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