Eng. Zaid Abed Aljasim Muhasain Eng. saif Abed Aljasim
Muhasain
Control Eng, Al- Technology
University. Computer and
software Eng, AL-Nahrain University
e-mail:zaid_logic@yahoo.com.
E-mail:safe_aljibouri@yahoo.com
Z. A. Muhasain S.A . Muhasain
Abstract:
This paper deals with process control,
generalized definition and modeling design of flow systems and control it based
on compare to constant as principle of operation approach. After reviewing the
operation of the plant, a compare system between water level and desire level
is formulated to control flow rate. The scheme is then designed and tested by
Matlab and Simulink Toolbox. Simulation
is presented and shown that on/off switch with constraint is better and more
versatile compare with conventional approach.
Keywords: Process; controller; flow.
1. Introduction
The liquid level control systems have
been of good interest to engineers for along time. In the development this
system has increased because of studies expansion, methods multitude and easier
to implement this system in digital computer.
These experiments have been design and set up for the laboratory .In the
simple model of this system consist the valve, tank or more tank, float
,transducer and controller. The water will going to the two tanks interactive
(in the simple model) and its level will
be measured by float or any sensor and transducer in the conventional
state and then compare with desired
level to control input signal(inflow) as shown
fig bellow:
Figure (1) Two tank fluid system using
transducer to measure level.
In this paper,
we design a new scheme of two
tanks system. The purpose of it to present a new approach is similar to the
previous without using any float, sensor and transducer if we know the
parameter of pipe resistance (Resistivity) and cross section are of the two
tanks. We use a generalized definition for modeling and block diagram in design
it. It can be designed and implemented by using Matlab program simulation. Show
that this method is better and easier compared with conventional approach. This
approach simulation by Matlab is allow us to solve more complicate problem and
developing the measuring states to make
better modeling and analyzing of system and control allow more in the designs.
The design of a tow tanks fluid system can
control it according to the level without use any transducer. And the effect of
Resistivity is observed on the level of the two tanks and controller designs,
and show that the controller affects to the system performance. All simulation
is performed using Matlab / simulink. These results are achieved for research
and future study.
2. Modeling of the Liquid System
The fluid flow system are very common in
the process control .It can be modeled by using generalized definition and
modeling of hydraulic system.
2.1 Single Tank
For a single tank liquid level system is
illustrated in fig. (2). It must be know that, how to simplify the design in
the equation. This type of the system consists of source inflow rate qi into
the tank. A drain valve in this to regulate the water out flow rate (qo):
Figure (2) Single tank liquid level
system
R is the Resistivity which represent a
parameter due to pipe resistance, s/m2
Q is the Volume flow rate, m3/s
C is the Cross sectional area of the
tank, m2
qi is the inflow rate, m3/s
qo is the outflow rate, m3/s
H
is the water level in the tank, m
For the liquid level system in Fig.(2).
It can be obtained a Mathematical Model to get the relationship between qi and
qo or between qi and H.
The turbulent flow resistance can be
determining by the following relationship:
R = in the steady state
We will obtain this equation
R=
if the relationship is linear
The system is modeled by using physical
principles .The physical equation governing the change in liquid store (ACC)
Change in the liquid store (ACC) = input
- output
Cross section area (C) =
C =
C is constant
So that .Applied the balance equation
Acc= I/P - O/P =
2.2 Two Tanks
Now we design a hydraulic system with
two tanks as interaction network and use this equation in the two tanks .It
consists of source, two tanks and
pipe between them. qi may be represent a
water from motor to tank 1 as show in fig (3) :
Figure (3) Liquid system in the two
tanks as interaction network
In the tank 1
Acc1=In – Out = q - q1 (1)
R = In the steady state
R1 = q1= (2)
The Laplace domain can be used to solve
this equation:
Q1(S) =
(3)
Modeling of system requires us to
determine the relationship between (h1-h2 ) and divided by R1 as show in the
block diagram fig. (4):
Figure (4)
Cross section area (C) = Acc =
From equation 1 we obtain this equation
Acc1=In – Out = q- q1
q - q1 =
We
take Laplace domain so we
get
Q (S) – Q1(S) =C1SH1 (4)
From the previous equation draw the
second block diagram by subtract Q – Q1 and divided by C1S as shown in fig.
(5).
Figure (5)
The liquid inflow q(s) and q1 as the
flow out from tank1 to tank2
In tank2
R2 = in the steady state
R 2=
The third block diagram from dividing H2
by R2
Acc2 = in – Out = q1-q2
Cross section area of tank 2 (C2) = = C2.
In Laplace domain Acc2=C2SH2
Applying these equations obtain
Q1(S) – Q2(S) =C2SH2 (5)
H2 =
This equation can be modeled by block
diagram by subtract Q1(S) – Q2(S) and divided by C¬2s and we get h2(s) as o/p
Figure (6)
It can obtain the produce block diagram
by getting the component block diagram from
the previous shape, and putting all
form pieces to make the final block as show in fig. (7) Diagram. It must determine what the input and
output for the block
Figure (7) Final block diagram
In this work, the output (level) is used
to control the input flow rate and maintained the water with the desired level
so as not to overflow the water.
3. Simulation and Controller
3.1 Simulation
After all block diagram was completed
for the liquid level system. It can now be implemented this diagram and system
in a simulation model. This block is used to represent the two tanks system.
