شناسايي ديناميكي يك وسيله‌ي زيرسطحي در حركت صفحه‌يي با استفاده از روش پاسخ فركانسي

Dynamic Model Identification of an Underwater Vehicle in Planar Motion Using Frequency Response Method

هدف نوشتار حاضر، شناسايي مدل ديناميك خطي حركت در صفحه‌ي افق يك وسيله‌ي زير‌‌سطحي بدون سرنشين به‌وسيله‌‌ي برازش توابع تبديل آن است. شناسايي، تحليل و تصحيح طراحي چنين وسايلي به‌دليل غيرخطي و مزدوج بودن ديناميك حاكم بر آن ها بسيار پر چالش است. در اين نوشتار براي نخستين‌بار به‌منظور حذف اغتشاشات و عدم قطعيت‌ها از شناسايي حوزه‌ي فركانس و الگوريتم‌هاي رياضي قوي در آن استفاده شده است. در اينجا پس از مدل‌سازي و شبيه‌سازي حركت ديناميكي، ورودي جاروي فركانسي در شبيه‌ساز غيرخطي به كنترل‌كننده‌ي سكان اعمال شده و با استفاده از تحليل حوزه‌ي فركانس توابع تبديل زوايه‌ي سمت و نرخ چرخش نسبت به اين ورودي محاسبه شده است. نتايج حاصله نشان‌گر مطابقت بسيار خوب اين مدل معادل خطي با مدل تحليلي غيرخطي، و عملكرد خوب آن در حضور نويز به‌لطف استفاده‌ي مناسب از توابع طيفي و تكنيك پنجره‌بندي است.

The current study aims to identify the equivalent linear dynamics of an autonomous underwater vehicle in the horizontal plane to be able to design an appropriate linear controller. Autonomous underwater vehicles are increasingly being used to provide researchers with a simple, low-cost, and rapid response capability to collect pertinent environmental data. They are fairly stable platforms with little roll and pitch. Nevertheless, dynamic coupling and non-linearities make it a challenging task to perform identification process, stability analysis, and control design. Here, for the first time, the frequency response analysis and the CIFER software, which utilizes strong mathematical algorithms, are employed to solve this problem. Advanced features such as the Chirp-z transform and composite window optimization are also used to extract high-quality frequency responses and best fit equivalent transfer functions. After formulating the problem, a frequency sweep input is designed and applied to the rudder controller in the nonlinear simulation and transfer functions for the heading angle and the rate of turn are derived. In addition, these transfer functions are obtained by perturbed equations of motion to be compared with the transfer functions from CIFER. To evaluate the accuracy of the identified models, time domain responses from a zig-zag test are compared with the responses predicated by the identified model and the linearized model. The results show that this model is in good agreement with the analytical linear model and performs significantly better in presence of noise, thanks to the precise spectral functions and windowing technique. The robustness of the proposed method and transfer functions are also assessed by evaluation of the coherence function and altering the window size, frequency bandwidth, and input commands. The results also show that in a specific frequency range, non-linear terms are negligible, and the turn rate could be easily predicted by the time derivative of the heading angle.