Tab. 5. Nonlinear model parameters of the VideoRay Automarine AUV obtained using the IS-O method

The method was also tested on FALCON ROV simulation model, Miskovic et al. (2008). Here we only give results of the IS-O method applied to the heave degree of freedom. The response is shown in Fig. 14 (it should be noted that in the simulation model the difference between weight and buoyancy was enlarged so that the infulence of the bias term in (6) would be emphasised). Using (33) it is easy to determine the difference between the weight and buoyancy.

Fig. 14. FALCON ROV simulation model response for IS-O depth experiment 4.5 Zig-zag Vs. IS-O

It is natural to compare these two identification methods because both of them are performed in a closed loop with a nonlinear element, and the system response is identical for both experiments. In addition to that, both methods can be used to determine linear models.

The main difference between the two methods is that the zig-zag method can be used on linear systems only. We have shown that the IS-O method can be applied to nonlinear systems. However, the IS-O method always gives approximate parameter values due to the harmonic linearization assumptions. When the zig-zag method is used, exact parameters are obtained under the assumption that there is no external disturbance. A downside to the zigzag method is that it uses integration which means that more complex algorithms are needed in comparison to the IS-O method which only uses extreme values of response to calculate the parameters. It should be mentioned that the IS-O requires more than one pair of extreme values so that a median value can be used in order to ensure accuracy. Fig. 15 shows the error which appears when there is external disturbance present during both experiments. The x-axis values are the percentage ratio between the disturbance and the maximum control value applied during the experiment. The figure clearly shows that the IS-O method is robust to external disturbance, i.e. if this experiment is performed in real conditions, the results will not be exacerbated. This is not the case with the zig-zag experiment. However, by modifying the zig-zag procedure, external disturbance can be taken into account, but the procedure itself becomes more complicated.

distrubance in relation to ma;; yaw thrust [%]

Fig. 15. External disturbance influence on the zig-zag and IS-O method distrubance in relation to ma;; yaw thrust [%]

Fig. 15. External disturbance influence on the zig-zag and IS-O method

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