*2.3. Performance Metrics Used*

To achieve the best performance, the gains of the controller were obtained through the minimization of the integral of the absolute error (*IAE*), which is given in Equation (17). This helps to adjust the controller parameters through a decrement in the tracking error in real-time.

$$IAE = \sum\_{i=1}^{N} |e\_i| \Delta t \tag{17}$$

where *ei* is the tracking error and N is an observation data length time for the calculation.

Since the main objective of this research is the tracking performance enhancement, not only was the *IAE* calculated but other types of metrics were also used to gather accurate results. These were the root-mean-square-error (*RMSE*) and the relative rootmean-square (*RRMSE*), which are reflected in Equations (18) and (19), respectively, where *ri* is the reference along the *i*-th *sample*.

$$RMSE = \sqrt{\frac{1}{N} \sum\_{i=1}^{N} (e\_i)^2} \tag{18}$$

$$RRMSE = \sqrt{\sum\_{i=1}^{N} (e\_i)^2 / \sum\_{i=1}^{N} (r\_i)} \times 100\% \tag{19}$$
