Case Study - Coupled Tanks

Table of Contents

1.0 Introduction 3

2.0 Background of the Project 3

3.0 System Modelling & Verification 3

3.1 Theoretical modelling 3

3.2 System Modelling 5

3.3 Calibration of transducers 5

3.4 System identification and parameter determination 5

3.5 Model verification 5

4.0 Controller Design 5

4.1 Design of analogue controller 5

4.2 Design of digital controller 5

4.3 Design of state variable feedback controller 5

5.0 Controller Implementation 5

5.1 Building of analogue controller 5

5.2 Implementation of digital controller 5

5.3 Implementation of state-variable feedback observer/controller 5

6.0 Results 5

6.1 Comparison of actual results against predicted results 5

6.2 Discrepancies 5

7.0 Conclusions and future directions 5

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1.0 Introduction

2.0 Background of the Project

The Control of liquid level between tanks is a basic problem in the process industries requires liquids to be pumped and stored in tanks. The level of the fluid in the tanks must always be controlled and the flow between tanks must be regulated. A common situation in the chemical industry is two or more tanks containing various reactants connected by pipes which can be represented by our coupled tank system project.

3.0 System Modelling & Verification

3.1 Theoretical modelling

The system model is determined by relating the flow Qi into the tank to the flow Qo leaving through the Valve at the bottom. Firstly for a single tank, using a balance of flows equation on the tank, it is possible to write:

Where, A is the cross-sectional area of the tank, and H is the height of the fluid in the tank.

At a certain operating point, the system can be linearised to:

From this we can find the open loop transfer function to be:

Applying the same theory to two coupled tanks we were able to derive the following equations:

Net Inflow Rate: Linearisation:

Modelling of first tank

Modelling of second tank

Therefore by combining the two models, we are able to derive a transfer function relating the height of the second tank H2, in reference to the Inflow rate of the first tank Q1.

As the parameters of interest will be the poles and gain of this open-loop system, we reduce the amount of variables by making these assumptions.

Let R2 = K,

A1R1 = T1

A2R2 = T2

We arrive at the following open loop transfer function for the system:

3.2 System Modelling

In order to model the system we applied a step response to the input and monitored the output. The step was achieved by applying a voltage of 4V to the input

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