Control System Design

Learning Outcomes

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Design controller using frequency domain methods
• Design pole placement state-feedback controller in the state space setting, also with observers in the loop
• Analyse stability of nonlinear autonomous systems by state space methods
• Check controllability/observability by rank test of the controllability/observability matrix
• Derive state space representation from a given transfer function representation
• Derive state space representations for nonlinear systems from first principles
• Analyse nonlinear input--output systems by describing functions
• Model, analyse, and synthesise nonlinear dynamical systems
• Analyse linear dynamical systems by state space methods

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

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

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.