I am trying to determine the Integral Square Error (ISE) and the Integral Absolute Error (IAE) of a certain process where the error is in centimetres (cm). What would be the units for ISE and IAE in this case ?
ISE is obtained by integrating the square of the system error (cm in your case) over a fixed interval of time. IAE uses the absolute value of the error. The integral of x (error) to the power of n equals x to the power of n + 1 divided by n + 1 plus c. Therefore the integral of squared error equals cubed error divided by 3 plus c, so the units of ISE are cm cubed. The integral of absolute error equals squared error divided by 2 plus c, so the units of IAE are cm squared :)
Standard integration measures area or volume, so solitary units become squared, squared units become cubed, etc :)
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