Digital Representations of Analog Systems for Control System Applications

Digital controllers can be created from an analog (or continuous) model. This is especially useful when a processor is used to control an analog system or to implement a filter. Peter Way, the author of a new whitepaper tried several approaches and two were selected for excellent results: Tustin's Method and Hold Equivalence. In the paper, these are evaluated to show how they compare with an analog system.

10/29/2009


The full article is available as a downloadable PDF.

Digital Representations of Analog Systems for Control System Applications by Peter Way

 

Digital controllers can be created from an analog (or continuous) model. This is especially useful when a processor is used to control an analog system or to implement a filter. Peter Way, the author of a new whitepaper tried several approaches and two were selected for excellent results: Tustin's Method and Hold Equivalence. In the paper, these are evaluated to show how they compare with an analog system. Some methods are algebra-intensive and now much easier to implement with symbolic math tools.

Way says there are two main options for designing a digital controller:
Method 1: Design an analog controller. Then convert it to digital form including the effects of sampling the analog plant and holding the output at the DAC. This approach is most intuitive for the designer since you are working in the familiar s-domain (Laplace domain).

Method 2: Convert the Plant, DAC/ZOH and ADC to digital form. Then design a digital controller to meet performance requirements. This model is not as intuitive, since the dynamic specifications for the system need to be defined in the discrete domain (z-domain). It does have the advantage of handling plants with delays easily.

Way assumes Method 1 for his paper and says, "You may have done a compensator design, either as a PID or a more sophisticated one. Since compensators are essentially filters, the discussion will show how to convert an example analog filter to a digital one. Then the whole system can be simulated to show differences between the digital and continuous systems."

- Edited by Renee Robbins, senior editor
Control Engineering News Desk





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