###### Abstract  
Modelling and controlling an electrical Power Generation System (PGS), which consists of an Internal Combustion Engine (ICE) linked to an electric generator, poses a significant challenge due to various factors. These include the non-linear characteristics of the system's components, thermal effects, mechanical vibrations, electrical noise, and the dynamic and transient impacts of electrical loads. In this study, we introduce a fuzzy modelling identification approach utilizing the Takagi-Sugeno (T-S) structure, wherein model and control parameters are optimized. This methodology circumvents the need for deriving a mathematical model through energy balance considerations involving thermodynamics and the non-linear representation of the electric generator. Initially, a non-linear mathematical model for the electrical power system is obtained through the fuzzy c-means algorithm, which handles both premises and consequents in state space, utilizing input-output experimental data. Subsequently, the Particle Swarm Algorithm (PSO) is employed for optimizing the fuzzy parameter \(m\) of the c-means algorithm during the modelling phase. Additionally, in the design of the Parallel Distributed Compensation Controller (PDC), the optimization of parameters pertaining to the poles of the closed-loop response is conducted also by using the PSO method. Ultimately, numerical simulations are conducted, adjusting the power consumption of an inductive load. fuzzy c-means; PDC controller; power generation +
Footnote †: journal: _Algorithms_  
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of power generation systems, with a particular focus on finding out how these methods can be used to evaluate, counteract, or withstand the effects of the associated uncertainties. The benefits of ML and DDC techniques are accordingly interpreted in terms of visibility, manoeuvrability, flexibility, profitability, and safety. The authors in [6] provide an overview of artificial-intelligence (AI) applications for power electronic systems. The applications of four categories of AI are discussed, which are expert system, fuzzy logic, metaheuristic method (like PSO), and machine learning. In [7], the authors discussed the design choices and parameters that affect the system performance, the closed-loop stability, and the controller robustness. Moreover, they presented the solvers and control platforms that can be employed for the real-time implementation of Model Predictive Control (MPC) algorithms. Furthermore, in [8], a comprehensive review is conducted on artificial-intelligence applications in regards to optimization system configuration and energy control strategy, along with the applicability of different energy storage technologies. Most of the control techniques used for voltage regulation require a mathematical model of the ICE coupled to the electric generator. However, obtaining a complete mathematical model is a challenging task due to the interrelation between all the system components and the corresponding determination of its parameters. In order to deal with this issue, the authors in [9] proposed the use of a non-linear mathematical model, as well as the combination of the first principle of thermodynamics, physical laws, and steady state data of the engine mass air flow, obtained empirically. This type of approach typically results in inaccurate models due to unmodelled system dynamics and, in addition, the resulting complex mathematical models are not suitable to be used to derive voltage regulation control laws. One of the major potential areas of application of this type of power generator system is autonomous vehicles. For instance, the authors in [10] developed an unmanned military action vehicle, which uses a power generator system composed of a gasoline engine together with an electric generator and a lithium iron phosphate cell.