-
Specialties::
• Flying Vehicles and Complexes Control Systems
• Control Systems and Automatics
• Aeronavigation Systems
discipline:
Automatic Control Theory
Course, semester, academic. year:
3, Fall, 2011/2012.
Department:
301 – Flying Vehicles Control Systems.
Training Manager:
Professor, Doctor of Science Anatoly S. Kulik
SUMMARY Lecture number 8
Theme number 1: QUALITY of automatic
Stabilization SYSTEMS
«No desire more natural than the desire for knowledge» Michel de Montaigne (1533 - 1592) - French philosopher and humanist, considered the human as the most valuable
Re
ASS automatic stabilization system can be in two states: operable and inoperable.
• Any other condition of the system will not function.
• Perform ance the required functions - is the stability and preservation of the setting values of parameters - quality!
Automatic stabilization system would work if it is stable and meets the specified quality parameters.
Thus, the stability is a necessary and sufficient condition for the quality of the practical suitability of ASS, i.e. efficiency.
Consider quality of ASS, in relation to the following functional diagram
Accuracy of stabilization - the main requirement for any ASS. Stabilization accuracy is characterized with the instantaneous values of deviation
indirect
characterization
where –
the set point
-
voltage of correcting element.
direct
response
where
-
setting value of the angular velocity of the working mechanism;
-
The current value of the angular velocity of the electric motor.
Indirect characterization
where
-
tachometer preset voltage, corresponds to a specified angular
velocity
-
tachogenerator current voltage.
How are errors
in the steady state?
But in the transition?
ASS reaction to a step change of the disturbance would be:
What will be the
schedule for the error
graphics?
?What
is the difference in
graphics?
Image of the ASS error caused by disturbance can be derived from the structural diagram of ASS
Where
-
the transfer function of the controller
-
PA transfer function
-
transfer function of the CE
-
the reference variable image
-
an image of rejection
-
the image of
;
-
an image of signal representative of the disturbance
;
=
Image of tachogenerator voltage
=Image
of voltage of correcting element.
Transform the block diagram to the form
Of this structural scheme transfer function followes
.
Then
.
.
Steady-state error is defined by the final value theorem
.
The theory of operational calculus
The total ASS error analytically determined from such an operator equation
Why
like that?
Why
sum?
?
Here
– the transfer function of the closed loop system error caused by
the reference variable
.
Full error in accordance with the final valuetheorem will be
.
Example 8.1. We define the steady-state values of laboratory errors from SAS disturbance for the following values
we
calculate value
Further,
since the
,
that
therefore,
So,by
setting the error value of the disturbance
Identify, please set the value for the error of the control action,
and the total value of the error!
Settling time - a direct indicator of the quality that characterizes the inertial properties of the SAS, and hence its swiftness.Settling time –
is
determined by the duration of the transition process. In theory, the
transition process lasts forever. (why?)
In practice,they consider that the transition process is completed
as soon as the deviation of stabilized value from the set point will
not exceed the specified accuracy of stabilization. Direct measures
are determined by the step response.
|
|
Let’s consider the effect of a negative feedback to the swiftness of SAS as an example of a closed loop system of laboratory. The converted block diagram of a closed loop system can be represented in a form
|
|
.
Lets
Then
.
If
то
.
Conclusion:
A
unit negative feedback led to a substantial decrease
and
,
consequently,using negative feedback we can change the dynamic
properties of the system.
If
then
.
Conclusion:
Transfer
coefficient of the open loop system influences more on
significantly.