elephant clock

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King Fahd University of Petroleum &Minerals Electrical Engineering Department Control Engineering ,Term Project, semester: 112 Elephant Clock Modeling & Simulating Prepared for : Dr. Ahmad Masoud By : Fares Ali Yahya AlAmri (Section: 3) ID# 200845960 Abdullah Jaber Yahya (Section: 1) ID# 200816940 Submitted:14/05/2012

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Page 1: Elephant clock

   

 

 

 King  Fahd  University  of  Petroleum  &Minerals  

Electrical  Engineering  Department     Control Engineering ,Term Project, semester: 112

Elephant Clock Modeling & Simulating

   

Prepared  for  :    Dr.  Ahmad  Masoud    By  :    

Fares  Ali  Yahya  Al-­‐Amri  (Section:  3)  -­‐  ID#  200845960  Abdullah  Jaber  Yahya  (Section:  1)  -­‐  ID#  200816940  

Submitted:14/05/2012    

     

Page 2: Elephant clock

 King  Fahd  University  of  Petroleum  &Minerals  

Electrical  Engineering  Department    

Control  Engineering,  Term  Project,  semester:  112  

2  |  P a g e    

 

 

Introduction:  

During this course, we appreciated the use of MATLAB as an important tool in electrical engineering in general and in control engineering precisely. This program allows a full platform of simulating different theories & aspects. In these papers, we will implement molding & simulation on an ancient clock called "Elephant Clock" with applying the knowledge we had from this course.

Page 3: Elephant clock

 King  Fahd  University  of  Petroleum  &Minerals  

Electrical  Engineering  Department    

Control  Engineering,  Term  Project,  semester:  112  

3  |  P a g e    

 

Brief  overview:    

The elephant clock was an Islamic invention by al-Jazari, consisting of a weight powered water clock in the form of an elephant. The various elements of the clock are in the housing on top of the elephant. They were designed to move and make a sound each half hour.

All details are specified on the presentation

Figure  1:  Elephant  clock        

   

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 King  Fahd  University  of  Petroleum  &Minerals  

Electrical  Engineering  Department    

Control  Engineering,  Term  Project,  semester:  112  

4  |  P a g e    

 

The  modeling  of  the  clock:    The  input  of  the  system:  Water  

The  output  of  the  system:  Time                Process  used  to  achieve  the  output:  

A-­‐ Tank-­‐string  system.  

figure2:  Tank-­‐string  System  

B-­‐ Ball  blocking  system.  

 figure3:  Ball  -­‐blocking  System  

 C-­‐ Ball  transferring  system.  

 figure4:  Ball-­‐transferring  System  

 D-­‐ Notification  system.  

 figure5:  Notification  System  

 

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 King  Fahd  University  of  Petroleum  &Minerals  

Electrical  Engineering  Department    

Control  Engineering,  Term  Project,  semester:  112  

5  |  P a g e    

       

E-­‐ Repeat.  

 figure6:  Repeat    System      

   

 So,  we  connected  these  processes  into  the  following  block  diagram:    

   

Figure  7:  Elephant  clock  block  diagram        

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 King  Fahd  University  of  Petroleum  &Minerals  

Electrical  Engineering  Department    

Control  Engineering,  Term  Project,  semester:  112  

6  |  P a g e    

 

Analysis:    

We  need  to  analyze  each  system  in  detail:    

A-­‐ Tank-­‐string  system  The  purpose  of  the  system  is  to  pull  the  string  if  the  Bucket  [in  the  tank]  is  full  of  

water.  The  process  will  be  as  the  follow:  the  water  enters  the  clock  at  a  specific  flow  rate.  The  flow  rate  of  the  water  =  1000  cm3/min.  So,  we  need  to  find  the  volume  of  the  water  after  each  half  an  hour:  

 𝑉𝑜𝑙𝑢𝑚𝑒 = 𝐹𝑙𝑜𝑤  𝑅𝑎𝑡𝑒 ∗ 𝑇𝑖𝑚𝑒  

                                               = 1000  𝑐𝑚!

𝑚𝑖𝑛  ∗ 30  𝑚𝑖𝑛  

                                                 = 30,000  𝑐𝑚! = 0.03  𝑚! = 30  𝑘𝑔  

       As  you  can  see  from  the  previous  result,  we  found  the  expected  water  weight  after  

each-­‐half  hour.  So,  now  we  need  to  use  a  string  that  has  a  maximum  tension  force  of:  

𝐹 = 𝑚  𝑔 = 30  𝑘𝑔 ∗ 9.8𝑚𝑠!= 294  𝑁    

Therefore,  each  half-­‐hour,  the  bucket  will  be  filled.  Then  the  weight  of  the  bucket  will  exceed  the  maximum  tension  force  of  the  string.  So,  the  string  will  be  pulled.  Thus,  the  process  will  continue  into  the  next  phase.  

