control system: Steady State Error

1. GREEN UNIVERSITY OF
BANGLADESH
Department: EEE (Eve)
Prepared By:
Md. Sahed Dewan
ID# 143010021
Prepared For:
Md. Joynal Abedin
Lecturer, GUB
Course Title: Control System

2. Steady State Error

3. Introduction
Control system analysis focus on three
specifications: i) transient response, ii) stability
& iii) steady-state errors.
Steady state error is the difference between the
input and output for a prescribed test input as
t  ∞
The steady-state error will depend on the type
of input (step, ramp & parabolic) as well as the
system type (0, I & II).

4. Test waveforms for evaluating steady state errors
of position control system.

5. ∑
R(s)
C(s)
E(s)
G(s)
H(s)
-
+
Steady State Error

6. E(s) = R(s) – H(s) C(s)
∑
R(s)
C(s)
E(s)
G(s)
H(s)
-
+
C(s) = E(s) G(s)
 C(s) = (R(s) – H(s) C(s)) G(s)
 C(s) + H(s) C(s) G(s) = R(s) G(s)
 C(s) (1 + H(s) G(s) ) = R(s) G(s)
 =
C(s)
R(s)
G(s)
1 + H(s) G(s)
Again, E(s) = R(s) – C(s) = R(s) –
So, E(s) =
G(s) R(s)
1 + G(s)
R(s)
1 + G(s)
For feedback, H(s) = 1
So, =
 C(s) = ● R(s)
G(s)
1 + G(s)
G(s)
1 + G(s)
C(s)
R(s)

7. Type 0: Step Input:
Kp = G(s)
lim
s  0
Type 1: Ramp Input:
Kv = s G(s)lim
s  0
Type 2: Parabolic Input:
Ka = s G(s)
lim
s  0
2

8. Steady State Error
Type Step Ramp Parabolic
0 A
(1+Kp)
∞ ∞
I 0 A
Kv
∞
II 0 0 A
Ka

9. Thank you