Digital control

Digital control is a branch of control theory that uses digital computers to act as system controllers. Depending on the requirements, a digital control system can take the form of a microcontroller to an ASIC to a standard desktop computer. Since a digital computer is a discrete system, the Laplace transform is replaced with the Z-transform. Since a digital computer has finite precision (See quantization), extra care is needed to ensure the error in coefficients, analog-to-digital conversion, digital-to-analog conversion, etc. are not producing undesired or unplanned effects. Since the creation of the first digital computer in the early 1940s the price of digital computers has dropped considerably, which has made them key pieces to control systems because they are easy to configure and reconfigure through software, can scale to the limits of the memory or storage space without extra cost, parameters of the program can change with time (See adaptive control) and digital computers are much less prone to environmental conditions than capacitors, inductors, etc. A digital controller is usually cascaded with the plant in a feedback system. The rest of the system can either be digital or analog. Typically, a digital controller requires: Analog-to-digital conversion to convert analog inputs to machine-readable (digital) format Digital-to-analog conversion to convert digital outputs to a form that can be input to a plant (analog) A program that relates the outputs to the inputs Outputs from the digital controller are functions of current and past input samples, as well as past output samples - this can be implemented by storing relevant values of input and output in registers. The output can then be formed by a weighted sum of these stored values. The programs can take numerous forms and perform many functions A digital filter for low-pass filtering A state space model of a system to act as a state observer A telemetry system Although a controller may be stable when implemented as an analog controller, it could be unstable when implemented as a digital controller due to a large sampling interval.