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Generic Sensor Model3
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Sensors Sensor Modeling
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1 Generic Sensor Model

Basic Sensor Model

The simple sensor model starts with a transfer function that represents the frequency response of the sensor. This frequency response is usually modelled with a second order system where the damping is equal to 1 or 0.707 (1/rt{2}) and the natural frequency is equal to the vendor provided bandwidth.

In addition to the frequency response of the sensor noise is modeled (simple band-limited white noise or PSD derived time history noise). Sensors are usually designed (and electronics or software added) to provide a linear response. In later design phases where the nonlinear aspects of the sensor response can be modeled. This is frequently unnecessary unless the limits of your sensors and controllers are being pushed.

1.1 Sensor Noise

Generic Random Noise Model

Most vendors provide noise measured on the sensor's output. (Be careful some vendors provide noise at the sensor input.) Noise will limit system performance. Noise passes straight through your control system to your output.

1.2 Nonlinear Models

Nonlinear models are typically much more difficult to model. Validation is even more difficult and time consuming. Save these for later development stages where lots of test data can be taken and you have weeks or months to really dive into the data.

Typical sources of nonlinear reponse

  • Quantization
  • Software thresholds
  • Limits of the physical principles underlying the sensor
  • Typically this is seen as a change in scale factor the frequency of the input reaches the frequency bounds of the sensors; see the rolloff of the second order system

These hard nonlinear steps can cause abrupt transient errors in the system. The abrupt steps will cause transients which need to settle before the system perofrmance will return to the expected behavior.