This chapter discusses the discrete time and digital control system. Advantages of digital control systems over their analogue equivalents, the sampling on which they depend does introduce inevitable performance degradation. In summary, this chapter discusses the delays introduced into a feedback loop by sampling are necessarily destabilising, and very rapid sampling of noisy continuous signals can amplify the noise content, particularly if differentiation of the signals is envisaged.

Chapter Contents:

• 10.1 Introduction
• 10.2 Computers as system components: devices that can change their state only at discrete times
• 10A A simple and informative laboratory experiment
• 10.3 Discrete time algorithms
• 10.4 Approaches to algorithm design
• 10.4.1 Direct controller synthesis
• 10B A clever manipulation: how the digital to analogue convertor (zero-order hold) is transferred for calculation purposes to become part of the process to be controlled
• 10.4.2 Gain plus compensation approach
• 10C Takahashi's algorithm
• 10.5 Overview: concluding comments, guidelines for algorithm choice and some comments on procedure
• 10D Some difficulties in moving from differential equations to approximating difference equations
• 10E Discretisation
• 10F A simple matter of quadratic behaviour
• 10G Continuous is not the limit of discrete as T → 0
• 10H Non-uniqueness of inverse Z transforms
• 10I The stability of a system can usually be considered independently of the nature of the inputs that it receives, but here is a counter-example

Inspec keywords: feedback; signal sampling; digital control; discrete time systems

Other keywords: noisy continuous signal sampling; noise content amplification; feedback loop; signal differentiation; discrete time system; digital control system

Subjects: Discrete control systems; Control engineering computing