Eastern Mediterranean University Department of Mechanical Engineering Laboratory Handout

COURSE: Control Systems MENG332

Semester: Spring (2012-2013)

Name of Experiment: Design and Simulation of Controller for Coupled Tanks System

Instructor: Assist. Prof. Dr. Mostafa Ranjbar

Assistant: Alireza Kazemini

Submitted by:

Student No:

Group No:

Date of experiment:

Date of submission:

------------------------------------------------------------------------------------------------------------EVALUATION

Activity During Experiment & Procedure 30 %

Data , Results & Graphs 35 %

Discussion, Conclusion & Answer to Questions 30 %

Neat and tidy report writing 5 %

Overall Mark

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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.

Capability to 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:

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Figure 1: A Single Tank Fluid Level and CE105 Coupled Tanks System

TheoryThe system model is determined by relating the flow Qi into the tank to the flow Q0 leaving through the valve at the tank bottom. Using a balance of flows equation on the tank, it is possible to write:

Qi−Q o=A dHdt (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=Cd a√2 g . 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).

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,

A dHdt

+C d a√2 g . H=Qi (3)

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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=H 0+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:

T dhdt

+h=g .q i (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 systemCalibration 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

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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).

5

0 20 40 80 100 120 140 160 180 200 220 240 2600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Calibrationg tank level-flow

time (second)

Heig

ht le

vel (

mm

)

Figure 3: The relationship between height level and the flow rate into the tank

[Q1=? Q2=? qi=? g(gain)=? (Your discussion and conclusion) = ?]

2. Level sensor characteristics:

The voltage (Yi) to level Hi relationship is quite linear and can be written as follows.

Yi = a + ks Hi (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 4 shows example of the relationship between the height of liquid in the tank and the corresponding voltage.

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Figure 4: 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).

7

0 1 2 3 4 5 6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Calibrationg level-sensor

Voltage (volt)

leve

l (m

m)

Figure 5: The relationship between the height of liquid in the tank and the corresponding voltage

[a=? ks=? (Your discussion and 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)

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Figure 6: 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).

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0 1 2 3 4 5 6 7 8 9 10 11 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Calibrationg the control inflow

Voltage (volt)

Flow

rate

(lite

r/m

inut

e)

Figure 7: The relationship between the voltage to the pump and the flow rate into the tank

[kp = ? (Your Discussion and Conclusion) = ?]

Process ControlProcess 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.

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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 8: 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)

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Figure 9: 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 10: Block diagram of the closed loop system

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Monitoring Output level, (0 to 250 mm)

Sensor

PumpTank

Monitoring Input level, (0 to 250 mm)

VoltageTransducer

+10V

VoltageRegulator Sensor

Controller (Mathematical models of Tank, Sensor & Actuator)

OutputPlant

(Tank)Actuator

(Water pump)

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.

Error Amplifier

It amplify the error signal and give to the controller because the error signal is very weak in amplitude, it may be not directly operate the controller, so this weak signal is amplified by error amplifier.

Controller

It produces the output signal for the process based on the input error signal.

Output attenuator

It controls the output of the controller stage and input of the process state.

Sensor feedback

It provides input from the process to the set point or comparator which compares the set point and feedback signals.

Disturbance

Each process with one or more disturbance tends to change the controlled variable. The main function of the close loop process control system is to regulate value of controlled variables, when disturbance change it.

Experiment 5: Design a closed-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. Finally compare errors in open loop and closed loop systems.

Desired output (mm) Actual output (mm) Closed-loop Error (mm)

Open-loop Error (mm)

[(Write down your Conclusion about experiment 4 and 5) =?]

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Figure 11: Block diagram of the closed loop tank level control system

You need to fill out and print out pages (1-6-8-10-11-13) and submit them before (31/May/2013)

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-

+Sensor

PumpTank

Monitoring Input level, (0 to 250 mm)

VoltageTransduce

r

+10V

VoltageRegulator Sensor

Controller (Mathematical models of Tank, Sensor & Actuator)

OutputPlant

(Tank)Actuator

(Water pump)

+

-