This research evaluates the helicopter turboshaft engines proposed dual-channel logic controller, demonstrating its effectiveness in controlling complex dynamic systems under parametric uncertainty. A structure and functioning algorithm for a dual-channel logic controller is proposed, accounting for both the dynamics of each separate subsystem and their mutual influence when generating the control action. The research assesses this controller using the TV3-117 engine across various flight parameters, including bench test conditions (H = 0 km, V = 0 Mach) and two flight scenarios (H = 2.5 km, V = 0.68 Mach; H = 4.2 km, V = 0.86 Mach). Results reveal that the controller reduces error from 2.58 to below 1 %, reflecting nearly a 40 % improvement in performance. Despite these gains, the research notes limitations: the controller's effectiveness is based on a specific engine model and may not generalize to other engines or more complex conditions. Additional research is necessary to explore its robustness and adaptability to a broader range of operational scenarios and engine types.
Modern complex dynamic systems (CDS), such as helicopter turboshaft engines (TE), consist of
several interconnected subsystems that interact through natural cross-links within the object [
Helicopter TE, as multi-dimensional control objects, are characterized by nonlinear system
elements and non-stationary processes, leading to significant changes in parameters under different
operating conditions [
An essential task is the control algorithms development that ensure the multi-connected system
effective operation across all operating modes. Traditional linear design methods for
multiconnected ACS in helicopter TE do not fully address the challenges related to achieving the required
tactical and technical performance [
The CDS control issue, including helicopter TE, is extensively discussed in the literature. Several
researches emphasize that such systems are characterized by significant nonlinearity and variable
parameters depending on operating modes, which complicates the traditional methods application
for designing ACS [
Other researchers focus on the linear control methods limitations, which often fail to provide
sufficient accuracy and reliability in multi-dimensional systems controlling like helicopter TE. The
researchers [
The most attention in modern literature is directed towards developing new methods for synthesizing multi-connected control systems that ensure stability and precision under various operating conditions [15, 16]. Specifically, algorithms incorporating neural networks and machine learning techniques have been proposed to predict system behavior and adjust control parameters in real time [17–19]. These innovative methods significantly enhance the ACS efficiency and help achieve the tactical and technical performance required in aviation technology.
Despite significant advances in complex dynamic systems controlling, such as helicopter TE, several unresolved issues remain related to ensuring the ACS accuracy and reliability in conditions with multiple dimensions and changing parameters. Current research does not sufficiently consider the cross-links impact between subsystems, which reduces the control effectiveness when operating modes change. Additionally, linear and traditional adaptive control methods are not always adequately capable responding to nonlinear processes and rapid transient modes, creating a need for the multi-channel logic controller development. Such a controller could provide more accurate realtime adjustments to control parameters, accounting for system interconnectivity and enhancing the ACS stability and adaptability across an operating conditions wide range.
In researchers [20–22], the helicopter TE properties as multi-connected control systems are explored. The helicopter TE is described as stable, non-stationary systems, whose dynamic parameters shift with changes in external flight conditions. The helicopter TE nonlinear dynamic model is complex, making the multi-connected automatic control systems (MCACS) synthesis and analysis challenging. To simplify this process, the model is typically represented by a system of linearized stationary differential equations [23, 24]. In this article, the helicopter TE (using the TV3-117 engine from the Mi-8MTV helicopter as an example [25, 26]) is presented as a multi-connected control system with three regulated coordinates, which are the engine functional parameters: the gas-generator rotor r.p.m. (nTC), the free turbine rotor speed (nFT), and the gas temperature before the compressor turbine ( ∗) [27]. The control input is the fuel consumption into the combustion chamber (GT). Based on this, the helicopter TE matrix transfer function (MTF), along with its actuator, is represented as follows [28]: where Tact is the actuator time constant, Teng is the engine time constant, τij are the subsystem forcing time constants, Kij are the gain coefficients.
