线性系统及其控制代写 MMAN3200代写

SCHOOL OF MECHANICAL AND MANUFACTURING ENGINEERING

MMAN3200 LINEAR SYSTEMS AND CONTROL

Assignment: Lab Report

Water Tank System Analysis and Control

TOTAL MARKS: 20

• Report content: 18
• Report format/presentation: 1
• Lab attendance and conduct: 1

 

Introduction  线性系统及其控制代写

Many industrial applications require an accurate control of liquid level, either in order to generate a constant flow of the liquid or a constant pressure. In this assignment, the liquid used will be water and a linearised model of the water tank system will be assumed (Figure 1).

 

 

The dimensions of the tanks are the horizontal cross-sectional area A and height h_max. The resistance of the outflow valve is R. The values of these three parameters are unknown at this stage, but we do know they are constant positive real numbers. Volumetric flows are q_i and q_o, which are the flows into and out of the tank, respectively, while h is the water level.

 

Modelling Tasks (2 marks)

Based on the one-tank system of Figure 1:

1. Determine the transfer function G(s) of the system where q_i is the input and h is the output variable. Identify the values (in terms of A and R) of the time constant and the steady state gain of the system. (1 mark)

2. Derive the response of the system to a step change to the input flow of magnitude B. Sketch h(t). (1 mark)

 

Laboratory 1 Tasks (8 marks)  线性系统及其控制代写

Rig 1 (PCT50 water level control)

Answer the following questions based on the activities and data from Lab 1.

1. When controlling the open loop system: (1 mark)

a. How many attempts did it take to reach the desired value of output?

b. How long (in minutes) did it take?

c. What was the accuracy of the final attempt?

d. What actions did you take when attempting to change the water level?

2. Using the value of the tank horizontal cross-sectional area, as well as the recording of the response h(t) to the step change of the pump speed, determine the values of: (2 marks)

a. The valve resistance R.

b. The magnitude of the step input (pump speed) in terms of volumetric flow in m³s^-1. Assume the transfer function is the same as determined in the previous section. If the h(t) graph from the 5% pump speed variation is incomplete, extrapolate the missing part until steady state of h(t) is achieved.

c. Calculate the time constant of this system.

3. Calculate the magnitude of the step change in outflow rate (in m³s^-1) when the solenoid valve is open. (1 mark)

 

Rig 2 (PCT51 water flow control)  线性系统及其控制代写

1. In order to establish the pump characteristics, plot the volumetric flow as a function of the pump speed setting. Use only the steady state values and ignore any transient processes. (1 mark)

2. When controlling the open-loop system: (1 mark)

a. How many attempts did it take to reach the desired value of output?

b. How long (in minutes) did it take?

c. What was the accuracy of the final attempt?

d. What actions did you take when attempting to change the water flowrate?

3.  Using the recording of the response q(t), is it possible to determine the time constant of the system? Briefly explain your answer. (1 mark)

Both Rigs

1. Compare the time responses of both rigs. Briefly comment on why there is a difference. (0.5 marks)

2. Use the relationship between pump speed setting and flowrate for Rig 1 and compare it with the pump characteristics obtained for Rig 2. What can be concluded about the similarity of the two pumps? (0.5 marks)

 

Laboratory 2 Tasks (8 marks)  线性系统及其控制代写

Rig 1 (PCT50 water level control)

1. Once the negative feedback loop is applied, determine the steady state error of the closed loop system: (0.5 marks)

a. In absolute terms

b. In terms of the steady state gain of the open loop system (including K_P)

2. Observe the reaction of the closed loop system to the solenoid valve perturbation. Compare the difference between the open-loop and closed-loop systems in the way perturbations are neutralised. (0.5 marks)

3.  Plot the steady state error vs the values of K_I (while K_P is constant). What value of K_I would ensure the steady state error would be zero? (1 mark)

4. For the process vessel simplified model created in the first part of this assignment, and with reference to Figure 1: (2 marks)

a. Treating G(s) as the open-loop system, apply the unity-gain negative feedback loop with a PI controller with gains KP and KI in the main branch.

b. Sketch the root locus of the closed loop system.

 

Rig 2 (PCT51 water flow control)  线性系统及其控制代写

1. Once the negative feedback loop is applied, determine the steady state error of the closed loop system: (0.5 marks)

a. In absolute terms

b. In terms of the steady state gain of the open loop system (including K_P)

2.  Observe the reaction of the closed loop system to the perturbation. Compare the difference between the open-loop and closed-loop systems in the way perturbations are neutralised. (0.5 marks)

3.  Plot the steady state error vs the values of KI (while KP is constant). What value of KI would ensure the steady state error would be zero? (1 mark)

Both Rigs

1. Discuss any sources of potential error in the measurements (of both labs) and the modelling of the system in Figure 1. (1 mark)
2. What settings made the control system unstable? (0.5 marks)
3. Describe the behaviour of an unstable flow control and/or level control system. (0.5 marks)

 

Submission Format (1 mark)  线性系统及其控制代写

• Maximum report length: 20 pages.
• All analytical work should be clearly presented, with the final results highlighted or underlined.
• References must use standard IEEE style, with references numbered in square brackets.
• Charts, tables and graphs must be labelled, including axes, keys and titles. Figures must be captioned and referred to in the main text.
• You do not need to write a traditional report with introduction, methodology, etc.; just the calculations and responses to the questions will suffice.
• The PDF version of the assignment should be submitted by the deadline indicated. Standard late penalties will apply. Submission details will be posted on MS Teams well in advance.
• Submissions will be assessed for plagiarism and academic misconduct, including traces of AI input from LLMs. Standard penalties apply.

 

 

 

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