Eastern Mediterranean University
Department of Mechanical Engineering
Laboratory Handout
COURSE: Control SystemsMENG332
Semester: Spring (2015-2016)
Name of Experiment: Design and Simulation of Controller for Coupled Tanks System
Instructor: Assist. Prof. Dr. Mostafa Ranjbar
Assistant: Amir Mirlatifi
Submitted by:
Student No:
Group No:
Date of experiment:
Date of submission:
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EVALUATION
Activity During Experiment & Procedure 30 %Data , Results & Graphs 40 %
Discussion, Conclusion & Answer to Questions 25 %
Neat and tidy report writing 5 %
Overall Mark
Introduction
Storage Tanks of various types are frequently used in industry to store fluids. Also, tanks can be used as a buffer between different unit operations so that a variable “incoming flow” can be averaged out so as to present a more uniform “outgoing flow” to the next unit operation.
This laboratory concentrates on the control of the level of fluid in a single tank. The apparatus that the laboratory is based on contains two tanks but this laboratory will only be concerned with the level in the first tank.
Objective
· To learn how to use sensors and actuators in control design during experimental study.
· To investigate the dynamics of a liquid-level control apparatus.
· Capabilityto predict behavior of system.
· To understand the controller design process for real-world systems.
· To compare result between experiment and simulation
· Do define and investigate the error in control system.
· To evaluate error in open-loop and close-loop control designs.
· The design of simple feedback control systems.
Why Coupled Tanks Systems?
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, and then pumped to another tank. Many
times the liquids will be processed by chemical or mixing treatment in the tanks, but always the level of fluid in the tanks must be controlled, and the flow between tanks must be regulated. Often the tanks are so coupled together that the levels interact and this must also be controlled. Level and flow control in tanks are at the heart of all chemical engineering systems. But chemical engineering systems are also at the heart of our economies.
Single Tank Model
It is important to understand the mathematics of how the coupled tanks system behaves. This is system modeling and it is a very important part of control systems analysis. First take a look at a single tank system in figure 1:
Figure 1: A Single Tank Fluid Level and CE105 Coupled Tanks System
Theory
The system model is determined by relating the flow Qiinto the tank to the flow Q0leaving through the valve at the tank bottom. Using a balance of flows equation on the tank, it is possible to write:
Qi-Qo=AdHdt (1)
Where, A is the cross-sectional area of the tank, and H is the height of the fluid in the tank.
If the valve is assumed to behave like an idea sharp edged orifice, then the flow through the valve will be related to the fluid level in the tank, H, by the expression,
Qo=Cda2g.H (2)
In this equation (a) is the cross sectional area of the orifice, (in practice the cross-sectional area will be given by the dimensions of the valve and the flow channel in which it is mounted).
(Cd) is called the discharge coefficient of the valve. This coefficient takes into account all fluid characteristics, losses and irregularities in the system such that the two sides of the equation balance. And (g) = (gravitational constant) = 980 (cm/sec2).
http://www.valvias.com/flow-equations-discharge-coefficient-c.php
Equation 2 assumes Cd is a constant so that Q0 has a nonlinear relationship to the level H for all possible operating conditions. Ideally the nonlinear relation is the square root equation 2, but in a practical valve there is a more complex non-linear equation. Combining Equations 1and 2 gives,
AdHdt+Cda2g.H=Qi (3)
This equation is the mathematical model that describes the system behavior, and again we see nonlinear things in the system model. Apparently it is just like my Servo Control white paper, but with an important difference. In the tank level problem the nonlinearity is smooth and can be made linear at a particular operating level H by using the slope of the nonlinearity at H. This has the important result that the linearized system model has parameters that depend upon the operating conditions. The system dynamics will change as the normal operating level changes. Please remember this, because it is very important that the tank level controller is insensitive to parameter changes in the model.
The system model, (equation 3), is a first order differential equation relating input flow rate, Qi, to the output water level, H. In order to design a linear controller for the tank level, we must linearize the equation by considering small variations h about the normal operating level of fluid in the tank. Let,
H=H0+h (4)
Where, Ho is the normal operating level, and is a constant, h is a small change about that level. Then, for small variations of h about Ho, we can approximate the nonlinear function by the tangent at H0.
This allows a linear differential equation to be obtained:
Tdhdt+h=g.qi (5)
Where qi the variation in the input flow (Qi), needed to maintain the normal operating level (Ho), the time constant (T) and the gain (g) are functions of the system parameters and the operating level.
Experimental set-up of the system
Calibration Process:
Calibration process is important in order to understand the characteristics of the main components of the coupled tank control and to relate the theoretical aspects of the function of the components. Besides, the relationship between the system parameters and its effect on the system response can be observed through this process. The block diagram of the single-tank control system is given as Figure 2.
Figure 2: The block diagram of a single tank control system
Basically, there are three important components of the apparatus that need serious studies and experimentation and these are:
(i) Tank dynamic characteristics
(ii) Level sensor characteristics
(iii) Pump characteristics
Calibration and measurement of the components characteristics are important to determine the relationship of the input and output of these components and also to determine whether there is non-linearity’s present which would explain some of the discrepancies in certain experimental results or any dead zones encountered in starting the flow of the pump.
