I some papers, the mean square error is considered. In some other, the mse is normalized by dividing the error by the (total sampling instants x the total length of the reference trajectory).
Which solution does represent the factual error?
Dear Samira Eshghi,
For comparison of desired trajectory with the controlled one, MSE evaluation would be sufficient.
However, to carry out comparative analysis of controller outputs at different scales (viz. simulation and experimental results may differ in few cases by a certain unknown factor), then MSE would not be a sufficient measure. Therefore, in this case, NMSE will bring out an efficient state of comparison.
Regards
Dear Samira Eshghi,
In order to get around the question, i suggest you to see links and attached files on topic.
https://en.wikipedia.org/wiki/Root-mean-square_deviation
https://publications.waset.org/abstracts/search?q=minimum%20root%20mean%20square%20%28RMS%29%20error%20matching%20algorithm
http://www.diva-portal.org/smash/get/diva2:1381562/FULLTEXT01.pdf
Best regards
Dear Samira Eshghi,
The performance of the controller is generally measured using the following parameters such as :
1) Maximum Overshoot
2) Settling Time
3) Rise Time
4) Steady State Error.
Additionally, there are other ways to measure performance in literature. This includes integrated absolute error (IAE), the integral of squared-error
(ISE), or the integrated of time-weighted-squared-error (ITSE). These performance measures have their own advantages and disadvantages. For example, the disadvantage of the IAE and ISE criteria is that its minimization can result in a response with relatively small overshoot but a long settling time because the ISE performance criterion weights all errors equally independent of time. Although the ITSE performance criterion can overcome the disadvantage of the ISE criterion, the derivation processes of the analytical formula are complex and time-consuming. The formulas for these performance measures or the performance measure based on overshoot, settling time, rise time and steady-state error can be found in the paper given below. Article A Particle Swarm Optimization Approach for Optimum Design of...
In discrete domain, ISE refers to Mean Square Error. I am unfamiliar with normalized-mean-square-error .
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