Analysis of First Order Systems.

1. Control Systems
18EC43

2. Contents
 Analysis of First Order Systems

3. Analysis of First Order
Systems
 A first order system is represented by
 Where input is R(s) and Process is
𝑎
𝑠+𝑎
,
 So C(s) /R(s) =
𝑎
𝑠+𝑎
 If R(s) = 1/s, then

4. Analysis of First Order Systems
 C(s) =
1
𝑠
∗ (
𝑎
𝑠+𝑎
) ;
 Which can be solved further by,
 C(s) =
𝐴′
𝑆
+
𝐵′
𝑠+𝑎
 Then, A′=1 and B′= -(1/𝑎)
 Therefore,
 C(s) =
1
𝑆
−
1
𝑠+𝑎

5. Analysis of First Order Systems
 Applying Inverse Laplace transforms,
 C(s) = L-1(
1
𝑆
) − L−1(
1
𝑠+𝑎
)
 C(t) = 1- e-at ------ (1)
 To Draw the Waveform, we need to Substitute,
 t =
1
𝑎
𝑖𝑛 𝑒𝑞𝑢 (1),

6. Analysis of First Order Systems
t
Vo
0
0
1
𝑎
0.63
1
2𝑎
0.9
∞
1

7. Analysis of First Order Systems
 Performance Parameters:
 Time constant : T =
1
𝑎
;
 Rise time tr =
2.2
𝑎
;
 Settling time ts =
4
𝑎
;