6 - Digital control principles

Abstract

This chapter discusses the principles applied in computer-based digital controllers. While selecting the type of control system required, the alternatives that exist between digital and analog systems must be examined. Digital systems are compatible with computers, distributed control systems, programmable controllers, and digital controllers. Digital control loops differ from continuous control loops and their analog cousins, in that a continuous controller is replaced by a sampler. This is a form of a computer performing discrete control algorithms and storing the individual results. Action is based on comparing the difference between the previous sampled value and the current value and generating an output, which is used to increment or decrement the final controller output, in conjunction with any other existing digital function. Laplace transforms perform a similar function in the solution of differential equations. The Laplace transform of a linear ordinary differential equation results in a linear algebraic equation. This is usually much simpler to solve than the corresponding differential equation. Once the Laplace domain solution has been found, the corresponding time domain solution can be determined by using an inverse transformation.