1. Chapter 4: Feedback Control System Characteristics Objectives
In this chapter we extend the ideas of modeling to include control system characteristics, such as sensitivity to model uncertainties, steady-state errors, transient response characteristics to input test signals, and disturbance rejection. We investigate the important role of the system error signal which we generally try to minimize.
We will also develop the concept of the sensitivity of a system to a parameter change, since it is desirable to minimize the effects of unwanted parameter variation. We then describe the transient performance of a feedback system and show how this performance can be readily improved. We will also investigate a design that reduces the impact of disturbance signals.

2. Open-And Closed-Loop Control Systems
An open-loop (direct) system operates without feedback and directly generates the output in response to an input signal.
A closed-loop system uses a measurement of the output signal and a comparison with the desired output to generate an error signal that is applied to the actuator.

3. Open-And Closed-Loop Control Systems
Error Signal

4. Sensitivity of Control Systems To Parameter Variations
For the closed-loop case if GH ( s )
> 1 1 Y ( s ) × R ( s )
Output affected only by H(s) H ( s ) G ( s ) + D G ( s )
Open Loop D Y ( s ) D G ( s ) × R ( s )
Closed Loop ( ) G ( s ) + D G ( s ) Y ( s ) + D Y ( s ) × R ( s ) ( ) 1 + G ( s ) + D G ( s ) × H ( s ) D G ( s ) D Y ( s ) × R ( s ) ( ) 1 + GH ( s ) + D GH ( s ) ( 1 + GH ( s ) ) GH ( s )
> D GH ( s ) D G ( s )
The change in the output of the closed system D Y ( s ) × R ( s )
is reduced by a factor of 1+GH(s) 2 ( 1 + GH ( s ) )

5. Sensitivity of Control Systems To Parameter Variations( ) Y R S D G d æ ç è ö ÷ ø × 1 H [ ] + GH 2
Sensitivity of the closed-loop to G variations reduced
Sensitivity of the closed-loop to H variations
When GH is large sensitivity approaches 1
Changes in H directly affects the output response -

6. Example 4.1

7. Control of the Transient Response of Control Systems

8. Control of the Transient Response of Control Systems

9. Control of the Transient Response of Control Systems

10. Disturbance Signals In a Feedback Control Systems
R(s)

11. Disturbance Signals In a Feedback Control Systems

12. Disturbance Signals In a Feedback Control Systems

13. Steady-State Error

14. The Cost of Feedback
Increased Number of components and Complexity
Loss of Gain
Instability

15. Design Example: English Channel Boring Machines

16. G Td Design Example: English Channel Boring Machines
Study system for different
Values of gain K G Td

17. Study Examples of 4.9 - Control Systems Using MATLAB
And
Apply concepts performing Lab 3