This unit introduces the fundamental principles in the modelling and control of linear time-invariant systems. On completion of this unit, you will be able to design a feedback controller. The unit begins with an introduction to feedback control systems with analogy to mechanical and electronic systems. These dynamic systems are described by deriving mathematical models in both the frequency domain and time domain. This leads to deriving characteristic equations for high-order systems which are illustrated using both system diagrams. Transformation techniques will be explored to convert system representations to controller design domains. System stability and steady state errors will be derived for various order inputs, while considering the effects of disturbances. This is followed by exploring parameter sensitivity to identify critical parts in the system. Once completed, the effects of adding feedback will be investigated using a root locus. The unit concludes with designing an active and passive PID controller using a root locus to meet specified output responses. These are fundamental control theory topics required for advanced automation and control systems, and embedded systems.