ENGINEERING TRIPOS PART IIA – 2012/2013

Module 3F2 – Systems & Control

AIMS

To make students familiar with “state-space” methods of modelling and analysing dynamic systems. These methods are extremely important for control engineering, signal processing, and related subjects.

SYLLABUS

State-space models (6L)

• Review of second-year material (linear algebra, transfer functions, poles)
• Formulation from physical models
• Linearising nonlinear models
• Relationship to transfer function matrix (multiple inputs/outputs)
• Free and forced responses (state-transition matrix convolution, stability)
• Interconnections of systems

Feedback system design (4L)

• Review of second-year material (feequency responses, controller structures, objectives of feedback design).
• The root-locus diagram
• Routh-Hurwitz criterion (examples of use).

State estimation (3L)

• Observability.
• State observer; Oberver design.
• Connections to Kalman filters, sensor fusion etc.

Control in state-space framework (3L)

• Controllability.
• State feedback and pole-placement.
• Optimal control.
• State observer combined with state feedback

OBJECTIVES

On completion of this course a student should:

• Understand what a state-space model is, and how to obtain such a model;
• Be able to relate state-space models to transfer-function models;
• Be able to analyse the behaviour and structure of a state-space model;
• Have some understanding of feedback design using state-space, transfer function and root-locus techniques, and be able to relate them to each other;
• Appreciate the need for and usefulness of state observers, and their role in feedback and other systems.

COURSEWORK

Inverted pendulum experiment (state feedback). Laboratory report and/or full technical report.

Ball and beam experiment (state trajectories, nonlinear control). Laboratory report only.

EXAMPLES PAPER SCHEDULE

Paper 1: State-space models - issued in week 3
Paper 2: Root locus - issued in week 5
Paper 3: Observers and state feedback - issued in week 7

REFERENCES

Please see the Booklist for Part IIA Courses for references for this module.