Dynamics and Control

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.

Figure 1 - Coupled Tanks Rig, Generation II

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.

Students are required to produce a report detailing the following four tasks:

Task 1: Determine the Inputs and Outputs of 3 Key System Components

Using the calibration data, 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.

Figure 2 - Component Block Diagram

Task 2: Develop the Transfer Functions of 3 Key System Components

Using the calibration data, develop the transfer functions of Sensor 2 and Valve 1.

Figure 3 - Coupled Tanks Dynamics and Properties

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:

H₂(s) = (M(s) + N(s))/(k₂T₁T₂s² + k₂(T₁ + T₂)s + k₂) = (M(s) + N(s))/(Js²+as +k₂)

Task 3: Develop the Closed-Loop Control System Block Diagram

Using the calculated transfer functions, signal flow and units from Task 1 and Task 2, develop the closed-loop control system block diagram for the control of the water level in Tank 2. The input to the system should be a desired water level for Tank 2 (mm) and the output should be the actual water level in Tank 2 (mm). Note that closed-loop is comprised of the following components: A controller (which will be developed in Project 1 - Parts 2 & 3), Valve 1, Sensor 2 and the Coupled Tanks.

Task 4: Discussion and Reflection

Provide an insightful, clear, relevant but brief discussion and reflection on the tasks performed in this report. Draw some conclusions about why modelling such a system might be useful in real life engineering practice.

Attachment:- Task description.pdf