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.
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.
During sampling the aliasing modifies the cutoff parameters.
Thus the sample rate characterizes the transient response and stability of the compensated system, and must update the values at the controller input often enough so as to not cause instability.
When substituting the frequency into the z operator, regular stability criteria still apply to discrete control systems.
Bode stability criteria apply similarly.
Jury criterion determines the discrete system stability about its characteristic polynomial.
The digital controller can also be designed in the s-domain (continuous).
: And its inverse Digital control theory is the technique to design strategies in discrete time, (and/or) quantized amplitude (and/or) in (binary) coded form to be implemented in computer systems (microcontrollers, microprocessors) that will control the analog (continuous in time and amplitude) dynamics of analog systems.
From this consideration many errors from classical digital control were identified and solved and new methods were proposed: The digital controller can also be designed in the z-domain (discrete).
represents the digital viewpoint of the continuous process
when interfaced with appropriate ADC and DAC, and for a specified sample time
denotes z-Transform for the chosen sample time
There are many ways to directly design a digital controller
[7] For a type-0 system under unity negative feedback control, Michael Short and colleagues have shown that a relatively simple but effective method to synthesize a controller for a given (monic) closed-loop denominator polynomial
exhibits integral action, and a steady-state gain of unity is achieved in the closed-loop.
The resulting closed-loop discrete transfer function from the z-Transform of reference input
, the synthesis method above inherently yields a predictive controller if any such delay is present in the continuous plant.