1. Ch3 Feedback control system characteristics
Main content:
Open- and closed-loop control systems
Sensitivity to Parameter variations
Transient response of control system
Disturbance in feedback control system

2. continue Main content: Steady-state error The cost of feedback
Examples and simulation

3. 3.1 Open-loop and closed-loop control systems
Review the concepts and structure
Refer to P

4. The roles of feedback Benefits: Reduce error (eliminating the error)
Reduce sensitivity or Enhance robustness
Disturbance rejection or elimination
Improve dynamic performance or adjust the transient response (such as reduce time constant)

5. 3.2 Sensitivity of system to parameter variations
System are time-varying in its nature because of inevitable uncertainties such as changing environment , aging , and other factors that affect a control process.All these uncertainties in open-loop system will result in inaccurate output or low performance. However, a closed-loop system can overcome this disadvantage.

6. Continue
A primary advantage of a closed-loop feedback control system is its ability to reduce the system’s sensitivity to parameter variation. Sensitivity analysis Robust control

7. Effect of parameter variations
If process is change as
Open-loop system
Closed-loop system

8. continue
In the limit, for small incremental changes, last formula is

9. Sensitivity comparison
Open-loop system
Closed-loop system

10. Sensitivity to parameters
If system TF is
System sensitivity to is

11. Example of sensitivity
Feedback amplifier
Goal: Reduce the sensitivity to parameters variation, that is enhance the robustness to change in amplifier gain.
Refer to

12. 3.3 Transient response of system
Transient response is the response of a system as a function of time. It is one of the most important characteristics of control system.
If transient response is not satisfying, what shall we do?

13. Control of transient response (Take speed control system as example)
Cascade controller
Feedback controller
Refer to P180 (Figure 4.6 and Figure 4.7)
Refer to P181 (Figure 4.8)

14. 3.4 Disturbance in a feedback control system
Disturbance signal is an unwanted extraneous input signal that affects the system’s output signal, such as noise for amplifier,wind gusts for radar antennas,etc.
Feedback control can completely or partially eliminate the effect of disturbance signal.

15. Example of steel rolling mill
Refer to P
Load changes or disturbances+Noise
Feedback can alleviate the effects of disturbances and noise signal occurring within the feedback loop.
If system exists noise at the input point, we can design a low-pass filter to improve SNR (signal-noise ratio)

16. System sensitivity
System sensitivity is defined as the ratio of the percentage change in the system transfer function to the percentage change of the process transfer function. It is defined as

17. 3.5 Steady-state error
Steady-state error is the error after the transient response has decayed,leaving only the continuous response.
Feedback can reduce the steady-state error of control system

18. How to define the error ? From input point: From output point:
E a (s)=R(s)-H(s)Y(s)
E (s)=R(s)-Y(s)
Only for unit feedback H(s)=1,We have
E a (s)= E (s)

19. Comparison of error
Open-loop system
Closed-loop system

20. continue Open-loop system under unit step input
Closed-loop system under unit step input

21. Example illustration Refer to P189-190
An example of first-order system

22. 3.6 The cost of feedback Increase of complexity Loss of gain
Instability

23. An unrealistic dream Why not simply set G(s)=Y(s)/R(s)=1?
Transfer function represent the physical system or process, Therefore G(s)=1 is unrealizable.

24. 3.7 Design examples English channel boring machines Mars rover vehicle
PD controller, and how to select K ?
To compare the sensitivity and steady-state error between open-loop and closed-loop system

25. 3.8 Simulation using MATLAB
Refer to P
Self-learning after class

26. Summary The fundamental reasons for using feedback are as follows:
Decrease the sensitivity to parameter variation
Improve transient or dynamic performance
Enhance the robustness
Reduce the steady-state error
Refer to P

27. Assignment
E4.1
E4.3
E4.4
E4.6
E4.8
P4.2 , P4.5, P4.7