# An Innovative Applied Control System of Helicopter Turboshaft Engines Based on Neuro-Fuzzy Networks
## 2 Materials and Methods
### Development of Helicopter Turboshaft Engine Adaptive Control Law
Traditional control systems [35; 36; 37] are often based on linear models that fail to account for nonlinear engine dynamics, resulting in reduced efficiency and increased risk under changing external conditions. Systems built on classical neural networks provide better adaptability [38; 39; 40; 41; 42; 43], but they lack interpretability, may struggle with uncertainty, require extensive training datasets, and are prone to overfitting. Neuro-fuzzy control systems based on adaptive neuro-fuzzy inference systems (ANFISs) [44; 45; 46] combine the strengths of fuzzy logic and neural networks, allowing for the processing of fuzzy data and the integration of expert knowledge. However, they may require retraining during rapid changes in conditions. On the other hand, neuro-fuzzy systems based on adaptive neural networks (AFNNs) [47] offer more powerful control strategies and quickly adapt to changes, although their implementation demands significant computational resources. A comparison of different systems shows that the FTCS is the most appropriate choice for implementing the developed helicopter TE control law (23), combining adaptability, interpretability, and the ability to handle uncertainty, thus enhancing the reliability, safety, and performance of the helicopter TE compared to traditional systems and those based on neural networks and ANFISs. Traditional systems based on linear models do not take into account the nonlinear dynamics of the engine, which reduces efficiency and increases risks when external conditions change. Systems based on classical neural networks provide better adaptability, but are inferior in interpretability and resistance to uncertainty. The proposed FTCS based on ANFISs or AFNNs combines neural networks and fuzzy logic advantages, which makes it the optimal choice for helicopter TE control due to the ability to adapt to changes, process uncertainty, and increase reliability. The proposed helicopter TE FTCS (Figure 4) consists of a fuzzy controller, an adaptation and reconfiguration module, a selector of engine parameters in control channels, an actuator block, an engine model, a fuel metering unit (FMU) model, and a sensor block for the measured parameters. The fuzzy controller, in turn, comprises a fuzzification block, an inference engine, a defuzzification unit, a fuzzy rule base, and a fuzzy control block. A key distinction of the proposed FTCS compared to the closest analogue [48] is the division of the engine model into the engine model itself and the FMU model, first introduced in [38; 41; 42]. It allows for more precise consideration of the interaction between the engine and the metering needle, improving control accuracy and adaptation to changing operat  
Figure 3: The proposed helicopter turboshaft engine fuzzy fault-tolerant control system. ing conditions [41; 42]. This approach provides better control of operational parameters, enhancing overall system efficiency and reducing the likelihood of emergencies. Furthermore, the model division [38; 40; 41; 42] enables more efficient integration of expert knowledge into the control process, further enhancing the system's flexibility and adaptability and ensuring high resilience to uncertainty and external influences. The proposed FTCS fault-tolerant system has the ability to adapt to changing operating conditions and maintain stable performance in the presence of uncertainty and external impacts. The adaptation and reconfiguration modules and the division into the engine and FMU models enable the system to respond quickly to malfunctions and ensure safe control, minimizing the risk of emergencies. For the fuzzification of input values, for example, the input variable \(x\) is transformed into fuzzy values \(\widetilde{x}\) using membership functions \(\mu_{A}(x)\)[46; 49; 50; 51]:  
\[ \begin{split}\widetilde{x}=(A_{1},A_{2},\dots,A_{n}),\\ \mu_{A}(x)=\exp\biggl{(}-\frac{(x-c_{i})^{2}}{2\cdot \sigma_{i}^{2}}\biggr{)}.\end{split}