## ELEC2540 Control Systems

### 10 creditsClass Size: 160

Module manager: Dr. Zoran Ikonic
Email: z.ikonic@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2022/23

This module is not approved as a discovery module

### Objectives

The aim of this module is to gain understanding of the theory and practice of control systems, including linear systems analysis using Laplace transforms and transfer functions, the transient response of feedback systems, and stability criteria.

Learning outcomes
On completion of this module students should be able to:

1. Draw block diagrams of simple feedback systems to represent an engineering problem, derive closed-loop transfer functions and sketch polar and Bode plots of systems which include cascaded terms.
2. Analyse the transfer functions of simple systems, obtain impulse and step responses and combine systems in series and in parallel.
3. Obtain steady-state responses by applying the final-value theorem and frequency response methods.
4. Explain the significance of the system's characteristic equation and how the poles of a system affect its transient response.
5. Explain the relationship between unity and non-unity feedback systems, determine the class of a feedback system and relate it to the system's steady-state error for standard reference inputs.
6. Explain the significance of stability in practical and mathematical terms, and how the stability of a feedback system can be inferred from the roots of its characteristic polynomial, from Bode plots, and by the use of Nyquist's criterion.

### Syllabus

Topics may include, but are not limited to:

Linear Systems: Laplace transforms and derivation of transfer functions
Standard form of a first-order system
Characteristic equation and significance of poles
Standard form of second-order system and its step response
Introduction to Feedback: Effects of feedback
Proportional, integral and differential control
System Classification: Relationship between unity and non-unity feedback systems
System type (class) and steady-state errors
Polar Frequency Response: Polar form of complex quantities
Frequency-response from transfer function
Bode plots
Stability: Concept of stability via roots of characteristic equation, from Bode plots, and from Nyquist's criterion

### Teaching methods

 Delivery type Number Length hours Student hours Laboratory 2 2.00 4.00 Office Hour Discussions 2 1.00 2.00 Examples Class 10 1.00 10.00 Seminar 10 1.00 10.00 Independent online learning hours 22.00 Private study hours 52.00 Total Contact hours 26.00 Total hours (100hr per 10 credits) 100.00

### Private study

Students are expected to use private study time to consolidate their understanding of course materials, to undertake preparatory work for seminars, workshops, tutorials, examples classes and practical classes, and also to prepare for in-course and summative assessments.

### Opportunities for Formative Feedback

Students studying ELEC modules will receive formative feedback in a variety of ways, including the use of self-test quizzes on Minerva, practice questions/worked examples and (where appropriate) through verbal interaction with teaching staff and/or post-graduate demonstrators.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment Lab report (project) 30.00 Total percentage (Assessment Coursework) 30.00

Resits for ELEC and XJEL modules are subject to the School's Resit Policy and the Code of Practice on Assessment (CoPA), which are available on Minerva. Students should be aware that, for some modules, a resit may only be conducted on an internal basis (with tuition) in the next academic session.

Exams
 Exam type Exam duration % of formal assessment Online MCQ 2 hr 00 mins 70.00 Total percentage (Assessment Exams) 70.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated