MSc Advanced Control and Systems Engineering / Course details
Year of entry: 2024
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Course unit details:
State-Space and Multivariable Control
|Unit level||FHEQ level 7 – master's degree or fourth year of an integrated master's degree|
|Teaching period(s)||Semester 1|
|Offered by||Department of Electrical & Electronic Engineering|
|Available as a free choice unit?||No|
Brief Description of the Unit:
- Introduction to state variables, order and state equations
- State space modelling of dynamical systems - applications and examples
- Controllable canonical form and observer canonical form
- State space realisation of transfer functions
- State transition matrix, matrix exponential and time response of state space models
- Laplace transform of state equations and matrix transfer functions for MIMO systems
- Use of eigenvalues and eigenvectors to diagonalise a state space model
- Modal form, modal behaviour and system dynamics
- Jacobi linearisation on nonlinear systems
- Controllability and observability and links to modal analysis
- Minimal representations
- State feedback control design
- Observer design
- Output feedback design and separation principle
- Discrete-time state-space counterparts to continuous-time
- State space and transfer function matrix representations of multivariable linear systems
- Realisation of a MIMO transfer function matrix: minimal representation
- Multivariable poles and zeros; directionality
- Closed-loop sensitivities; design tradeoffs
- Diagonal controllers and decoupling
- Internal model control structure design for both single variable and multivariable control
- Inner-outer factorisations
- Design example
This course unit detail provides the framework for delivery in the current academic year and may be subject to change due to any additional Covid-19 impact. Please see Blackboard / course unit related emails for any further updates
The course unit aims to:·
- Give students a sound understanding of control systems analysis and synthesis using state space techniques
- Introduce multivariable control systems
- Give students an introduction to internal model control design.
On the successful completion of the course, students will be able to:
Describe dynamical systems in mathematical terms using state-space representations.
Analyse dynamical system properties of state-space models.
Develop feedback controllers for state-space models using state-feedback and observer techniques.
Design PID type decoupling controllers for the MIMO systems with transfer function representation
Design IMC type controllers for both minimum phase and non-minimum phase MIMO systems
Evaluate the MIMO control system performance in terms of reference tracking, noise suppression and disturbance rejection.
Coursework assessment: quiz and report based on laboratory work. Feedback is provided two weeks after report submission
1 J. M. Maciejowski: Multivariable Feedback Desgin. Addison Wesley 1989
2 K. Zhou, J. C. Doyle and K. Glover: Robust and Optimal Control. Prentice Hall 1996
3 S. Skogestad and I. Postlethwaite: Multivariable Feedback Control (2nd ed). Wiley 2005.
4 M. Morari and E. Za
riou: Robust Process Control. Prentice Hall 1989.
5 T. Glad and L. Ljung: Control Theory. Taylor and Francis 2000.
6 G. C. Goodwin, S. F. Graebe and M. Salgado: Control System Design. Prentice Hall 2001.
7 K. H. Johansson: The quadruple-tank process: a multivariable laboratory process with an adjustable zero, IEEE Trans. Control Systems Technology, 8, 456465, 2000.
1 “Modern control engineering” by Ogata, Prentice-Hall
2 “Feedback control of dynamic systems” by Franklin and Powell, Prentice-Hall
3 “Modern control systems” by Dorf and Bishop, Prentice-Hall
|Scheduled activity hours|
|Practical classes & workshops||6|
|Independent study hours|
|Alexander Lanzon||Unit coordinator|
|Long Zhang||Unit coordinator|