The Coupled Tanks System (Figure 1) emulates an engineering scenario where it is critical to...

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The Coupled Tanks System (Figure 1) emulates an engineering scenario where it is critical to maintain a desired fluid level. The coupled tanks system can have single or multiple inputs and output(s). The rigs were designed to allow students to acquire data from a physical dynamic system to develop a simplified model of the underlying dynamics. Students are asked to design controllers for the dynamic system and to analyse the performance of the controllers in maintaining the water level in Tank 2. You are required to read the documents “Coupled_Tanks_Generation II_UserGuide_V2- 3.pdf” and “Coupled_Tanks_Calibration_Data_ XXXXXXXXXXpdf” for detailed information about the coupled tank system. Figure 1 - Coupled Tanks Rig, Generation II P. 2 This project requires you to design P and PD controllers for the remote lab’s coupled tank system by applying the design methods covered in the lecture and tutorial classes. The purpose of the controller is to make the water level of tank 2 ( ) track a reference level . The block diagram of the control system for the coupled tanks is shown in Figure 2. Your task is to design the controller to meet certain design specifications.
	
Document Preview: 48660 Dynamics and Control 
Project 1 - Parts 2 and 3: Design of controllers for a coupled 
tank system (Part 2); and experimental verification (Part 3) 
 
The Coupled Tanks System (Figure 1) emulates an engineering scenario where it is critical to 
maintain a desired fluid level. The coupled tanks system can have single or multiple inputs and 
output(s). The rigs were designed to allow students to acquire data from a physical dynamic 
system to develop a simplified model of the underlying dynamics. Students are asked to design 
controllers for the dynamic system and to analyse the performance of the controllers in 
maintaining the water level in Tank 2. 
 
Figure 1 - Coupled Tanks Rig, Generation II 
 
You are required to read the documents “Coupled_Tanks_Generation II_UserGuide_V2- 3.pdf” 
and “Coupled_Tanks_Calibration_Data_ XXXXXXXXXXpdf” for detailed information about the 
coupled tank system.  
 
P. 1This project requires you to design P and PD controllers for the remote lab’s coupled tank 
system by applying the design methods covered in the lecture and tutorial classes. The purpose 
of the controller is to make the water level of tank 2 ( ) track a reference level    . The 
        
block diagram of the control system for the coupled tanks is shown in Figure 2. 
h h
2,ref      G 2,m
o
 +        
C(s)
2
reference
measured
    ?
s + as + b
level
level
controller
coupled tanks plant
 
Figure 2 - Closed Loop Block Diagram of the Coupled Tanks System 
 
Your task is to design the controller      to meet certain design specifications. The general 
form of this controller is given by:

The transfer function of the coupled tanks plant is given by:

Where the coefficients of the plant transfer function are:

P. 2Students are required to produce a report detailing the following four tasks: 
Task 1: Controller Design 
 
You are asked to design the following controllers to meet the...

Robert · Accepted Answer

TASK 1
a) In this task we need to design a proportional controller for a given control system in order 
to achieve the steady state error of 8% of the reference level.
Now, the coupled tank closed loop system with controller C(s) is as shown in figure 
 
 
Let the proportional controller be  
( ) PC s k
 
 
The transfer function of the coupled tank system is given by  
2
( ) o
s
G
G s
s 

   
 
Now, the transfer function for closed loop system will be  
2, 2,( ) ( ) ( )ref mE s H s H s   
 2,( ) ( ) ( ) ( ) ( )refE s H s E s G s C s   

2, ( )
( )
1 ( ) ( )
refH s
E s
G s C s


 

2
2
, ( )
( )
1
ref
P o
H s
E s
k G
ss  


 
 
Apply final value theorem  
2,
2
0
( )
( )
1
ref
P os
H s
e s
k G
ss
Lim
 

  
  
  
       
  
Now, we have  
2,
50
( ) , 0.009534, 0.277, 0.00815ref o
mm
H s G
s
   
On putting this value we have 
 
0
2
2
50
( )
s P o
s
s
s
e
s k G
Lim
 
 
  
 
   
 
  

 50
( )
P o
e
k G





Now, we have  ( ) 4e    

 
 
0.00815
0.00815
50
0.08*50
0.009534Pk


 
     0.08*50 0.0095340.00815 0.0081550Pk   
 10Pk 
b) In this task we need to design a PD controller for a given control system in order  to ensure 
a rise time of about 5 seconds and a 1% settling time of about 15 seconds.
Now, the coupled tank closed loop system with controller C(s) is as shown in figure 
 
 
Let the proportional controller be  
( ) P dC s k sk 
 
 
The transfer function of the coupled tank system is given by  
2
( ) o
s
G
G s
s 

   
 
Now, the transfer function of closed loop system will be given by  
2,
2,
( ) ( ) ( )
( ) 1 ( ) ( )
m
ref
H s C s G s
H s C s G s

  

 
 
2,
2
2
,
2( )
( )
1
o
P d
m
ref o
P d
G
k sk
H s s
H s G
k sk
s
s
s
 
 
 
  
  
 
   
  
 

 
 2
2,
2,
( )
( )
m o P d
ref P d o
H s G k sk
H s s s k sk G 


     
    
2,
2
2
,

The Coupled Tanks System (Figure 1) emulates an engineering scenario where it is critical to maintain a desired fluid level. The coupled tanks system can have single or multiple inputs and output(s)....

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