Matlab program was used to simulate this system. A step input in the simulink
is referred to the process input as an
inflow rate (qi). The simulation in the system consists of a function block of
the cross section area(C) and parameter resistivity (R) in a transfer function;
we can obtain it from a block transfer function. A scope is used to display
output (q2) and scope1 to display the water level. In the two tanks (h1, h2)
this figure illustrates a simulation of model of this system:
Figure (8) Simulation represents block
diagram of the
Liquid level system with two tanks
In the simulink, simulate inflow (Q=2
m3/s) as a step input is 2 and step time is zero. Let cross section area in
tank 1 (C1) equals 0.785 m2 and in tank 2 (C2) is equal 0.635 m2 (C1 and C2 is
constant) in this design. Firstly assume the Resistivity parameters equal
(R1=100 s/m2, R2= 100 s/m2). We must change a stop time 1000 (remember that
simulink used second as time unit). From simulink scope monitors (q out),
scope1 monitors water level in the two tanks h1 and h2. This figure below
illustrates the trajectory of these scopes.
Figure (9) response of liquid level in
the two tanks with time
To know that the level in both tanks is
less or more than the desire level, A (Compare To Constant) block from simulink
is used for implementing this and connect to the level (h1, h2). In this design
assume that the height (in both tanks) is 13m and the water level must be less
than 10 m. It can implement by using a (Compare To Constant) block from
simulink and go to the logic and bit operation. The constant value is compared
with h1, h2. If the level of the water equals or less than 10m, The (Compare To
Constant) will give an o/p equals 1, else of this (the water level is more than
10m) the o/p is zero. The figure illustrates this process.
Figure (10) show the detection the level
in the tank by using compare constant
From this design (Compare1) is shown
from scope1. Firstly Compare To Constant 1
equals 1 depending on h1. If h1 reaches to 10m, constant compare will
being to zero. Also compare 2 is used for h2 if h2 reaches to 10 m compare2
drops to zero, it illustrates by scope1 in fig. (11)
Figure (11) changing in the Compare to
constant corresponding with the level in the two tanks
3.2 Controller Design
After a (Compare To Constant) block is
used in the previous to detect if the water is less or more than ten meters. A
control system can be used to open or close the i/p depending on (Compare To
Constant) block. The output signal from a (Compare To Constant) block is back
to the input and multiplying by using Product from simulink for implementing
this controller as show in fig. (12):
Figure (12) controller design by used
product
This control will make the input is
close if water in tank 1 is more than 10m , also input is close if water level
in tank 2 is more than 10m . The table blow illustrates this process with
Q = i/p * Compare To Constant 1 *
Compare To Constant 1
Water level in
Tank1(h1) Water level in
Tank2(h2) Compare To Constant 1 Compare
To Constant 2 q
Less or equal 10 m Less or equal 10 m 1 1 i/p(open)
More than 10 m Less
or equal 10 m 0 1 0(close)
Less or equal 10 m More than
10 m 1 0 0(close)
More than 10 m More
than 10 m 0 0 0(close)
Table (1) controller effect in the i/p
If h1 < = 10 and h2 <= 10 q is open else q is zero
We conclude from this if the level of
the water accesses more than ten meter, the inflow will closed depending on the
controller so as no to overflow any tank of this system .The next simulation
show in fig. (13) Illustrates this control in the system.
Figure (13) Simulation of the system
with controller design
4. Implementation and Result
From fig.(13), after run the system the
scope1 shows that the level in both tanks (h1, h2) will increase with the time.
The research finds another way to control. The controller is close the input
and prevent any increase of the level of the water so as not to overflow any
tank. The simulink specification provides information about the level with time
and time of open and closes the input by the controller. The system adjusted to
control the water level. Firstly assume that the resistivity parameters is
R1=100 and R2=100 and stopping time is 50 seconds. A scope1 shows this process
as show in the figure:
Figure (14) result of control of liquid
level and inflow using controller design R1=100 R2=100.
From fig (14) one can notice that, the
level in tank1 doesn’t increase of ten meters and the input will be close from
2 to zero when the water level will reach to 10m at 4 sec .A series of tests
using in the system by changing the parameters R1, R2 and show the comparative
result and efficiency of system and controller which describe the output
response.
In case 2 .We try to change this
parameter by increasing R2 and parameters will be R1 =100, R2=200 to show the
ability and effect in the controller as show in fig. (15):
Figure (15) System behavior and
controller by changing Parameters to R1=100 R2=200.
From fig (15), When a scope1 trajectory
is finished the change in the resistivity parameter (increasing R2) from 100 to
200 in the system will cause increasing of height
in tank2 (R2) from 4 to 4.5
m. The tank 1 stills in the same height.
In case3, Change the resistivity
parameters (by decreasing R1) R1= 50,
R2 = 200 in the system and the test results are showed by scope1 as show
in figure below:
Figure (16) System behavior and
efficiency by changing parameters to R1=50 R2=200.
From fig.(16) (case3), The changing in
the parameters will cause change in the level in tank2 which reach to 7 m and
input will close and open more than time.
In the case 4 .Change the
resistivity by decreasing R1 , R1= 10
,R2 = 200 and change stop time to 1000
to show more effect of controller with the time .This leads to the steady state
as show in the fig.(17).
:
Figure (17) Show results in the level in
the two tanks and controller efficiency.
And it notice that the level in both
tanks will reach almost to ten meter and doesn’t access this level. The change
in the parameters can be adjusted the
water level.
5. Conclusion:
The purpose of this paper is to present
a controller of the liquid system with two tanks without using any float,
sensor, transducer if we know the parameters of pipe resistance. The problem
used to control level in the tanks by adjusting flow rate of the liquid
entering the tank. After reviewing the operations of the system, simulation are
present and are showed that the level of the water doesn’t access the desire
level although of a little error of a few accessing of the water from desire
level because of (Compare to Constant). In this work will be shown that high
efficiency, fast response and accuracy in the controller. It can be conclude
that the controller yield is better performance than the other controller. The
results of modeling can be present an important means to measure and control
more instruments and support the studies in the scientific laboratories. In the
experiments installation in Matlab program, we must interface computer with
electrical instruments that give the facilities understanding.
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