           

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 King  Fahd  University  of  Petroleum  &Minerals  

Electrical  Engineering  Department    

Control  Engineering,  Term  Project,  semester:  112  

7  |  P a g e    

   B-­‐ Ball  blocking  system  

 After  the  string  is  pulled,  the  ball  will  be  released.  This  ball  will  go  to  the  tip  of  the  

see-­‐saw  in  the  top  of  the  elephant.  This  ball  will  pull  the  solid  string  that  is  attached  to  the  water  bucket.  Therefore  this  ball  will  pull  the  bucket  out  of  the  water.  Then  the  system  will  go  to  next  phase.      

 C-­‐ Ball  transferring  system  

 The  ball  will  be  transferred  back  to  its  original  place.  Obviously,  that  is  because  of  the  

"see-­‐saw  mechanism"  that  exists  in  the  top  of  the  elephant.  When  the  ball  fall  to  the  tip  of  the  see-­‐saw  system,  it  will  go  back  to  the  original  place.  

 Meanwhile,  the  process  of  returning  the  ball  back  will  lead  in  pulling  another  string.    D-­‐ Notification  system  

 That  string  will  pull  the  hand  of  the  Mahout  (machine-­‐man),  so  he  will  hit  the  drum.  

This  drum  is  considered  to  be  the  time  notification,  which  means  that  a  half-­‐hour  has  passed.  And  this  is  our  desired  output.  

 E-­‐ Repeat  

 The  whole  system  will  be  automatically  repeated.    The  bucket  is  empty  because  of  

the  whole  under  it,  so  it  will  wait  for  another  30  minutes  to  be  filled.  Therefore,  the  pervious  processes  will  be  repeated  over  and  over  again.  

           

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 King  Fahd  University  of  Petroleum  &Minerals  

Electrical  Engineering  Department    

Control  Engineering,  Term  Project,  semester:  112  

8  |  P a g e    

 

Simulation:     But  before  that,  we  need  to  convert  our  system  into  a  "mathematical  model"  .So:  

The  input:  it  is  clear  from  the  analysis  of  this  system  is  that  the  input  is  water.  And  we  have  said  that  the  input  can  be  determined  by  the  following  equation:  

= 𝐹𝑙𝑜𝑤  𝑅𝑎𝑡𝑒 ∗ 𝑇𝑖𝑚𝑒  = 𝑓𝑟 ∗ 𝑡  

The  output:  We  said  that  the  output  of  our  system  is  a  time  notification  each  30  minutes.  So,  we  let  the  output  increase  by  1  each  30  minutes.  Which  means  that  if  the  output  changed  by  1,  that  means  the  water  bucket  has  been  pulled  out  from  the  water.  Which  means  30  minutes    passed.    The  Processes:  We  can  simplify  all  of  the  systems  into  one  block.  So  how  can  we  find  its  function?    Well,  since  we  have  the  output  and  the  input,  we  can  draw  its  own  block  diagram  as  seen  in  Figure  8.  

Figure  8:  Input-­‐output  block  diagram    

As  you  can  see  from  figure  2,  we  can  find  the  function  of  all  of  the  process  by  seeing  how  the  output  and  the  input  behave.  So,  our  function  is:  

= 𝑥 − 𝑦  = 𝑓𝑟 ∗ 𝑡 − 𝑦  

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 King  Fahd  University  of  Petroleum  &Minerals  

Electrical  Engineering  Department    

Control  Engineering,  Term  Project,  semester:  112  

9  |  P a g e    

     So  now  we  can  simulate  it.  

   

We  used  the  MATLAB  to  simulate  our  system.    MATLAB  code:      

        These  are  the  results:              

%Choose the time you want (in minutes) t=0:0.1:75; %The input, which is flow rate of the water =1000 cm^3/min, which is the input fr=1000; %The output of the system: y= round((t*fr/(30*1000))-0.5); %processes: u=(t*fr/(30*1000))-y; figure(1) plot(t,u) title('Tank String System') grid figure(2) plot(t,y) title('The output of the system') grid  

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 King  Fahd  University  of  Petroleum  &Minerals  

Electrical  Engineering  Department    

Control  Engineering,  Term  Project,  semester:  112  

10  |  P a g e    

 

     

0 10 20 30 40 50 60 70 80-1

-0.5

0

0.5

1

1.5

2The output of the system

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 King  Fahd  University  of  Petroleum  &Minerals  

Electrical  Engineering  Department    

Control  Engineering,  Term  Project,  semester:  112  

11  |  P a g e    

 

                 

0 10 20 30 40 50 60 70 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Tank String System

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 King  Fahd  University  of  Petroleum  &Minerals  

Electrical  Engineering  Department    

Control  Engineering,  Term  Project,  semester:  112  

12  |  P a g e    

   

   

Conclusion:   In this project the implementation was performed via MATLAB. The elephant clock may consider as a closed system and its behavior is continuous with the help of the automaton. As you can see from the previous graphs:

In the first graph, the output of the system [which is the time notification] will only occur after every half-hour. Please notice that the output will increase by 1 every 30 minutes.

Whereas in the second graph, the inside system [with the feedback effect] will be repeated after each half-hour. Which means the bucket is empty at t = 0, and it starts to take the water until its full after 30 minutes. Then the system will be repeated, and it will make a time notification as an output. Then the system will be repeated over and over again.