# Lab 3 nust control

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Published on March 8, 2014

Author: talhawaqar

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TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST 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]; Zero/pole/gain: d=[2 4 6]; 0.5 (s+1) S1=tf(n,d) -------------- size(S1) %no. of inputs and outputs. (s^2 + 2s + 3) pole(S1) % no.of poles . pzmap(S1) %pole/zero map. Eigenvalue Damping K=dcgain(S1) -1.00e+000 1.73e+000 zpk(S1) % zero /pole/gain . -1.00e+000 - 1.41e+000i damp (S1) % damping coefficients. wn = [wn,z] = damp(S1) % naturalfrequency 1.41e+000i 5.77e-001 5.77e-001 1.73e+000 1.7321 step(S1) % assinging input for analysis + Freq. (rad/s) 1.7321 z= Transfer function: s+1 0.5774 0.5774 --------------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 CONTROL SYSTEM LAB SYSTEM RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST 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 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 2 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 RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST Lab task: Task# 1: CONTROL SYSTEM LAB SYSTEM RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST Task# 2a: num=[25]; >> den=[1 4 25]; >> trans=tf(num,den); >> step(trans); >> zero(trans) p=pole(t1) p= -2.0000 + 4.5826i2.0000 - 4.5826i >> z=zero(t1) z= Empty matrix: 0by-1 >> y=pzmap (t1) CONTROL SYSTEM LAB SYSTEM RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST CONTROL SYSTEM LAB SYSTEM RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST Task # 2b >> trans=tf(num,den) 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 Transfer function: 36 ----------------s^2 + 7.86 s + 36 >> step(trans) num=[36]; den=[1 7.86 36]; CONTROL SYSTEM LAB SYSTEM RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST 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 RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST 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 RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST 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 CONTROL SYSTEM LAB SYSTEM RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST Task # 3a: For 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 2times ove that of prelab 2(a) and repeat prelab 2(a) A=4,b=88 num=[88]; >> den=[1 4 88]; >> trans=tf(num,den); >> step(trans) CONTROL SYSTEM LAB SYSTEM RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST p=pole(t1) p= -2.0000 + 9.1652i -2.0000 - 9.1652i z=zero(t1) z= Empty matrix: 0-by-1 >> y=pzmap(t1) y= -2.0000 + 9.1652i -2.0000 - 9.1652i Task # 3b CONTROL SYSTEM LAB SYSTEM RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST For 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=340 num=[340]; >> den=[1 4 340]; >> trans=tf(num,den) Transfer function: 340 --------------s^2 + 4 s + 340 >> step(trans) CONTROL SYSTEM LAB SYSTEM RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST 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 CONTROL SYSTEM LAB SYSTEM RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST Task # 4a 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 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 RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST Task # 4b: CONTROL SYSTEM LAB SYSTEM RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST 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=20 omega=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: 400 s^2 + 16 s + 400 CONTROL SYSTEM LAB SYSTEM RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST CONTROL SYSTEM LAB SYSTEM RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST 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. a=tf([25],[1 4 25]); >> b=tf([37],[1 8 37]); >> c=tf([22],[1 2 22]); >> step(a,b,c) CONTROL SYSTEM LAB SYSTEM RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST 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]); >> a=tf([340],[1 4 340]); >> step(a,b,c) CONTROL SYSTEM LAB SYSTEM RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST 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 RESPONSE DATED: 25-FEB-14

TALHA WAQAR EE-805 PAKISTAN NAVY ENGINEERING COLLEGE NUST CONTROL SYSTEM LAB SYSTEM RESPONSE DATED: 25-FEB-14

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