Prepare For: Dr.Samir Al-Bayiat Electrical Engineering Department EE 550 Electrical Engineering...
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Transcript of Prepare For: Dr.Samir Al-Bayiat Electrical Engineering Department EE 550 Electrical Engineering...
Prepare For: Dr.Samir Al-Bayiat
Electrical Engineering Department
EE 550
Electrical Engineering Department
EE 550
الرحيم الرحمن الله بسم
King Fahd University of Petroleum and Minerals
الرحيم الرحمن الله بسم
King Fahd University of Petroleum and Minerals
5 June
Presented By: Fahd a. al-Khuraish
Presentation Outline
BACKGROUND • INTRODUCTION • TIME DELAY ANALYSIS • TIME DELAY APPROXIMATION • SYSTEM MODELING WITH DELAY • SIMULATIONS• CONCLUSION
BACKGROUND
FOR SIMPLIFICATION OF DYNAMIC SYSTEM:
System Response (depend on the present stare+ initial condition) Which leads to ingoing the time delay.
If we consider it , what will happen.
INTODUCTION
Delay might be from certain factors:
- Energy transmission.
- System physical properties.
- System variable measurement.
Examples will provided to understand these factors.
DELAY SYSTEM ANALYSIS
One can ask how is the time delay modeled? One can ask how is the time delay modeled?
Tank,heater & agitator motor
Outlet:F and G (20 meters far a way ) temperature sensors
At reset all off & no heat loss between F & G Then , responses will be as follows: (after to for G)
Tank,heater & agitator motor
Outlet:F and G (20 meters far a way ) temperature sensors
At reset all off & no heat loss between F & G Then , responses will be as follows: (after to for G)
to= Pipe length/fluid velocity , or
Pipe volume/volumetric flow rate
For instant, if the fluid velocity is 1 m/s and the two sensors have a
distance 20 meters between them, the delay time is calculated as
to=20/1 =20 s, in this case.
to= Pipe length/fluid velocity , or
Pipe volume/volumetric flow rate
For instant, if the fluid velocity is 1 m/s and the two sensors have a
distance 20 meters between them, the delay time is calculated as
to=20/1 =20 s, in this case.
• The time delay at time domain and lap lace transform
can be written as follows.
g(t)=f(t-to) u (t-to)
G(s)=e-sto F(s)
• We noticed that delay time is considered by multiplying the system transfer function by nonlinear function of e-sto that is called pure time delay.
• It has a formula ‘can be calculated :average velocity and it is not applicable for all systems. Therefore, the time delay function is usually approximated.
DELAY SYSTEM ANALYSIS (Cont.)
TIME DELAY APPROXIMATION
• The pure time delay can be expanded using the Taylor series as:
• The above equation is approximated into rational functions by
different formulas. The widely used approximation rational function is named as Pade approximation. It can be approximated simply as one pole and one zero (called 1/1):
•
• Or two zeros and two poles (2/2):
...!3
33
!2
221
sdsd
sde sd
21
21
ds
ds
e sd
1221
1221
22
22
ds
ds
ds
ds
e sd
SIMULATIONS (Part 1& 2)
• First:The 1st, 2nd, 3rd and 4th orders of pade approximation with open loop simple transfer function G(s) Simulation.
• Second: Three blocks Simulation which having same a mount of delay but delay location has been assumed differently.
1
1
s
tG
1
1
s
tG 1
1
s
tH
RESULTS• The many term we include in the exponential (high
order pade approximation) the better performance we get (Response shape & Less Oscillation).
• Having a delay in the feedback will lead to less oscillation in case of there is no delay in the feed foreword function. On the other hand, if there is a delay in the feed foreword function and no delay in the feedback function, the system will have an oscillation but it will be less than the first one. In case of having both delays in the feed foreword and feedback functions the will we have biggest oscillation and the system will take long time to go to steady state.