Question

Could you teach me the way to solve Lab 1,2?

Cyber Exploration Laboratory Cyber Exploration Laboratory Experiment 4.1 Objective To evaluate the effect of pole and zero location upon the time response of first- and second-order systems. Minimum Required Software Packages MATLAB, Simulink, and the Control System Toolbox Prelab 1. Given the transfer function G(s)evluate settling time and rise time for the following values of a: 1, 2, 3, 4. Also, plot the poles. 2. Given the transfer function G)+as +b a. Evaluate percent overshoot, settling time, peak time, and rise time for the following values: a4, b-25. Also, plot the poles. b. Calculate the values of a and b so that the imaginary part of the poles remains the same but the real part is increased two times over that of Prelab 2a, and repeat Prelab 2a e. Calculate the values of a and b so that the imaginary part of the poles remains the same but the real part is decreased by one half over that of Prelab 2a, and repeat Prelab 2a 3 a. For the system of Prelab 2a, calculate the values of a and b so that the real part of the poles remains the same but the imaginary part is increased two times over that of Prelab 2a, and repeat Prelab 2a. b. For the system of Prelab 2a, calculate the values of a and b so that the real part of the poles remains the same but the imaginary part is increased four times over that of Prelab 2a, and repeat Prelab 2a. 4. a. Forthe system of Prelab 2a, calculate the values of a and b so that the damping ratio remains the same but the natural frequency is increased two timวes over that of Pelab 2a, and repeat Prelab 2a b. For the system of Prelab 2a, calculate the values of a and b so that the damping ratio remains the same but the natural frequency is increased four times over that of Prelab 2a, and repeat Prelab 2a. 5. Briefly describe the effects on the time response as the poles are changed in each of Prelabs 2, 3, and 4. Lab 1. Using Simulink, set up the systems of Prelab1 and plot the step response of each of the four transfer functions on a single graph by using the Simulink LTI Viewer (See Appendix E.6 online for tutorial). Also, record the values of settling time and rise time for each step response 2. Using Simulink, set up the systems of Prelab 2. Using the Simulink LTI Viewer, plot the step response of each of the three transfer functions on a single graph. Also, record the values of percent overshoot, settling time, peak time, and rise time for each step response. 3. Using Simulink, set up the systems of Prelab 2a and Prelab 3. Using the Simulink LTI Viewer, plot the step response of each of the three transfer functions on a single graph. Also, record the values of percent overshoot, settling time, peak time, and rise time for each step response. 224 Chapter 4 Time Response 4. Using Simulink, set up the systems of Prelab 2a and Prelab 4. Using the Simul Viewer, plot the step response of each of the three transfer functions on a singl Also, record the values of percent overshoot, settling time, peak time, and rise

Answer 1

Ans 1:

in MATLAB command prompt

G = tf([1],[1 1])

G = tf([2],[1 2])

G = tf([3],[1 3])

G = tf([4],[1 4])

to find settling time in MATLAB use below function

stepinfo(G)

for a = 1

settling time: 3.9121s

rise time:2.1970s

for a = 2

settling time: 1.9560s

rise time:1.0985s

for a = 3

settling time: 0.7323s

rise time:1.3040s

for a = 4

settling time: 0.5493s

rise time:0.9780s

to plot poles and zero use below command in MATLAB

pzmap(G)

pole zero plot for a = 1

Pole-Zero Map 0.8 0.6 A 0.4 D 0.2 0.2 O-0.4 -0.6 -0.8 -1 1 -0.9 -0.8 0.7 -0.6 -0.5 -0.4-0.3 -0.2 -0.1 0 Real Axis (seconds)

for a =2

Pole-Zero Map 0.8 0.6 A 0.4 D 0.2 0.2 O-0.4 -0.6 -0.8 -1 Real Axis (seconds)

for a=3

Pole-Zero Map 0.8 0.6 A 0.4 D 0.2 0.2 O-0.4 -0.6 -0.8 -3 -2 0.5 -2.5 Real Axis (seconds)

for a = 4

Pole-Zero Map 0.8 0.6 A 0.4 D 0.2 -0.2 0.4 0.6 0.8 -4 3.5 3 2.5 21.5 1 0.5 0 Real Axis (seconds)

Ans 2:

in MATLAB command prompt

G= tf([25],[1 4 25])

in MATLAB command prompt

stepinfo(G)

RiseTime: 0.2930
SettlingTime: 1.6819
SettlingMin: 0.9065
SettlingMax: 1.2537
Overshoot: 25.3741
Undershoot: 0
Peak: 1.2537
PeakTime: 0.6908

pole zero plot in MATLAB use below command

pzplot(G)

Pole-Zero Map 5 4 CD-2 -3 -4 -5 Real Axis (seconds)