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

2. ) s ( R
E(s): Laplace transform of the error
G(s): Forward path transfer function
Steady state error:

3. System type: Roots at s=0 of the denominator of the forward path transfer function denote the sytem type.
Example:
System type: 1
System type: 2
System type: 0
System type: 1

4. Position error coefficient
Step Input:
Step input ) s ( R
Position error coefficient
System type:
ess 1

5. Velocity error coefficient
Ramp Input: ) s ( R
Ramp input
Velocity error coefficient
System type:
ess 1 2

6. Acceleration error coefficient
Parabolic Input:
Parabolic input ) s ( R
Acceleration error coefficient
System type:
ess 1 2 3

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

10. Example 3.2: ) s ( R
System type: 0
ess:
Step
Ramp
Parabolic
Stability

11. Integral control improves the steady state error performance
Example 3.3 : ) s ( R
Sistem tipi: 1
Integral control improves the steady state error performance
ess:
Step
Ramp
Parabolic

12. Derivative control does not change the error performance
Örnek 3.4 : ) s ( R
Sistem tipi: 0
ess:
Step
Ramp
Parabolic
Derivative control does not change the error performance