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## Four Coupled Tanks Case Study

### Background

The Four Tank Laboratory Apparatus is a multivariable laboratory process, which consists of four interconnected tanks. The project was inspired by a paper published for the 17th Annual Control Conference in Philadelphia by the Department of Automation and Control at the Lund Institute of Technology. This paper described a multivariable process with four interconnected tanks with an adjustable zero, which can be moved along the real axis in the left or right hand plane.

The purpose for replicating this process was to introduce this apparatus into the Centre of Integrated Dynamics and Controls (CIDAC) short course program at the Newcastle University. It is anticipated that the patrons of the short course program will be given hands on experience in the
control of this multivariable (MIMO) process. This apparatus allows patrons to practice system modeling, investigate the effects of moving the adjustable multivariable zero and hence investigate the limitations of MIMO control. The system was seen as a very useful tool to illustrate the various phenomena associated with the control of a multivariable process.

The apparatus is made up of four tanks and two pumps. The inputs being a voltage output from a PC and the outputs are levels in two of the four tanks represented by a voltage and fed back to the PC. Valves are used to adjust the multivariable zero. Implementation of this design involved the identification of the various systems dynamics. This involved analysis of flows, pump characteristics, sensor responses, effects of noise, power consumption and voltage requirements.

Non-linear equations are derived for the physical apparatus using various formulas and equations that describe the various components of the apparatus and describe the process in terms of tank height. These were used firstly in the specification of the various apparatus components and secondly used as the equations that are linearized later in the report so that a linear representation of the plant in the form of a transfer function can be achieved and investigated.

Simulations were initially used to verify the accuracy of the linearized equation modeling by running simulations on a simple SISO system with both non-linear and linear representations. Once it was verified that the responses did closely match a detailed simulation of the whole process was undertaken. This was achieved using Decentralized PID control. Tests including the systems response to noise and stability were undertaken on the simulation model of the plant.

Comparison of results between the simulated plant response and the real plants response controlled using a PID block in the UNAC program are made. The simulation model represented the real apparatus and a hence an investigation into how accurately the simulation model represented the
real process was of interest. The accuracy of the linearized equations, which represent the system model, is investigated from these results.

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