This thesis aims to explore and compare the performance of fractional proportional-integrative-derivative controllers in the DC motor system and the fractional leaky integrate and fire (FLIF) model for neuron spike signals. The objective is to determine whether FPID controllers exhibit superior performance and significant improvements in control compared to PID controllers. In the study, FPID controllers were found to be crucial for effectively controlling complex systems with nonlinear or long memory behavior, addressing challenges that regular PID controllers struggle to handle. The results indicate that in the DC motor system, both FPID and PID controllers performe similarly, without significant differences in their effectiveness. However, when it comes to controlling and simulating neuron spike signals using the FLIF model, the FPID controller demonstrates significant improvements compared the PID controller. These findings suggest that while FPID controllers may not universally outperform PID controllers, they do offer advantages and improvements in certain scenarios. The effectiveness of FPID controllers is particularly highlighted in the context of the FLIF model, where they show significant enhancements in control compared to PID controllers.

<p>Rad je posvećen robusnom upravljanju sistemima čiji je linearni regulator i/ili dinamika necelog reda, kao i upravljačkim problemima gde regulator necelog reda u sebi poseduje i linearnu i nelinearnu dinamiku, a koji upravlja procesima čija dinamika može i linearna i nelinearna.</p> / <p>The thesys is dedicated to robust control systems problems with linear<br />controllers and/or process dynamics of noninteger order, as well as control<br />issues with combination of linear and nonlinear controllers of noninteger<br />order that control either linear or nonlinear systems.</p>