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Timing and Structure
Weeks 1-4 and 7-8, 2 lectures/week. Weeks 5-6, 1 lecture/week. 14 lectures.
Aims
The aims of the course are to:
- Introduce and motivate the use of feedback control systems.
- Introduce analysis techniques for linear systems which are used in control, signal processing, communications, and other branches of engineering.
- Introduce the specification, analysis and design of feedback control systems.
- Extend the ideas and techniques learnt in the IA Mechanical Vibrations course.
Objectives
As specific objectives, by the end of the course students should be able to:
- Develop and interpret block diagrams and transfer functions for simple systems.
- Relate the time response of a system to its transfer function and/or its poles.
- Understand the term 'stability', its definition, and its relation to the poles of a system.
- Understand the term 'frequency response' (or 'harmonic response'), and its relation to the transfer function of a system.
- Interpret Bode and Nyquist diagrams, and to sketch them for simple systems.
- Understand the purpose of, and operation of, feedback systems.
- Understand the purpose of proportional, integral, and derivative controller elements, and of velocity feedback.
- Possess a basic knowledge of how controller elements may be implemented using operational amplifiers, software, or mechanical devices.
- Apply Nyquist's stability theorem, to predict closed-loop stability from open-loop Nyquist or Bode diagrams.
- Assess the quality of a given feedback system, as regards stability margins and attenuation of uncertainty, using open-loop Bode and Nyquist diagrams.
Content
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Section numbers in books |
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(1) |
(2) |
(3) |
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Examples of feedback control systems. Use of block diagrams. Differential equation models. Meaning of 'Linear System'. |
1.1-1.11, 2.2-2.3 |
1.1-1.3, 2.1-2.6.1 |
1.1-1.8, 3.1-3.5, 3.18 |
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Review of Laplace transforms. Transfer functions. Poles (characteristic roots) and zeros. Impulse and step responses. Convolution integral. Block diagrams of complex systems. |
2.4-2.6 |
3.1-3.2 |
3.8-3.14, 4.1-4.8, 6.1-6.2, 7.1-7.8 |
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Definition of stability. Pole locations and stability. Pole locations and transient characteristics. |
5.6, 6.1 |
3.3-3.4, 4.4.1 |
5.1-5.2, 6.4 |
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Frequency response (harmonic response). Nyquist (polar) and Bode diagrams. |
8.1-8.3 |
6.1 |
6.5, 11.2, 11.5, 15.1-15.5 |
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Terminology of feedback systems. Use of feedback to reduce sensitivity. Disturbances and steady-state errors in feedback systems. Final value theorem. |
4.1-4.2, 4.4-4.5 |
4.1 |
9.2, 9.5 |
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Proportional, integral, and derivative control. Velocity (rate) feedback. Implementation of controllers in various technologies. |
10.6, 12.6 |
4.2 |
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Nyquist's stability theorem. Predicting closed-loop stability from open-loop Nyquist and Bode plots. |
9.1-9.3 |
6.3 |
11.10 |
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Performance of feedback systems: Stability margins, speed of response, sensitivity reduction. |
6.3,8.5, 9.4, 9.6, 12.5, 12.8-12.9 |
6.4, 6.6, 6.9 |
10.4, 11.11, 13.2, 15.6-15.7 |
REFERENCES
(1) DISTEFANO, J.J., STUBBERUD, A.R. & WILLIAMS, I.J. FEEDBACK AND CONTROL SYSTEMS
(2) FRANKLIN, G.F., POWELL; J.D. & EMAMI-NAEINI, A. FEEDBACK CONTROL OF DYNAMIC SYSTEMS
(3) OPPENHEIM, A.V., WILLSKY, A.S. & NAWAB, S.H. SIGNALS AND SYSTEMS
(4) ÅSTRÖM, K.J. & MURRAY, R.M. FEEDBACK SYSTEMS: AN INTRODUCTION FOR SCIENTISTS AND ENGINEERS
(5) DORF, R.C. & BISHOP, R.H. MODERN CONTROL SYSTEMS
Booklists
Please see the Booklist for Part IB Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
Last modified: 17/05/2018 15:26