The input to the pump motor is the voltage (Ui) acting as the actuated signal that control the input flow rate (Qi) to each tank.
The liquid then goes into the tank and causes the level to rise to a certain height (Hi). The level in the tank is measured using a sensor which consist of a capacitance probe and associated electronics.
1. Tank dynamic characteristics:
Try to define the relation between input flow rate and height level in a constant level, and continue this measurement for more than one water height level. This condition is presenting equations (1) & (3) while (Qi - Qo= 0).
After changing flow rate, while level is changing to new position, record all levels every few seconds and draw is graph to define a linear relation between flow rate and height level using equations (5) & (2).
Experiment 1: Prove the equation (3) following explanations above and define suitable gain in equation (5) for (CE105 COUPLED TANK) to determine the tank dynamic characteristic. Draw the graph shows the relationship between flow rate and height level in the tank.(The blank graph is given below).
Figure 3: The relationship between height level and the flow rate into the tank
[Q1=? Q2=? qi=? g (gain at each specific volume flow rate)=? (Your discussion and conclusion) = ?
Table: gain at each volume flow rate
Volume Flow Rate (Qi lit/min) / Gain2
2.2
2.4
2.6
2.8
3.0
Draw the transient response of the tank at a specific volume flow rate when the input is a unit step function.
Figure 4: Transient response of the system at a specific volume flow rate
Regarding the figure 4, Can you give a rough estimate for the gain and the time constant (T)?
2. Level sensor characteristics:
The voltage (Yi) to level Hi relationship is quite linear and can be written as follows.
Yi = a + ksHi (6)
Where ks= gain of level sensor (V/cm)
And (a) is the voltage in zero level (V)
The value of (ks)is important to obtain the relationship between the height of liquid in the tank and the converted voltage corresponding to it. Figure 5 shows example of the relationship between the height of liquid in the tank and the corresponding voltage.
Figure 5: Example for the relationship between the height of liquid in the tank and the corresponding voltage
Experiment 2: Define the value of (a) and (ks)for CE105 COUPLED TANK and draw the graph shows the relation between the height of liquid in the tank and the corresponding voltage.(The blank graph is given below).
Figure 6: The relationship between the height of liquid in the tank and the corresponding voltage
[a=? ks=?(Your conclusion) = ?]
3. Pump characteristics:
The relationship of the pump flow rate (Qi) and the input voltage (Ui)are also linear.
It can be written as equation (7).
Qi = kpUi (7)
Where kp= gain of the pump (cm3/sec/V)
Figure 7: Example for relationship between the voltage to the pump and the flow rate into the tank
The controlled inflow for every tank also has to be calibrated. It is needed in order to obtain the relationship between the voltage to the pump and the flow rate into the tank. Figure 6 shows an example for relationship between the voltage to the pump and the flow rate into tank. From linearization, we can obtain the value of kp(cm3/ sec/V).
Experiment 3: Define the value of kp for CE105 COUPLED TANK and draw the graph shows the relationship between the voltage to the pump and the flow rate into the tank.(The blank graph is given below).
Figure 8: The relationship between the voltage to the pump and the flow rate into the tank
[kp=? (Your Discussion and Conclusion) = ?]
Process Control
Process control can be defined as the function and operation necessary to change or stop a device or material either chemically or physically.
There are two main types of this system, which are given below.
Open loop System - Process Control:
It is control system in which a control action is applied on the output of the system. Such system are simply command by the input, an open loop control system is shown in the below figure 8. The process is controlled by providing the input to the control of the open loop system to keep the output at a desired level. The set point of the open loop system is also called “Command”.
It is necessary to achieve the ideal operating point for the process and observe the result at the output manually, since the only one input is applied to the control in form of set point, so it is clear that an open loop control system control the process blindly and the controller receive no information in the form of feedback to control the output status of the process.
The open loop control systems are cheaper and less complex then the closed loop control systems, while the controlling efficiency of this system is nearly zero.
Figure 9: Block diagram of the open loop system
Set point
The set point is the input that determines that the desired operating point of the process.
Controller
Makes the system’s decision based on the input signals, generates output signals, which operate actuators to carry out the decision.
Actuators
It converts system output electrical signals in to physical action.
Process
Process means to change the material chemically or physically.
Disturbance
Each process has one or more disturbances; Disturbance tends to change the control variables.
Error
E = (Output) - (input)
Experiment 4:Design an open-loop control circuit to control the height level in tank, record different output height levels refers to desired level input and fill the table below to evaluate the error of each experiment.
Desired output (mm) / Actual output (mm) / Error (mm)Figure 10: Block diagram of the open-loop tank level control system
Closed loop system:
The closed loop system is one of the control system in which the feedback taken from the output and then this feedback is feed is applied to the comparator for the comparing with the set point and the error is then apply to the further circuit, The operation and Block diagram of the closed loop system is shown in the below figure.
Figure 11: Block diagram of the closed loop system
Set point
It is the input that determines the desired operating point for the process.
Comparator
It is used to obtain the difference between actual outputs with set point, the set point signal is applied at the positive terminal and output sensor is applied at negative terminal.
If the negative terminal is on low potential then positive terminal potential comparator generates positive signal, which is used to operate final control element after amplification.