Dates and Mechanisms for Assessment Submission and Feedback

From May 19th to May 21st, 2025, relevant content for your assignment will be provided during lectures, and teaching materials will be circulated by email. These materials will serve as useful starting points, but you are expected to go beyond them in your assignment. Seminar sessions during this period will provide an opportunity to discuss the assignment content with the module teaching team.

Instructions on Assessment

In this assignment, you will learn how to describe, analyse, and model a linear time-invariant (LTI) system. Additionally, you will learn how to discuss the effect of the PID parameters on the system's performance and how to tune the controller parameters.

Module Specific Assessment Criteria and Rubric

The marking scheme is given below.

ASSESSMENT REGULATIONS

Assessment Brief

Late submission of work

Where coursework is submitted without approval, after the published hand-in deadline, the following penalties will apply.

For coursework submitted up to 1 working day (24 hours) after the published hand-in deadline without approval, 10% of the total marks available for the assessment (i.e.100%) shall be deducted from the assessmentmark.

Coursework submitted more than 1 working day (24 hours) after the published hand-in deadline without approval will be regarded as not having been completed. A mark of zero will be awarded for the assessment and the module will be failed, irrespective of the overall module mark.

These provisions apply to all assessments, including those assessed on a Pass/Fail basis.

The full policy can be found here.

Students must retain an electronic copy of this assignment (including ALL appendices) and it must be made available within 24hours of them requesting it be submitted.

Academic Misconduct

The full policy is available at here

You are reminded that plagiarism, collusion and other forms of academic misconduct as referred to in the Academic Misconduct procedure of the assessment regulations are taken very seriously. Assignments in which evidence of plagiarism or other forms of academic misconduct is found may receive a mark of zero.

Figure 1: Two-tank hydraulic system of Question 1

Its governing equations are described by:

(a) Assuming that the inlet flow qi is the control input (i.e., u(t) = qi) and the height of the fluid h2 is the measured output (i.e., y(t) = h2), express the system in the state space form by setting h1 = x1 and h2 = x2. (10 marks)

(b) Assuming that A1 = A2 = 1 m2 and R1 = R2 = 0.1 K/W, analyse the system stability (5 marks)

(c) Find the equivalent transfer function T(s) = H2(s)/Qi(s), where H2(s) and Qi(s) are, respectively, the Laplace transform of qi and h2 (5 marks)

Figure 2: Closed-loop system of Question 1Assessment Brief

Figure 3: Mass-Spring-damper system of Question 2

(15 marks)

The block diagram shown in Figure 4 represents the closed-loop control of a welding system. The system has a constant rate of feeding the wire to be melted.

Figure 4: Mass-Spring-damper system of Question 2

Briefly explain the Ziegler-Nichols methods for tuning a PID controller. Illustrate the impact of the three controller parameters (Kp, Ki, and Kd) on the steady-state error, system overshoot, and settling time.Additionally, describe how the controller can position the system poles in the s-plane to ensure system stability. (20 marks)