# Case Study - Coupled Tanks

Topics: Control theory, Open-loop controller, State space Pages: 4 (805 words) Published: March 29, 2008
Table of Contents
1.0Introduction3
2.0Background of the Project3
3.0System Modelling & Verification3
3.1Theoretical modelling3
3.2System Modelling5
3.3Calibration of transducers5
3.4System identification and parameter determination5
3.5Model verification5
4.0Controller Design5
4.1Design of analogue controller5
4.2Design of digital controller5
4.3Design of state variable feedback controller5
5.0Controller Implementation5
5.1Building of analogue controller5
5.2Implementation of digital controller5
5.3Implementation of state-variable feedback observer/controller5 6.0Results5
6.1Comparison of actual results against predicted results5 6.2Discrepancies5
7.0Conclusions and future directions5

1.0Introduction

2.0Background 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.

3.0System Modelling & Verification
3.1Theoretical 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...

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