Download - Steady State Error
GREEN UNIVERSITY OF BANGLADESHDepartment: EEE (Eve)
Prepared By:
Md. Sahed DewanID# 143010021
Prepared For:
Md. Joynal AbedinLecturer, GUB
Course Title: Control System
Steady State Error
IntroductionControl 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).
Test waveforms for evaluating steady state errors of position control system.
∑R(s)
C(s)
E(s)
G(s)
H(s)
-+
Steady State Error
E(s) = R(s) – H(s) C(s)∑
R(s) C(s)E(s)
G(s)
H(s)
-
+
C(s) = E(s) G(s)Þ C(s) = (R(s) – H(s) C(s)) G(s)Þ C(s) + H(s) C(s) G(s) = R(s) G(s)Þ C(s) (1 + H(s) G(s) ) = R(s) G(s)Þ =
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, =
Þ C(s) = ● R(s)
G(s)1 + G(s)
G(s)
1 + G(s)
C(s)R(s)
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
Steady State ErrorType Step Ramp Parabolic
0 A (1+Kp)
∞ ∞
I 0 AKv
∞
II 0 0 AKa
Thank you