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
continue
Main content:
• Steady-state error
• The cost of feedback
• Examples and simulation
3.1 Open-loop and closed-loop
control systems
• Review the concepts and structure
• Refer to P174-175
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)
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 closedloop system can overcome this disadvantage.
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
Effect of parameter variations
If process G (s ) is change as G ( s)  G ( s)
• Open-loop system
Y ( s)  G ( s) R( s)
• Closed-loop system
G ( s)
Y ( s) 
R( s )
(1  GH )(1  GH  GH )
G ( s)

R( s )
2
(1  GH )
continue
In the limit, for small incremental changes, last
formula is
T ( s) / T ( s) InT
S

G ( s) / G ( s) InG
Sensitivity comparison
• Open-loop system
S 1
T
G
• Closed-loop system
1
S 
1  G( s) H ( s)
T
G
Sensitivity to parameters
If system TF is
N ( s,  )
T ( s,  ) 
D ( s,  )
System sensitivity to

is
InT InN InD
N
D
S 


 S  S
In In In
T
Example of sensitivity
• Feedback amplifier
Refer to 178-179
• Goal: Reduce the sensitivity to parameters
variation, that is enhance the robustness to
change in amplifier gain.
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?
Control of transient response
(Take speed control system as example)
• Cascade controller
Refer to P180 (Figure 4.6 and Figure 4.7)
• Feedback controller
Refer to P181 (Figure 4.8)
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.
Example of steel rolling mill
• Refer to P183-187
• 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)
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
T ( s) / T ( s)
S
G( s) / G( s)
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
How to define the error ?
• From input point:
E a (s)=R(s)-H(s)Y(s)
• From output point:
E (s)=R(s)-Y(s)
Only for unit feedback H(s)=1,We have
E a (s)= E (s)
Comparison of error
• Open-loop system
Eo ( s)  R( s)  Y ( s)  (1  G( s)) R( s)
• Closed-loop system
1
Eo ( s) 
R( s ) ,
1  G( s)
for H ( s)  1
continue
• Open-loop system under unit step input
1
eo ()  lim sEo ( s)  lim s(1  G ( s ))  1  G (0)
s 0
s 0
s
• Closed-loop system under unit step input
1
1
1
ec ()  lim sEc ( s)  lim s(
) 
s 0
s 0
1  G ( s) s 1  G (0)
Example illustration
• Refer to P189-190
An example of first-order system
3.6 The cost of feedback
• Increase of complexity
• Loss of gain
• Instability
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.
3.7 Design examples
• English channel boring machines
PD controller, and how to select K ?
• Mars rover vehicle
To compare the sensitivity and steady-state error
between open-loop and closed-loop system
3.8 Simulation using MATLAB
• Refer to P196-202
• Self-learning after class
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 P205-207
Assignment
•
•
•
•
•
•
E4.1
E4.3
E4.4
E4.6
E4.8
P4.2 , P4.5, P4.7