0.3 0.6 0.9 1.5]; % zeta funtion is assigned with four different values.for k=1:4; % k is assigned from 1-4 so as to run the program four times in a loop. num=[0 1 2]den=[1 2*zeta(k) 1]; % den take out four different values of zeta . TF=tf(num,den) step(TF)hold on; % hold on restores the previous graphs.end; % end represent the completion
num =
0 1 2 Transfer function: s + 2---------------s^2 + 0.6 s + 1
num = 0 1 2
Transfer function: s + 2---------------s^2 + 1.2 s + 1 num =
0 1 2
Transfer function: s + 2---------------s^2 + 1.8 s + 1 num =
0 1 2
Transfer function: s + 2-------------s^2 + 3 s + 1
Exercise:
1. Given the transfer function, G(s) = a/(s+a), Evaluate settling time and rise time for the following values of a= 1, 2, 3, 4. Also, plot the poles.
for k=1:4; num=[k]den=[1 k]; TF=tf(num,den) step(TF)hold on; end
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
Lab task:
Task# 1:
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
Task# 2a:num=[25];>> den=[1 4 25];>> trans=tf(num,den);>> step(trans);>> zero(trans)
p=pole(t1)p =-2.0000 + 4.5826i-2.0000 - 4.5826i>> z=zero(t1)z =Empty matrix: 0-by-1>> y=pzmap (t1)
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
Task # 2b >> trans=tf(num,den)
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
G(s)= b/s^2+as+b
Coefficent of damping I will represent with C
poles= -C wn + -j wn sqrt 1-C^2
wn sqrt 1-C^2= 5*sqrt 1-a4^2=4.5826
C wn= 4 now wn=6.0828 & C=0.6575
Tp= .6949, Ts=1.0139, OS = .0645
a=7.89, b=36
num=[36];
den=[1 7.86 36];
Transfer function:
36
-----------------
s^2 + 7.86 s + 36
>> step(trans)
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
p=pole(t1)p =-4.0000 + 4.5826i-4.0000 - 4.5826i>> z=zero(t1)z =Empty matrix: 0-by-1>> y=pzmap(t1)y =-4.0000 + 4.5826i -4.0000 - 4.5826i
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
Task # 2c:Calculate the values of a and b so that the imaginary part of the poles remains the same, but the real part is decreased ½ time over that of (a), and repeat the 2(a). num=[22];>> den=[1 2 22];>> trans=tf(num,den);>> step(trans)>>zero(trans)ans =
Empty matrix: 0-by-1
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
p=pole(t1) p =-1.0000 + 4.5826i-1.0000 - 4.5826i>> z=zero(t1)z =Empty matrix: 0-by-1>> y=pzmap(t1)y =-1.0000 + 4.5826i-1.0000 - 4.5826i
Task # 3a:For the system of prelab 2(a) calculate the values of a and b so that the realpart of the poles remains
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
the same but the imaginary part is increased 2times ove that of prelab 2(a) and repeat prelab 2(a)A=4,b=88num=[88];>> den=[1 4 88];>> trans=tf(num,den);>> step(trans)
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
p=pole(t1)p =-2.0000 + 9.1652i-2.0000 - 9.1652iz=zero(t1)z = Empty matrix: 0-by-1>> y=pzmap(t1)y =-2.0000 + 9.1652i-2.0000 - 9.1652i
Task # 3bFor the system of prelab 2(a) calculate the values of a and b so that the realpart of the poles remains the same but the imaginary part is increased 4times over that of prelab 2(a) and repeat prelab 2(a)A=4,b=340num=[340];>> den=[1 4 340];>> trans=tf(num,den) Transfer function: 340---------------s^2 + 4 s + 340 >> step(trans)
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
p=pole(t1)p =-2.0000 +18.3303i-2.0000 -18.3303i>> z=zero(t1)z =Empty matrix: 0-by-1>> y=pzmap(t1)y =-2.0000 +18.3303i-2.0000 -18.3303i
Task # 4aFor the system of 2(a), calculate the values of a and b so that the damping ratio remains the same, but the natural frequency is increased 2 times over that of 2(a), and repeat 2(a). num=[100];>> den=[1 8 100];>> trans=tf(num,den)Transfer function: 100---------------s^2 + 8 s + 100 >> step(trans)
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
Task # 4b:For the system of 2(a), calculate the values of a and b so that the damping ratio remains the same, but the natural frequency is increased 4 times over that of 2(a), and repeat 2(a).eeta=0.4>> omega=20omega=20>> b=omega*omegab =400>> a=2*eeta*omegaa =16>> num=[b]num=400>> den=[ 1 a b]den =1 16 400>> t=tf([num],[den]) Transfer function:400s^2 + 16 s + 400
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
Exercise:Using Simulink, set up the systems of Q 2. Using the Simulink LTI Viewer, plot the step response of each of the 3 transfer functions on a single graph.
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
a=tf([25],[1 4 25]);
>> b=tf([37],[1 8 37]);
>> c=tf([22],[1 2 22]);
>> step(a,b,c)
task # 3:Using Simulink, set up the systems of Q2(a) and Q3. Using the Simulink LTI Viewer, plot the step response of each of the 3 transfer functions on a single graph.c=tf([25],[1 4 25]);
>> b=tf([88],[1 4 88]);
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
>> a=tf([340],[1 4 340]);
>> step(a,b,c)
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
Task # 4:Using Simulink, set up the systems of Q 2(a) and Q 4. Using the Simulink LTI Viewer, plot the step response of each of the 3 transfer functions on a single graph.a=tf([25],[1 4 25]);
>> b=tf([100],[1 8 100]);
>> c=tf([400],[1 16 400]);
>> step(a,b,c)
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14
PAKISTAN NAVY ENGINEERING COLLEGE NUSTTALHA WAQAR EE-805
CONTROL SYSTEM LAB SYSTEM RESPONSEDATED: 25-FEB-14