48660: Dynamics & Control- The Coupled Tanks System- Modelling Dynamic System Assignment

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Internal Code: TV217
Modelling Dynamic System Assignment:
Task:

Project 1 – Part 1: Modelling of a practical dynamic system (i.e. coupled-tank system)

The Coupled Tanks System (Figure 1) emulates an engineering scenario where it is critical to maintain a desired fluid level. The coupled tanks system can have single or multiple inputs and output(s). Students are asked to characterise the behaviour of the system (find the transfer function of the plant). The rigs were designed to allow students to acquire data from a physical dynamic system to develop a simplified model of the underlying dynamics.

Once the model is developed in Project 1 – Part 1, students will be asked (in Project 1 – Parts 2 & 3) to design controllers for the dynamic system and analyse the performance of the controllers in maintaining the water level in Tank 2.
You are required to read the document “Coupled_Tanks_Generation II_UserGuide_V2- 3.pdf” for detailed information about the coupled tank system.

Task 1: Determine the Inputs and Outputs of 3 Key System Components
Using the calibration data (“Coupled_Tanks_Calibration_Data_2016-08-04.pdf”), produce the component block diagrams for Sensor 2, Valve 1 and the Coupled Tanks. Diagrams for each key system component should be similar in format to that presented in Figure 2, with inputs and outputs fully defined.

modelling
Task 2: Develop the Transfer Functions of 3 Key System Components
Using the calibration data (“Coupled_Tanks_Calibration_Data_2016-08-04.pdf”), develop the transfer functions of Sensor 2 and Valve 1.
modelling1
Develop the differential equations and the transfer function of the coupled tanks system (using the equations for Tank 1 and Tank 2 in Figure 3). At steady-state mass flow rate in is equal to mass flow rate out. Combining the two differential equations (Tank 1 Equation and Tank 2 Equation shown in Figure 3) and then taking Laplace transform (or taking Laplace transform of the two equations and then combining the two linear equations), the transfer function of the coupled tanks takes the form of:
modelling2
Important: Students are required to derive this equation and show the derivation steps!
Where:
modelling3
T1 and T2 are time constants that are related to the cross-sectional area of the tanks, the operating levels in the tanks and the difference in levels in the tanks. To determine the values of , and , follow the steps detailed below which uses an empirical approach.

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