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).
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.
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.