Reference no: EM132284487
Dynamics and Control Project - 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 outputs. 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 Assessment Task #1 (Project 1 - Part 1), students will be asked in Assessment Task 4 (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.
Students are required to produce a report (by using the provided MATLAB Live Script template) detailing the following three 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
- Coupled tanks
clearly labelling the input and output, including units. Diagrams for each key system component should be similar in format to that presented below in Figure 2, with inputs and outputs fully defined (students need to simply edit the variables names in the MATLAB Live Script).
For the 'coupled tanks' component, the two tanks should be treated as a single component. Refer to Figure 3 to see how they are connected.
Task 2: Develop the Transfer Function of the Coupled Tanks System
Tank 1 Equation:
M(t) + N(t) - X1(t) = A1 dH1/dt
Tank 2 Equation:
X1(t) - X2(t) = A2 dH2/dt
Use the two dynamic equations (Tank 1 Equation and Tank 2 Equation) to develop the transfer function of the coupled tanks system. This is found by combining the two differential equations (Tank 1 Equation and Tank 2 Equation) and then taking the Laplace transform (or taking the Laplace transform of the two equations and then combining the two linear equations). The output of the coupled tanks system (tank 2 water level) is then:
H2(s) = (M(s)+N(s))/(k2T1T2s2+k2(T1+T2)s+k2) = (M(S)+N(S))/(Js2+as+k2)
Important: Students are required to derive this equation and show the derivation steps!
Where:
k2 = K2
T1 = A1/K1
T2 = A2/K2
J = k2T1T2
a = k2(T1+T2)
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 J, a and k2, follow the steps detailed below which uses an empirical approach.
Step 1: Measure the Open-loop Response of the Coupled Tanks Using the Remote Lab
Students are required to measure the open-loop response of the coupled tanks system from the coupled tank test rigs in the UTS remote labs by following these steps:
1. Login to the remote coupled-tanks.
2. Select "Manual" on the interface.
3. Check the "Valve %" is 0; and make sure the water level is at its minimum (normally less than 10mm), otherwise wait until the water level is decreased to the minimum.
4. Click "Logging" and select format.
5. Set the "Valve %" from 0 to 20% (or from 0 to 15% if the tanks overflow. But you need to wait until the tanks are empty).
6. Wait until the water level in Tank 2 (H2) reaches steady-state (about 700-800 seconds).
7. Set the "Valve %" to 0.
8. Download the session file(s).
9. Follow the "Assignment 1 - Preparing your data.pdf" instructions.
10. Use the MATLAB live script to generate a graph of the open loop response, plotting (in the same graph, similar to Figure 4):
a. Water level (mm) vs time (s).
b. Flow rate (L/min) vs time (s).
Figure 4 shows an EXAMPLE of an open loop response, which illustrates how the water level in Tank 2 changes when the flow into the system changes.
Step 2: Determine the Values of J, a, and k2
Parameters J, a and k2 can be calculated based on the measured open-loop response of the water level in Tank 2. There is more than one method for empirically determining the values of J, a and k2; for brevity, we have only included one method for use in this project. Follow the steps below (under Method) to calculate the values of J, a and k2.
In Project 1 - Parts 2 & 3 (assessment task 4), the model developed in Part 1 (assessment task 1) will be used to design a controller for the coupled tank system. It should be noted that the parameters obtained through these methods are empirical and therefore have limited accuracy. The key limiting value is ∑Tε2 as it imposes the limit on what can be achieved. If ∑Tε2 is underestimated then the resulting controller may be too fast for the system's dynamics and the closed loop will be severely under-damped or even unstable.
Task 3: Discussion and Reflection
Provide an insightful and concise discussion on the validity of the methods used for acquiring and analysing the data, as well as on the validity of the conclusions made about the system characteristics. You should identify and discuss the underlying axioms for this work and comment on their validity.
Note - All required figures are in attached file.
Attachment:- Assignment File.rar