System Dynamics

• To analyse a range of both continuous and discrete time systems. 
• To introduce the concept of state-space.
• To introduce frequency-domain system analysis.
• To further the use of Matlab and Simulink in laboratories 

Outcomes:

On successful completion of the module, students should be able to:

 Develop mathematical models for a range of dynamical systems.

 Change between different mathematical model representations (differential equation, state-space and transfer function).

 Linearise a nonlinear system about an operating point.

 Calculate responses of simple dynamical systems.

 Analyse simple systems using Bode plots.

 Use Matlab and Simulink to simulate and analyse a range of systems. 

Syllabus.

· Brief revision - dynamic and static systems, categorizing systems, transfer functions, block algebra

· Mathematical modelling of systems - Continuous-time and discrete-time modelling (Differential and difference equation models; transfer function models)

· State-space representation including relationship between state-space and transfer function forms

· Linearisation

· Solution to linear differential and difference state-space equations (using state transformation)

· Stability

· Frequency domain analysis

- Nyquist diagram

- Bode plots