Discrete Control Sysfstem in LabVIEW.pdf

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1. Hans-Petter Halvorsen
https://www.halvorsen.blog
Discrete Control
Systems in LabVIEW

2. •Introduction
•Mathematical Model
–Discretization –We will make a Discrete version of the Model/Differential Equation
•PID Controller
–Discrete PI Controller –We will make a Discrete version of the standard continuous PI Controller
•Control System
–We make a basic Control System where the Discrete Model and Discrete PI Controller are used
Contents

3. Hans-Petter Halvorsen
https://www.halvorsen.blog
Introduction
Table of Contents

4. Introduction
•We will simulate a 1. Order
Process/Differential Equation
–We will Implement a Discrete version of
the Model and perform Simulations
•We will create a basic Control System
–We will make and Implement a Discrete
PI Controller and perform Simulations

5. Control System
ControllerProcess! "#
−
Reference
Value Control
Signal%
%PID Controller
The purpose with a Control System is to Control a Dynamic System, e.g., an industrial
process, an airplane, a self-driven car, etc. (a Control System is “everywhere” today)
Feedback Loop

6. Hans-Petter Halvorsen
https://www.halvorsen.blog
Mathematical Model
Table of Contents

7. 1. Order System
1. Order
Process
" %
̇"=−%"+'(
)="
In order to simulate this model in LabVIEW you can make a discrete version of the
model, or you can implement it as a “Block Diagram” using the features in
LabVIEW Control Design and Simulation Module
Differential Equation of a 1. order System:

8. ̇%=1
)(−%+,")
Where !is the Gain and "is the Time constant
̇"=−%"+'( Dynamic
System"(.)%(.)
Assume the following general Differential Equation:
or:
Where #=!
"and %=#
"
This differential equation represents a 1. order dynamic system
Assume &(()is a step (*), then we can find that the solution to the differential equation is:
+(=!*(1−.$%
")
Input SignalOutput Signal
(byusingLaplace)
1. Order System

9. 100%
63%
,3
.
)
%.=,3(1−#/0
1)
45=%(5)
"(5)=,
)5+1
%(.)1. Order Step Response
Time constant
!is the Gain

10. Discretization
We have the continuous differential equation: ̇3=−#3+%&
We apply Euler: ̇3≈&'(!$&'
"!
Then we get:
36+1−36
")=−#3(6)+%&(6)
This gives the following discrete differential equation (difference equation):
)*+1=(1−-!%))(*)+-!'((*)
This equation can easily be implemented in any text-based
programming language or the Formula Node in LabVIEWWhere #=!
"and %=#
"

11. Discrete Model in LabVIEW
"#+1=(1−)!*)"(#)+)!,-(#)

12. Simulation in LabVIEW

13. Code

14. Hans-Petter Halvorsen
https://www.halvorsen.blog
PID Controller
Table of Contents

15. Control System
ControllerProcess! "#
−
Reference
Value Control
Signal%
%PID Controller
The purpose with a Control System is to Control a Dynamic System, e.g., an industrial
process, an airplane, a self-driven car, etc. (a Control System is “everywhere” today)
Feedback Loop

16. PID Controller
!"=$*%+$*
'+(
,
-
%)*+$*'.̇%
PID
Proportional GainIntegral TimeDerivative Time
/.-/-0Tuning Parameters:

17. !!=!!"#+$$%!−%!"#+$$
'%'&%!
%/=,/−./
DiscretePI Controller that we can implement in different programming languages:
(0=1!2+1!
3"4
#
$
256
PI Controller
Very often we just need a PI Controller:

18. -1=2"3+2"
)#4
$
%
356
We start with the continuous PI Controller:
̇"≈"#−"#−1
)!
We can use the Euler Backward Discretization method:
Where ")is the Sampling Time
Then we get:
-&−-&'(
)!=2"3&−3&'(
)!+2"
)#3&
We derive both sides in order to remove
the Integral:
̇&=!*̇.+!*
"+.
Finally, we get:
"7="7/8+,9#7−#7/8+,9
):);#7
Where.'=<'−+'
Discrete PI Controller

19. Hans-Petter Halvorsen
https://www.halvorsen.blog
Control System
Table of Contents

20. Control System
ControllerProcess! "#
−
Reference
Value Control
Signal%
%
PID Controller
The purpose with a Control System is to Control a Dynamic System, e.g., an industrial
process, an airplane, a self-driven car, etc. (a Control System is “everywhere” today)
Feedback Loop

21. Control System in LabVIEW

22. Built-in PID Controller

23. Discrete PI Controller
!!=#!−%!
&!=&!"#+($!!−!!"#+($
)%)&!!
Discrete PI Algorithm:

24. Discrete PI Controller (Alternative Solution)

25. Control System in LabVIEW

26. Control System Code

27. Summary
•A Basic Control System has been made using LabVIEW
•Lots of Improvements can be made, e.g.,:
–Improve GUI
•More Features/Functionality, More Intuitive and more user-friendly
–Improve Code Structure, e.g., use a State Machine principle
–Make a more robust PI(D) Controller
–Use and Test with a more complicated Process/Model
–Find better PI(D) Parameters using different Tuning methods, e.g., Ziegler-Nichols, Skogestad, etc.
–Connect and Control a Real Process using a DAQ Device
–Etc.

28. Hans-Petter Halvorsen
University of South-Eastern Norway
www.usn.no
E-mail: [email protected]
Web: https://www.halvorsen.blog