The module descriptors for our undergraduate courses can be found below:

• Four year Aeronautical Engineering degree (H401)
• Four year Aeronautical Engineering with a Year Abroad stream (H410)

Students on our H420 programme follow the same programme as the H401 spending fourth year in industry.

The descriptors for all programmes are the same (including H411).

## Control Systems

### Module aims

This module builds on prior understanding of dynamical systems and expands fundamental concepts in the analysis and design of automatic control systems for use in a wide range of technologies (not just Aeronautics, but also Mechanical Engineering, Electrical Engineering, Chemical Engineering, Finance, Biology). It introduces some applications of control systems in the aerospace industry and provides a framework and language to communicate fluently with professional control engineers.

### Learning outcomes

On successfully completing this module, you should be able to:
1. Give examples of feedback in dynamical systems and discuss some of the basic properties of a feedback system.
2. Convert an ODE of a dynamical system into alternative, but equivalent forms, such as the state space and transfer function form.
3. Compute the equilibrium points of a nonlinear system and classify their stability properties and compute a linear approximation of a nonlinear system about an equilibrium point.
4. Design an output feedback controller for a linear system using pole placement and the separation principle.
5. Formulate and design a linear quadratic regulator (LQR) controller.
6. Analyse and predict the closed-loop stability from open-loop Nyquist and Bode plots.
7. Design and analyse the performance of a controller for a linear system in the frequency domain or using the root locus.
8. Evaluate the performance of a control system, modify an existing control design in order to meet design specifications and critically analyse and discuss the results obtained from a control experiment.

### Module syllabus

Introduction: Examples and properties of feedback, simple forms of feedback.
System Modelling: Modelling concepts, state space models, block diagrams, input-output models. Examples from aerodynamics, aerostructures, flight mechanics, astronautics.
Dynamic Behaviour: Solving differential equations, phase portraits, equilibrium points, stability.
Linear Systems: Definition of a linear system, stability and performance, second order systems, linearization.
State Feedback: Reachability, stabilization by state feedback, design issues.
Output Feedback: Static and dynamic output feedback, observability, state estimation, control using estimated state, separation principle.
Transfer Functions: Laplace transforms, definition of the transfer function, block diagrams of complex systems, pole and zero locations, stability, the Final Value Theorem.
Frequency Response and Bode Diagrams: frequency domain analysis, Bode plots.
Feedback Systems: LQR Control.
Feedback Systems: Stability and Performance: Nyquist plots, Nyquist's stability criterion, gain margin and phase margin, sensitivity function, feedback design via loop shaping, lead/lag compensation.
Root Locus Techniques: Basic methods for sketching the root locus, introduction to root locus design.

### Teaching methods

The module will be delivered primarily through large-class lectures introducing the key concepts and methods, supported by a variety of delivery methods combining the traditional and the technological.  The content is presented via a combination of slides, whiteboard and visualizer.

Learning will be reinforced through tutorial question sheets and laboratory exercises, featuring analytical, computational and experimental tasks representative of those carried out by practising engineers.

### Assessments

This module presents opportunities for both formative and summative assessment.

You will be formatively assessed through progress tests and tutorial sessions.

You will have additional opportunities to self-assess your learning via tutorial problem sheets.

You will be summatively assessed by a written closed-book examination at the end of the module as well as through online assignments and a practical laboratory assessment.

 Assessment type Assessment description Weighting Pass mark Examination 1hr 15 mins closed-book written examination in the Summer term 45% 40% Coursework Applications of Control Theory coursework exercises and laboratory 55% 40%

You will receive feedback both during the laboratory sessions and following the online assignments.

You will receive feedback on examinations in the form of an examination feedback report on the performance of the entire cohort.

You will receive feedback on your performance whilst undertaking tutorial exercises, during which you will also receive instruction on the correct solution to tutorial problems.

Further individual feedback will be available to you on request via this module’s online feedback forum, through staff office hours and discussions with tutors.