1.0
Introduction
1.1
Project Background In many industries process such as petro chemical industries, paper making industries and water treatment industries are using the tank system to control the liquid level. The liquid level must be controlled by the proper controller. The objective of the controller in the level control is to maintain a level set point at a given value and be able to accept new set point. The conventional proportional- integral- derivative (PID) is commonly utilized in controlling the level. On the other hand, the fuzzy logic controller (FLC) is also popularly implemented in many practical industries application.
The use of feedback control strategies is one of the most common ways to control a process, but it is important to consider that feedback control is an errordriven strategy; correction to any upset in the process we want to control depends on the error or difference between the desired value of the “controlled” variable variable and its current value. By the other hand, the feed forward control strategies use the knowledge of the process behavior to take action before a perturbation to the process has any effect on the controlled variable. Several methods has been discussed to implement a feed forward control strategy, one of them is steadystate models, which is the process to determinate the value that the manipulated variable should has to compensate the effect of perturbations on the controlled variable.
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1.2
Problem Statement The control of liquid level in tanks and flow between tanks is a basic problem in the process industries. The process industries require liquids to be pumped, stored in tanks, then pump to another tank, as an example the water closet (WC) toilet in our house is also a liquid level control system. The swinging arm attached to the input valve of the WC water tank allows water to flow into tank until the float rises to a point that closes the valve. Many times the liquids will be processed by chemical or mixing treatment in the tanks, but always the level of liquid in the tanks must be controlled, and the flow of the tank must be regulated because of avoiding the water level at critically level due to continuously operation. There are many alternative controller design theories that can be used to control the level of liquid on tanks. Proportional integral derivative control is one of a kind of control strategies that uses to control the level and flow of liquid. Proportional control, PI control, PD control and PID control will be investigate to determine which controller is the best for liquid level control.
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1.3
Objectives
The objectives of the project are:
To analyze the current system
To improve the system response of pump using PID controller with desired condition i. Rise Time < 0.2s ii. Overshoot = 20% iii. Settling Time < 0.8s iv. Damping in between 0.4
1.4
Design the PID based on the reference performance system.
Scope of Project 1.4.1
Study a mathematical modeling of the system
1.4.2 Analyze the current system in term of stability, performance specification and response. 1.4.3
Design the system to fulfill the desired requirement related to objectives
1.4.4 Study the simulation tools MATLAB and SIMULINK for analysis and design to express system stability, performance specification and response.
.
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1.5
Schematic Diagram
Pump
Tank
Reservoir
Figure 1.5.1 - without PID
Controller
Sensor
Pump Tank
Reservoir
Figure 1.5.2 - with PID
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2.0
Mathematical Modeling
Tank :-
Mass In = Mass Out Rate Mass In – Rate Mass Out = Accumulate fluid in tank
w (i) – w (o) = rho*
;
= A ()() =
sH(s) =
()()
H(s) =
()()
W (i)
W (o)
Figure 2.0 - Tank 5
2.1
Block Diagram
Controller
input
Pump
Tank
P
T
C
h
S Sensor
Figure 2.1.1 - Block Diagram
() ()
Parameters:
A = (rho*area) = 2
a=3
b = 1
() ()
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U(s)
Y(s)
b
Figure 2.1.2
U(s)
Y(s)
( )
b
Figure 2.1.3
U(s)
Y(s)
Figure 2.1.4 7
3.0
Design Using Simulink
Without PID Controller:-
Figure 3.0.1 – without PID
Figure 3.0.2 – Response without PID 8
With PID Controller:-
Figure 3.0.3 – with PID
Figure 3.0.4 – Response with PID
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The Simulink without PID and with PID result shown as below:Without PID
With PID
Overshoot
high
<20%
Rise Time
high
<1s
Settling Time
high
<1s
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4.0
Design Using Matlab
4.0.1
Design Requirement:i. Rise Time < 0.2s ii. Overshoot = 20% iii. Settling Time < 0.8s iv. Damping in between 0.4
4.0.2
Without PID:-
Figure 4.0.2 – Response without PID (Step Response, Bode Diagram, Root Locus, Nyquist Diagram)
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4.0.3
With PID:-
Figure 4.0.3 – Response with PID (Step Response, Bode Diagram, Root Locus, Nyquist Diagram)
The comparison result between PID and without PID in Matlab:Without PID
With PID
Overshoot
No overshoot
<20%
Rise Time
4s
5s
Settling Time
15s
20s
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4.0.4
Choosing The Value of Gain, K
K = 0.3
K = 0.4
K =0 .5
K = 0.6
K = 0.7
Peak
1.05
1.09
1.11
1.14
1.16
Overshoot (%)
4.81
9.37
11.4
13.8
15.9
Rise Time, s
5.38
3.92
3.44
2.96
2.62
Settling Time, s
14.9
12.5
11.4
13.9
13.5
4.0.5
The gain was chosen is K = 0.5.
Compensator Equation By using the gain selected, an estimation of equation can be made using
Sisotool.
Compensator, C = 0.5 x
()() ()
Figure 4.0.5 – Compensator Diagram 13
5.0
Optimization of PID
Optimization is done by apply the compensator formula to the equation in the PID using the Sisotool. The result shown as be low:-
Figure 5.0 – Root Locus, Bode Diagram
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Figure 5.1 – Step Response, Bode Diagram, RootLocus, Nyquist Diagram
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Figure 5.2 – Root Locus,
The poles located in between 0.4 to 0.7 damping ratio which is 0.56 whereas in the range of stability.
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Figure 5.2 – Step Response
PID before Optimize
PID after Optimize
Overshoot
<20%
20%
Rise Time
5s
0.135s
Settling Time
20s
0,752s
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6.0
Conclusion
The objectives are achieved after optimization, and the system operates with the desired condition:-
7.0
Overshoot at 20%
Rise time at 0.1s
Settling time at 0.7s
Damping ratio at 0.56
References Textbook Control System Engineering Lecturer Notes http://www.alexmichinel.net/1/post/2013/07/consideringfeedforward-strategy-for-process-control.html http://www.plctalk.net/qanda/uploads/Tank_simulation_answ.jpg
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