Module overview
- To develop skills for design of linear multivariable control systems by pole placement.
- To introduce basic nonlinear system analysis and design methods.
Aims and Objectives
Learning Outcomes
Knowledge and Understanding
Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:
- Design pole placement state-feedback controller in the state space setting, also with observers in the loop
- Check controllability/observability by rank test of the controllability/observability matrix
- Analyse stability of nonlinear autonomous systems by state space methods
- Analyse linear dynamical systems by state space methods
- Derive state space representations for nonlinear systems from first principles
- Derive state space representation from a given transfer function representation
- Design controller using frequency domain methods
- Model, analyse, and synthesise nonlinear dynamical systems
- Analyse nonlinear input--output systems by describing functions
Syllabus
Frequency Domain Methods for Controller Design
- Lead-lag compensator
- Introduction to loop shaping
State-space representations for linear systems
- Transfer function canonical realisations
- State space representations
Structural properties
- Controllability and state transfer
- Observability and state estimation
Multivariable control by pole placement
- Pole placement by state feedback
- Elements of optimal control
State estimation
- Observer design by pole placement
Joint observer-controller schemes
Nonlinear systems and mathematical modelling
Introduction to the phase plane analysis method
Stability and Lyapunov analysis
- Lyapunov indirect method
- Lyapunov direct method
- Lasalle’s Theorem
Describing functions
Nonlinear control system design
- Design via linearisation
- Design via feedback linearisation
- Introduction to Lyapunov based design method
Learning and Teaching
| Type | Hours |
|---|---|
| Preparation for scheduled sessions | 18 |
| Completion of assessment task | 13 |
| Revision | 10 |
| Lecture | 36 |
| Follow-up work | 18 |
| Wider reading or practice | 55 |
| Total study time | 150 |
Resources & Reading list
Textbooks
K. Astrom and B. Wittenmark (1997). Computer-controlled systems: theory and design. Prentice Hall.
H. Khalil (2002). Nonlinear Systems. Prentice Hall.
K. Astrom and R. Murray. Feedback Systems: An Introduction for Scientists and Engineers.
Slotine and Li (1991). Applied Nonlinear Control. Prentice Hall.
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Problem Sheets | 20% |
| Examination | 80% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Examination | 100% |
Repeat
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
| Method | Percentage contribution |
|---|---|
| Examination | 100% |
Repeat Information
Repeat type: Internal & External