# 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
}\) become less than the specified tolerances \(\varepsilon_{n}\) and \(\varepsilon_{T}\):  
\[|\Delta n_{FT}(t)|\leq\varepsilon_{n},\,\,|\Delta n_{FT}(t)|\leq\varepsilon_{ T}. \tag{22}\]  
The proposed model employs numerical solutions to solve the differential equation system that describes the helicopter TE dynamics and the rotor blades. The system enablesreal-time numerical solutions for regulating fuel flow and the blade pitch angle through the discretization of equations and the Euler method. In the research's next stage, the helicopter TE control program in limitation modes is developed. To achieve this, the following aspects must be considered:  
1. Determining limiting modes by establishing a limiting-mode line. This is based on the relations between the maximum allowable values for the parameter \(n_{TC}^{given}\) and temperature at the input to the gas generator (in this case, temperature \(T_{N}\)). 2. Establishing the dependence on temperature through the expression \(\left(n_{TC}^{given}\right)_{lim}=f(T_{N})\)[31], which includes segments (Figure 1) 1-2 for \(\left(n_{TC}^{given}\right)_{\max}\); 2-3 for \(n_{TC\max}\); and 3-4 for another limiting parameter (for example, limitations on power \(N_{e}\)). 3. Identifying areas of limitation modes based on changes in temperature \(T_{N}\). In this case, three areas are distinguished (Figure 2) [31]: \(\bullet\) At low values of \(T_{N}\) (for example, \(T_{N}<T_{N2}\)), a limitation on \(\Delta K_{\min}\) is observed. \(\bullet\) In the temperature range from \(T_{N2}\) to \(T_{N3}\), a limitation on \(n_{TC\max}\) must be maintained. \(\bullet\) When \(T_{N}>T_{N3}\), a limitation on another limiting parameter takes effect. 4. Additional limitations involve adding a power limitation line \(N_{e}^{\max}\) to the limiting-mode line, resulting in a structure consisting of four segments that account for all constraints. In this case, equations describing the relations between power \(N_{e}\), engine parameters, and temperature are represented by (9). 5. Under limitation conditions, the proposed control program forms an equation system linking fuel supply \(G_{T}\), blade pitch angle \(\varphi_{m.r. }\), and power parameters, presented in (11). Thus, the developed helicopter TE control adaptive mathematical model is presented as follows:  
\[ \begin{array}{c}\left(n_{\text{TC}}^{given}\right)_{lim}=f(T_{N}),\\ G_{T}=G_{T}^{base}+k_{G}\cdot\Delta n_{FT}(t),\\ \varphi_{m.r.}(t+\Delta t)=\varphi_{m.r.}(t)+k_{\varphi}\cdot\Delta T_{m.r.}(t),\\ N_{e}=N_{e}^{\text{max}},\ n_{\text{TC}}\ \leq\ n_{\text{TCmax}},\ T_{G}^{*}\leq T_{G}^{ \text{max}}.\end{array}  \tag{23}\]  
The innovative aspect lies in the developed helicopter TE adaptive control law that enhances performance and safety compared to traditional control systems [35; 36; 37; 38; 39; 40]. This adaptive approach dynamically adjusts fuel supply and blade pitch angle based on real-time conditions, ensuring constant free turbine rotor speed and optimal engine operation under varying flight parameters. Unlike conventional methods that rely on fixed settings, the proposed model integrates real-time feedback to maintain safe operational limits, addressing constraints such as maximum power, gas generator rotor r.p.m., and gas temperature. The model facilitates real-time regulation by employing numerical optimization techniques and discretizing differential equations, improving responsiveness and efficiency in diverse flight modes, thus significantly advancing the helicopter TE control system's capabilities. The developed model is presented in Figure 3.  
Figure 2: The limiting-mode line. The Development of an Intelligent Automatic Control System for the Implementation of the Helicopter Turboshaft Engine Adaptive Control Law  
The research proposes a helicopter TE fuzzy fault-tolerant control system (FTCS) (Figure 4) aimed at implementing the developed control law (23).