4. Parabolic Input:
R(t)
t (s)
(Parabolic input error coefficient)

6. 3. Steady State Error and Time Response Performance) s ( R
Final Value Theorem:
Parabolic input
Step input
Ramp input

7. Example 3.1 a) ) s ( R System type: 0 Stability test
Final value theorem:
Step
Ramp
Parabolic
ess:
Step
Ramp
Parabolic
[cn]ss:
Step
Ramp
Parabolic
System type: 0
Stability test

8. Integral control improves the steady state error performance
Example 3.1 b) ) s ( R
ess:
Step
Ramp
Parabolic
System type: 1
Integral control improves the steady state error performance
ess:
Step
Ramp
Parabolic
System type : 0
Derivative control does not change the error performance

9. Example 3.1 d) ) s ( R System type: 2 DcDp  s0 System type: 0
ess:
Step
Ramp
Parabolic
System type: 2
DcDp  s0 System type: 0
Overshoot
DcDp  s1 System type: 1
DcDp  s2 System type: 2
DcDp  s3 System type: 3