1. Lecture 9: Time-Response Characteristics (II) TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA A AAA A A A A A A A A

2. Sampled-Data Systems Dominant closed-loop poles: the closed-loop pole(s) furthest away from 0 Transient response largely determined by the dominant closed-loop pole(s) Problem: quantify the response characteristics based on dominant pole locations

3. Continuous-Time Feedback Systems Dominant closed-loop poles: the closed-loop pole(s) furthest to the right Transient response largely determined by the dominant closed-loop pole(s)

4. Time Specifications of Continuous-Time Systems

5. Time Specifications for a Real Dominant Pole Time Specifications:

6. Time Specifications for Complex Dominant Poles Dominant closed-loop poles: Time Specifications:

7. Example

8. Relating the Closed-Loop Poles Sampled-data system Continuous-time system Closed-loop poles: Characteristic equation: Closed-loop poles: Transfer function: hold

9. to the closed-loop poles of the sampled-data system (approximately)

11. Inverse Map (General Case)

12. Time Specifications of Sampled-Data Systems

13. First Order System Example Approximate settling time for the system response to unit step input?

14. Second Order Example Closed-loop transfer function: Taking the inverse transform:

15. Second Order Example: Simulation

16. Constant Damping Loci

17. Constant Frequency Loci Constant frequency loci correspond to closed-loop poles with the same oscillation frequency in step response (or the same peak time)

18. Constant Damping Ratio Loci

19. Time responses for different closed-loop pole locations

20. Systems Considered So Far

21. Characteristic Equation of General Sampled-Data Systems (independent of input)

22. Finding Characteristic Equation via SFG Signal Flow Graph: 2. Find the transfer function from the output of the sampler to its input: 3. Take star transform:

23. Example with Multiple Samplers Characteristic equation: