# An Innovative Applied Control System of Helicopter Turboshaft Engines Based on Neuro-Fuzzy Networks
## 3 Results
### Results of Computational Experiment  
A semi-physical modeling stand (SPMS) was developed to conduct the computational experiment, representing an improved version of a similar stand previously designed [57]. This SPMS is intended to simulate helicopter TE parameters in real time and replicate operational modes within altitude and flight speed ranges. Additionally, it facilitates interaction with higher-level systems through data exchange channels, testing the control system unit and addressing other tasks [57]. Figure 8 illustrates the interaction scheme between the developed neuro-fuzzy network (Figure 5) and the SPMS. On the SPMS, the helicopter TE malfunctions are displayed by introducing artificial perturbations into the model parameters or modifying the input data corresponding to certain failure scenarios. The neural network model integrated into the stand analyzes changes in the dynamics of parameters such as rotor speed, temperature indicators, and fuel consumption, which allows us to identify deviations associated with malfunctions. This provides an opportunity to test the developed control system's stability and assess its adaptability in the event of failures. The research examines an example of constructing a failure model related to the fuel flow actuator \(G_{T}\) control loss, which is the gas generator rotor r.p.m. \(n_{TC}\) channel. The failure model, represented as a production rule set (the fuel flow actuator \(H=0\), \(M=0\) failure), is expressed as follows:  
Figure 8: A scheme showing the interaction between the helicopter turboshaft engine model and the semi-physical simulation stand. \[ \begin{split}\text{Rule 1}:\text{ If }e_{n_{TC}}>0.706\text{ and }\frac{\partial e_{n_{TC}}(t)}{ \partial t}\leq-0.00027,\text{ then }u_{n_{TC}}=4.383-6.708\text{-}e_{n_{TC}}-0.336\text{-}\frac{ \partial e_{n_{TC}}(t)}{\partial t},\\ \text{Rule 2}:\text{ If }e_{n_{TC}}>0.707\text{ and }e_{n_{TC}}\leq-0.00028, \text{ then }u_{n_{TC}}=-1.113+1.003\text{-}e_{n_{TC}},\\ \text{Rule 3}:\text{ If }e_{n_{TC}}>0.709,\text{ then }u_{n_{TC}}=-1.136+1.013 \text{-}e_{n_{TC}},\\ \text{Rule 4}:\text{ If }e_{n_{TC}}\leq 0.706\text{ and }\frac{ \partial e_{n_{TC}}(t)}{\partial t}\leq-0.00027,\text{ then }u_{n_{TC}}=-5.993+8.029\text{-}e_{n_{TC}}+0.487 \text{-}\frac{\partial e_{n_{TC}}(t)}{\partial t},\\ \text{Rule 5}:\text{ If }e_{n_{TC}}\leq 0.71\text{ and }\frac{ \partial e_{n_{TC}}(t)}{\partial t}\leq-0.00027,\text{ then }u_{n_{TC}}=-0.011+0.492\text{-}e_{n_{TC}}+0.117\text{-}\frac{ \partial e_{n_{TC}}(t)}{\partial t}.\end{split}  \tag{43}\]  
Figure 9 presents the failure \(u_{n_{TC}}=f\Big{(}e_{n_{TC}},\frac{\partial e_{n_{TC}}(t)}{\partial t}\Big{)}\) \"profile\", where \(e_{n_{TC}}\) is the signal representing the change in the control error in the rotational speed channel; \(\frac{\partial e_{n_{TC}}(t)}{\partial t}\) represents the error signal derivative. The developed failure models are stored in the control system's knowledge base and are utilized to assess the control situation to generate corrective actions to switch control channels for helicopter gas turbine engines. The study investigates the transient characteristics of the failure model related to the control loss in the fuel flow actuator within the gas generator rotor r.p.m. channel (Figure 10). Figure 10: The diagram of the transient process during the fuel flow actuator control loss is the gas-generator rotor r.p.m. channel. Figure 9: Failure “profile” diagram related to fuel flow actuator control loss. In Figure 10, surge and decay indicate the sudden failure of the fuel flow actuator. This failure resulted in a sharp reduction in fuel supply, leading to a drop in gas generator rotor r.p.m. and a deterioration in engine dynamics. The dotted red line on the diagram represents the engine's trajectory under normal operating conditions for comparison with the failure scenario.