Effects of computation delay in digital control

This text discusses signal issues in

QFIRE Studio

a digital computer.

Computation problems

In

QFIRE Studio

, a complete simulation of digital control is achieved by reproducing three fundamental aspects of digital computers:

  1. Discrete-time: any signals either acquired or generated by digital controllers are defined at specific instants. Usually, sampling instants.
  2. Quantization: any stored values, parameters or signals have their range and resolution limited by word length.
  3. Computation delay: any processing operation takes time to be executed. This time is finite but not null.

The third aspect is rarely simulated by the most used simulation tools in control design field.

QFIRE Studio

knows the duration and order of execution of each block in a hybrid or signal flow diagram. In addition, preemptions are fully simulated. These characteristics make possible the simulation of digital controls with computation delay.

Consider the example below:

Figure 1 - Simple acquisition, computation, and command diagram

This model repeats its input signal in its output. However, it takes time to execute even a simple control task. Figure 2 below shows the effect of computation delay

(Tci)(T_{ci})
in the generation of the computed sample.

Figure 2 - Computation time effect sketch

Note that

TsT_s
(sampling period) is constant, but
TcT_c
(computation time) is not always the same because it depends on:

  • How many tasks the

    QFIRE

    executes.
  • Priorities defined.
  • Complexities of the tasks et coetera.

The most important fact is that

TciT_{ci}
can be predicted in

QFIRE Studio

and its effects taken into account prior to getting the real controller running in the actual application.

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