The helicopter TE MTF parameters are determined by flight parameters. There are altitude (H, km) and speed (V, M), where M is the Mach number. Since altitude and speed vary significantly during flight, the helicopter TE parameters also fluctuate considerably [29]. A linear approach to MCACS designing [30] will not provide the required control quality for helicopter TE. This underscores the need to develop new control algorithms that effectively utilize all available resources to meet the technical requirements across all operating modes. Based on [31, 32], this research proposes using logic controllers within the helicopter TE MCACS separate subsystems to address this issue.
A promising approach for synthesizing helicopter TE MCACS is the logic controllers use that adjust both the control device’s structure and parameters based on their operational logic. These logic controllers greatly enhance the ability to direct control processes, thereby improving the entire system dynamic and static properties [33]. Consider the helicopter TE MCACS [34], which includes logic controllers within its separate subsystems. The structural diagram is shown in Figure 1, where G(t), U(t), and Y(t) represent the vectors for reference, control, and regulated coordinates, respectively, and ε(t) denotes the control errors vector.
ε*(t) G(t) ε(t)
and for helicopter TE specifically.
εi(t) y1(t) yn(t) yi (t) d dt
y1‘(t) dt d yn‘(t)
yi‘ (t) and
To address this issue, a dual-channel logic controller is proposed, which generates control actions for each separate subsystem while accounting for the cross-links impact on the output variables dynamics. This MCACS structure is shown in Figure 2, where U*(t) represents the logically adjusted control coordinates vectors.
The proposed dual-channel logic controller operation, presented in Figure 3, is based on integrating a primary control algorithm for each separate subsystem. This algorithm adjusts the control error signal by analyzing both the current and predicted states. Additionally, a secondary logic algorithm creates artificial cross-links between subsystems to coordinate and the MCACS overall movement harmonize.
G(t) ε(t)
U*(t)
Y(t) channel logical controller structural diagram.
The logic correction algorithm [38, 39] generates the primary logic error ∗( ) by discretely analyzing the current control error εi(t) and its rate of change ( ) for the i-th separate subsystem. The primary logic error includes dynamic changes to coefficients Tlog and Klog, allowing the system to adapt to varying conditions: ( ) ( ( ) ∙ ( ) ≤ 0)˄ ( ) ∙ ( ) ≥ 0 ∗( ) = ( ) + ∙ ( ) ( ( ) ∙ ( ) ≤ 0)˄ ( ) ∙ ∗( ) predicted value. Here, Tlog and Klog adapt based on the following relation: ( ) = + ∙ | ( )|,
are initial values, and β and γ are adaptive coefficients. εi(t) εi‘ (t)
εi*(t) yi‘ (t)
ui(t) ui(t) + + ui*(t)
The predicted error value is also updated to include nonlinear effects, which can improve prediction accuracy under high oscillation conditions:
The coordinating logic algorithm [40] establishes the coordinating signal ( ) based on the logic signal ( ), which is derived from a comparative analysis of the dynamics ( ) of the i-th subsystem with the dynamics ( ) of the other j-th subsystems. The coordinating signal incorporates a nonlinear dependence on the parameter αlog(t), which adapts based on the mismatch in the subsystems dynamics: ( ) = − ∙ ( ) ( ( ) ∙ ( ) ≥ 0)˄ ( ) = ( ) − ( ) ∙ (− ∙ | ( ) − ( )|), (8) (9) (10) (11) where δ is an adaptive coefficient.
The dynamics deviation of the i-th separate subsystem from the “leader” dynamics is determined according to the expression: dynamics.
where λ is a damping coefficient, reducing the large deviations impact.
The proposed dual-channel logical controller allows generating a control signal for MCACS each separate subsystem, taking into account the remaining subsystems influence. This enhanced model, featuring adaptive and nonlinear elements, provides more precise correction and coordination in control systems and is particularly useful in situations involving unpredictable changes in subsystem
The key improvements in this model lie in the adaptive parameters Tlog, Klog and αlog introduction which dynamically adjust based on system conditions, enhancing the control system responsiveness and stability. Nonlinear functions like tanh and exponential damping ensure smoother transitions, better handling of abrupt changes, and reduced oscillations, enhancing control precision. These improvements make the model more robust and effective in complex, nonlinear environments. This research addresses the evaluation of the effectiveness of the proposed dual-channel logic controller within the helicopter TE MCACS separate subsystems under flight parameter variations from test conditions (H = 0 km, V = 0 M). As a multi-input control object, the helicopter TE (with three regulated coordinates (nTC, nFT, ∗) and one control input (GT), see Table 1 [41–43]) in test mode is described by the following transfer matrix function, considering the time constant Tact = 0.35 second for the aperiodic actuator [44]: rotor r.p.m. nTC
The gas temperature in front of the compressor turbine ∗
The free turbine rotor speed nFT 1 … 42 … 139 … 256 … … … their respective critical limits, specifically 84 samples, respectively). Cluster analysis (Table 1) identified eight distinct classes (I...VIII), confirming the presence of these groups and demonstrating consistency between the training and test subsets (Figure 4). These results helped determine the optimal sample sizes: the full training dataset consists of 256 elements, the validation dataset includes 172 elements (67 % of the training dataset), and the test dataset contains 84 elements (33 % of the training dataset).
a b framework, the main multidimensional linear controller parameters were calculated: conditions for coordination and stabilization of all output variables: • Subsystem controlling the gas-generator rotor r.p.m. (nTC): Tlog = 0.6 second, Klog = 1, αlog = 0.2; • Subsystem controlling the free turbine rotor speed (nFT): Tlog = 0.5 second, Klog = 2, αlog = 0.35; • Subsystem controlling the gas temperature before the compressor turbine ( ∗): Tlog = 0.8 second,
Klog = 4, αlog = 0.3.
According to the dual-channel logical controller configuration (Figure 3), the additional linear regulator within each i-th separate subsystem is described by the specified transfer function [49–51]: ( ) = , = 1,2,3.
(14)
The transition process diagrams for the output coordinate Y(t) in the analyzed helicopter engine control system (using the TV3-117 engine as an example) with the proposed two-channel logical controller are shown in Figure 5. automatic control systems in the bench mode (author’s research).
It is evident that the studied MCACS with the proposed dual-channel logical controllers ensures the desired performance for the TV3-117 engine control in the bench mode. This research examines the helicopter TE (using the TV3-117 engine as an example) two operating modes, corresponding to the following flight conditions: • Point P1 (H = 2.5 km, V = 0.68 Mach), where the helicopter TE (using the TV3-117 as an example) is represented by the following MTF: 0.72 is represented by the following MTF: (15) (16) × 0.42 ∙ (0.55 ∙ + 1) 1.76 ∙ (0.88 ∙ + 1) 0.62 ∙ (0.35 ∙ + 1) −1.34 ∙ (0.32 ∙ + 1) −0.12 ∙ (0.89 ∙ + 1) . 0.32 ∙ (0.68 ∙ + 1)
The transition process diagrams for Y(t) in the TV3-117 engine studied MCACS, without the dualchannel logical controller, with a unit step input signal for each specified point P1–2, are shown in Figures 6 and 7, respectively.
It is clear that the linear control algorithm fails to maintain the helicopter TE control quality when flight conditions change. However, the dual-channel logical controllers introduction significantly enhances the helicopter TE control quality with the control component remaining unchanged, as evidenced by Figures 8 and 9 for points P1 and P2, respectively.
Thus, based on the helicopter TE MCACS computer simulation results (using the TV3-117 engine as an example), it is established that the proposed dual logical control algorithm significantly improves control quality across various flight modes.
