King Fahd University of Petroleum and Minerals Electrical

ﺑﺴﻢ ﺍﻟﻠﻪ ﺍﻟﺮﺣﻤﻦ ﺍﻟﺮﺣﻴﻢ King Fahd University of Petroleum and Minerals Electrical Engineering Department EE 550 Prepare For: Dr. Samir Al-Bayiat Presented By: Fahd a. al-Khuraish 5 June

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.

Examples:

DELAY SYSTEM ANALYSIS 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) 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.

DELAY SYSTEM ANALYSIS (Cont. ) • 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.

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):

SYSTEM MODELING WITH DELAY

SIMULATIONS (Part 1& 2) • First: The 1 st, 2 nd, 3 rd and 4 th 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.

SIMULATIONS (Part 1& 2)

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.

CONCLUSION • OVERALL SUMMARY : • BENEFIT FROM THIS SEARCH