Meteorological Instrument Performance Characteristics

Dynamic Response » Response to Specific Input Functions » Ramp Input Exercise

Using the image below estimate the dynamic lag and the dynamic error for a second-order ramp input. You will use the figure to estimate the lag and error between the input (red line) and measurand (green line).

First-order (M1) and second-order (M2) response to a ramp input.

First-order (M1) and second-order (M2) response to a ramp input.

Question

For 𝛄 = 1, 𝜔n = 1, estimate the dynamic lag for a second-order ramp input.

The correct answer is c.

The dynamic lag is 2 seconds.

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Question

For 𝛄 = 1, 𝜔n = 1, estimate the dynamic error in units of the measurand for a second-order ramp input.

The correct answer is b.

You can estimate the dynamic lag 𝚫t and dynamic error 𝚫x using the image below. Using a horizontal line, determine the 𝚫t as shown. It is important that this determination is carried out after the solution has become steady, beyond the transient period. The correct answer is 2 𝛕. We can verify our estimate quantitatively since for a second-order ramp input, the dynamic lag 𝚫t = 2 𝛄/𝛚, and since 𝛄 = 1, 𝜔n = 1 s-1, 𝚫t = 2 seconds. To obtain an estimate of the dynamic error, use a vertical line through the data as shown to determine the difference between the input and the measurand at a specific time after the transient solution has disappeared.

The values can be verified on this graph.

Answer to the questions on dynamic lag and dynamic error.

Answer to the questions on dynamic lag and dynamic error. Image from NCAR/EOL.

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