In this research, a dual-channel logic controller (see Figure 2) was synthesized, which generates control actions for each separate subsystem while considering the impact of cross-links on the output variables dynamics. The proposed dual-channel logic controller operation principle (see Figure 3) is based on integrating a primary logic control algorithm for the separate subsystem, which adjusts the error signal based on the current and predicted states analysis, and a secondary logic algorithm that creates artificial cross-links between subsystems to coordinate and harmonize the helicopter overall movement.
The research addresses the effectiveness evaluating task of the helicopter TE (using the TV3-117 engine as an example) proposed dual-channel logic controller within the separate subsystems under varying flight parameters compared to the bench test conditions (H = 0 km, V = 0 Mach) (see Figure 5), as well as in two flight scenarios: at H = 2.5 km, V = 0.68 Mach (see Figures 6 and 8) and at H = 4.2 km, V = 0.86 Mach (see Figures 7 and 9). The results obtained demonstrate that the synthesized dual-channel logic control algorithm enhances performance across different helicopter flight modes. The error at the transient process final stage is defined as:
= − , (15) where yfinal is the output signal final value at the transient process end, yss is the output signal steady-state value.
Figure 10 shows the error at the transient process end calculating results (“blue columns” represents the dual-channel logic controller use, “red columns” indicates no dual-channel logic controller) for points P1 (Figure 10a) and P2 (Figure 10b). As seen from Figure 10, without the dualchannel logic controller, the error reaches 2.58 %, while with its application, the error decreases by nearly 40 % and does not exceed 1 %. This indicates a significant improvement in the transient process control quality when using the dual-channel logic controller, demonstrating its effectiveness in reducing error and enhancing system accuracy.
In this research, while the proposed dual-channel logic controller (see Figure 2) demonstrates improved control performance across various flight modes, certain limitations must be acknowledged. The controller effectiveness, evaluated under different flight conditions (H = 0 km, V = 0 Mach; H = 2.5 km, V = 0.68 Mach; and H = 4.2 km, V = 0.86 Mach), is based on the TV3-117 engine specific case and may not fully generalize to other engine models or more complex operational scenarios. Additionally, the improvements observed, such as a reduction in error from 2.58 to below 1 %, are contingent on the controller's implementation and may vary with changes in system dynamics, external disturbances, or unmodeled interactions.
The analysis presented in Figure 10 confirms significant enhancements in transient process control but does not account for potential limitations in robustness or scalability, which require further investigation to confirm the controller's effectiveness across a broader range of conditions and applications.
This research presents the proposed dual-channel logic controller within the helicopter turboshaft engines control systems evaluating results, demonstrating the effectiveness of this approach for controlling complex dynamic systems operating under conditions of parametric uncertainty. The developed dual logic algorithm stands out by considering not only the dynamics of output variables but also the influence of cross-links when generating control signals for each separate subsystem.
The research addresses the proposed dual-channel logic controller effectiveness assessing task within the helicopter turboshaft engines separate subsystems (using the TV3-117 engine as a case study) under varying flight parameters compared to bench test conditions (H = 0 km, V = 0 Mach), as well as in two flight scenarios: at H = 2.5 km, V = 0.68 Mach and at H = 4.2 km, V = 0.86 Mach. The results reveal that the synthesized dual logic control algorithm enhances performance across different helicopter flight modes.
It was found that the error at the end of the transient process, in the dual-channel logic controller absence, reaches 2.58 %, while with the controller's application, the error decreases by nearly 40 % and does not exceed 1 %. This indicates a substantial improvement in the transient process control quality with the dual-channel logic controller use.
The research was supported by the Ministry of Internal Affairs of Ukraine “Theoretical and applied aspects of the development of the aviation sphere” under Project No. 0123U104884. The research was carried out with the grant support of the National Research Fund of Ukraine “Methods and means of active and passive recognition of mines based on deep neural networks”, project registration number 273/0024 from 1/08/2024 (2023.04/0024). Also, we would like to thank the reviewers for their precise and concise recommendations that improved the presentation of the results obtained.
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