Control Systems

Module aims

• To provide students with the 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, etc.)
• To introduce some applications of control systems in the aerospace industry.
• To provide a framework and language to communicate with professional control engineers in their terms about control issues.
• To introduce the student to using industry-standard software, such as Matlab and Simulink, for control system analysis and design.

Learning outcomes

Knowledge and understanding:
On successfully completing this course unit, students will be able to:
• Give examples of feedback in dynamical systems and discuss some of the basic properties of a feedback system.
• Convert an ODE of a dynamical system into alternative, but equivalent forms, such as the state space and transfer function form.
• Compute the equilibrium points of a nonlinear system and classify their stability properties.
• Compute a linear approximation of a nonlinear system about an equilibrium point.
• Design an output feedback controller for a linear system using pole placement and the separation principle.
• Design a proportional-integral-derivative (PID) controller.
• Analyse and predict the closed-loop stability from open-loop Nyquist and Bode plots.
• Design and analyse the performance of a controller for a linear system in the frequency domain or using the root locus.
Skills and other attributes:
On successfully completing this course unit, students should be able to:

Intellectual skills
• Assimilate and apply the basic principles of control theory on a range of engineering and non-engineering applications.
• Formulate design specifications for a control system.
• Assess and discuss the trade-offs that have to be made in a control design.
• Evaluate the performance of a control system.
• Modify an existing control design in order to meet design specifications.
• Critically analyse and discuss the results obtained from a control experiment.
Practical skills
• Design and implement a controller on a laboratory experiment using Matlab and Simulink.
Transferable skills
• Develop independence in studying and manage their time in order to meet deadlines.
• Use self-assessment to monitor their ability to learn and apply new material.
• Collaborate with peers outside lecture hours in order to master the course material.
• Make their own course notes from attending lectures.
• Locate, extract and assimilate additional material from a variety of references, such as books and web-based sources, to supplement course notes.
• Collaborate in small groups during tutorial classes in order to solve problems.
• Write a report on the design process followed during 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, convolution, 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.
• Simple Feedback Systems: PID Control: Closed loop characteristic equation, PID controllers.
• 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.

Pre-requisites

AERO50002 Flight Dynamics and Control
AERO50003 Computing and Numerical Methods 2
AERO50006 Mathematics 2
AERO50007 Mechatronics
AERO50008 Structures 2

Teaching methods

Lectures/Tutorials
Lectures, tutorial classes, surgery/revision class

Laboratory exercises
The Twin Rotor Multivariable System: Feedback control of a pseudo-helicopter

Assessments

Examined Assessment:
1.5 hour written examination in Summer Term (65%),
a series of online coursework assignments & laboratory (35%)

Non-Examined Assessment

Blackboard quizzes

Core

• Feedback Systems: An Introduction for Scientists and Engineers

Karl J. Åström and Richard M. Murray

2nd, Princeton University Press

• Feedback systems [electronic resource] : an introduction for scientists and engineers

Åström, Karl J.

Princeton University Press

Supplementary

• Feedback and control for everyone [electronic resource]

Albertos Pérez, P.

Springer

• Signals and systems / Alan V. Oppenheim, Alan S. Willsky, with S. Hamad Nawab.

Oppenheim, Alan V.

2nd ed., Prentice Hall

• Feedback control of dynamic systems

Franklin, Gene F.,

Eighth edition., Pearson

• Modern control systems

Dorf, Richard C,

Thirteenth edition, global edition., Pearson

• Modern control systems

Dorf, Richard C.,

Thirteenth edition, Global edition., Pearson