1. Automatic control by Meiling CHEN
2. Analysis
Lesson 7
Relative Stability
Automatic control by Meiling CHEN

2. Automatic control by Meiling CHEN
= natural response + forced response
Part I :
Characteristic roots
Part II :
Input function
Steady state error
Sensitivity …etc.
Automatic control by Meiling CHEN

3. Automatic control by Meiling CHEN
= transient response + steady state response
rising time
delay time
maximum overshoot
settling time
…etc.
Steady state error
Automatic control by Meiling CHEN

4. Automatic control by Meiling CHEN
Im-axis
Dominant pole
Re-axis
Relative
stability
Automatic control by Meiling CHEN

5. Automatic control by Meiling CHEN
Steady state error ＋ －
Steady state error
Final values theorem
Automatic control by Meiling CHEN

6. Automatic control by Meiling CHEN

7. Automatic control by Meiling CHEN
Some testing signals
(1) Unit step function
(2) Unit ramp signal
Automatic control by Meiling CHEN

8. Automatic control by Meiling CHEN
(2) parabolic signal
Automatic control by Meiling CHEN

9. Automatic control by Meiling CHEN
(4) Unit impulse function
Area=1
Amplitude
width
Automatic control by Meiling CHEN

10. Automatic control by Meiling CHEN
Error constant:
Automatic control by Meiling CHEN

11. Automatic control by Meiling CHEN
Open loop transfer function :
The type of system :
n=0 the system is type 0
n=1 the system is type 1
n=2 the system is type 2 …
Automatic control by Meiling CHEN

12. Automatic control by Meiling CHEN
Type 0 ＋ －
Automatic control by Meiling CHEN

13. Automatic control by Meiling CHEN

14. Automatic control by Meiling CHEN
Type 1 ＋ －
Automatic control by Meiling CHEN

15. Automatic control by Meiling CHEN

16. Automatic control by Meiling CHEN
Type 2 ＋ －
Automatic control by Meiling CHEN

17. Automatic control by Meiling CHEN