1. Control System Toolbox (Part-II)

2. Outline Time Domain Analysis of 1st Order Systems
Step Response
Impulse Response
Ramp Response
Parabolic Response
Time Domain Analysis of 2nd Order Systems
Step Response, Impulse Response, Ramp Response and Parabolic Response
Time Domain Specifications

3. Introduction The first order system has only one pole.
Where K is the D.C gain and T is the time constant of the system.
Time constant is a measure of how quickly a 1st order system responds to a unit step input.
D.C Gain of the system is ratio between the input signal and the steady state value of output.

4. Step Response To obtain the step response of the system num = 10;
den = [ ];
step(num,den) or
num = 10;
den = [ ];
sys=tf(num, den)
step(sys)

5. Impulse Response To find the step response of the system num = 10;
den = [ ];
impulse(num,den)
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6. Ramp Response To find the ramp response of the system t = 0:0.01:10
r = t;
num = 10;
den = [2 1];
lsim(num,den,r,t)
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7. Exercise-1: Obtain the step and ramp responses of the following 1st order system for T=1, 2, 3 5, 10 seconds.
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8. Exercise-2: Obtain the step and ramp responses of the following 1st order system for K=1, 5, 10 and 15.
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9. 1st Order System with a Zero
Zero of the system lie at -1/α and pole at -1/T.

10. Exercise-3: Obtain the step response of the following 1st order system with zero for
K=1, α=4 and T=3 sec
K=1, α=3 and T=4 sec
K=1, α=2 and T=3 sec
And compare the results with system w/o zero
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11. Time Response of 2nd Order Systems

12. Introduction
A general second-order system is characterized by the following transfer function.

13. Undamped Natural Frequency & Damping ratio
Determine the un-damped natural frequency and damping ratio of the following second order system.
To find the undamped natural frequency and damping ratio in matlab
num=4
den=[ ]
sys=tf(num, den)
damp(sys)

14. Exercise-4: Obtain the pole zero map and step response of the 2nd order system and determine the mode of damping in the system. If the system is underdamped obtain the time domain specifications. On the pole zero map show that corresponding damping ratio and natural undamped frequency of the poles.
ωn=3 r/s and ζ=1
ωn=3 r/s and ζ=2
ωn=3 r/s and ζ=0.1
ωn=3 r/s and ζ=0.5
ωn=3 r/s and ζ=0

15. Exercise-5: Obtain the step response of the 2nd order system if
ωn=0.1 r/s and ζ=0.5
ωn=0.3 r/s and ζ=0.5
ωn=0.6 r/s and ζ=0.5
ωn=1 r/s and ζ=0.5
ωn=1.5 r/s and ζ=0.5

16. Exercise#6
Consider the system shown in following figure, where damping ratio is 0.6 and natural undamped frequency is 5 rad/sec. Obtain the rise time tr, peak time tp, maximum overshoot Mp, and settling time 2% and 5% criterion ts when the system is subjected to a unit-step input.

17. Exercise#6
Describe the nature of the second-order system response via the value of the damping ratio for the systems with transfer function

18. End of Tutorial You can Download this tutorial from
End of Tutorial
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