RESEARCH OF KINEMATICS AND SOLUTIONS TO OVERCOME THE DELAY CAUSED BY THE STEERING CONTROL UNIT IN THE AUTOMATIC SYSTEM OF CONTROLLING THE ANGLE STABILITY OF THE AIRCRAFT

ABSTRACT

This paper presents the research results on the factors affecting the control kinematics of the automatic system of controlling the angle stability of the aircraft. In which, the influence of the delay time caused by the steering control unit (SCU) is focused on research. Then, the paper presents studies on solutions to overcome the effects of delay time to improve the kinematic quality of the automatic control system on aircraft. The results of the dynamic simulation of the system by the automatic control system modeling and analysis software will demonstrate the studied solutions.

АННОТАЦИЯ

В статье представлены результаты исследования факторов, влияющих на динамику управления системой автоматического регулирования угловой устойчивости самолета. В частности, на исследовании сосредоточено влияние задержки, создаваемой механизмом управления рулями направления (рулем направления). Далее в статье представлены исследования решений по повышению динамического качества системы автоматического контроля угловой устойчивости летательных аппаратов. Результаты динамического моделирования системы с использованием программного обеспечения для моделирования и анализа систем автоматического управления продемонстрируют решения по повышению качества исследованной системы автоматического регулирования угловой устойчивости самолета.

Keywords: Control kinematics, the angle stability, Steering control unit, the aircraft, automatic system, the kinematic structure.

Ключевые слова: кинематика управления, угловая устойчивость, рулевой орган, летательный аппарат, автоматика, кинематическая структура.

Introduction

The kinematics of the automatic system of controlling the angle stability of the aircraf are described through the angular stability automatic control loops. They play a very important role in the flight control system. These loops ensure stable and tuning kinematics for the aircraf. It contributes to eliminating the error of controlling the flight trajectory, reducing the control work for the pilot in the steady-state flight mode. The stability of the aircraft's angular position is a necessary condition to ensure the normal operation of the main equipment on the aircraft.

When considering the motion of the aircraft in space, it is necessary to consider the problems of stabilizing the angles of the aircraft around the center of mass such as pitch angle, inclination angle and deflection angle; problems about plane coordinates, airspeed, altitude. When integrated analysis all those processes will be very complex. Hence for simplification, the plane motion is subdivided into the simpler vertical and edge motions. Vertical motion is the motion that the aircraft maneuvers in the vertical plane along its axis according to the following parameters: x coordinate, altitude H, angle of attack α, pitch angle υ, and orbital inclination angle θ. Edge motion is the motion in which the aircraft maneuvers in the horizontal plane in terms of side offset z, pitch angle γ, deflection angle ψ, slip angle β, and orbital turn angle θ_Г. Thus, when solving the problem of stable control of the aircraft's angles around the center of mass, the coordinates of the plane are not taken into account.

The basic structure of the aircraft's angle stability automatic control system is shown in Figure 1. In which, X is the preset signal (depending on the flight post or flight mission); Y is the output signal of the automatic system, which will be provided to the power steering to control the rudders; The SCU is the actuator of the automatic control system that will move the oil needle in the hydraulic power steering unit of the rudder according to the control signal of the system. This is the general structure of the plane's angle control channels.

Figure 1. Structural diagram of the automatic system of controlling the angle stability of the aircraft

Within the limits of this paper, the control loop that stabilizes the pitch angle of the aircraft and the kinematic effect of the delay time caused by the SCU are focused on for illustration purposes.

Materials and Methodology

When analyzing the control kinematics, from the diagram of Figure 1, the basic kinematic structure diagram of the automatic control system for the stability of the angular position of the aircraft is built as shown in Figure 2, this is in simple form. Where, k is the gain of the control signal; W_MB(P) is the transfer function of the plane; d_B is the altitude rudder deflection angle signal.

Figure 2. Diagram of the kinematic structure of the automatic system of controlling the angle stability of the aircraft

After simplification, the transfer function of the plane according to the pitch angle is built in the form [1, 3, 4], as (1), (2).

                                                 (1)

In there:                                                       (2)

In (1), (2), the coefficients n₀, n_B, n₂₂, n₃₃, n₃₂ are known functions, time-dependent, dimensionless, determined depending on the aircraft structural design. For short periods not greater than the aerodynamic constant t_a they can be assumed to be constant. In which, the coefficient n_B characterizes the correction stage of the control loop circuit; coefficients n₂₂, n₃₃ characterize the level of stability according to the control channel of the angle of attack, the angle of angle, the larger it is, the faster the oscillation will decrease; n₃₂ characterizes the crosslinks between channels a, u, shows vertical static stability, if n₃₂ > 0, the aircraft is stable.

In autopilot systems, when considering the effect of hysteresis, a dynamic structure diagram as shown in Figure 3 is used [2, 5]. The delay time in the control channel is due to the limited speed of the control signal processing mechanism of the hydraulic mechanism, so it is not possible to control the rudder into the necessary angular position to control the aircraft immediately.  It gets delayed after some time.

W_Dt(P) is the transfer function of the delay unit defined by (3).

                                                   (3) 

Figure 3. Schematic of the kinematic structure of the aircraft's angular stability automatic control system with the effect of hysteresis

On aircraft, in order to improve the kinematics of the automatic angular stability control system, the system structure diagram is supplemented with speed and acceleration feedback loops of the angle signal [1, 6]. In this paper, that solution is also studied, proposed and applied to overcome the effect of delay caused by the SCU. The structure diagram was built as shown in Figure 4. Where, k', k'' are the feedback gain of the changing speed and acceleration signal of the pitch angle.

Figure 4. Dynamic structure diagram with speed and acceleration feedback

The coefficients given in the transfer functions, the kinematic structure diagram above are dimensionless and it would be difficult to assess the change in the kinematic properties of the aircraft. So when calculating, the coefficients with dimensions will be used, the coefficients n₀, n_B, n₂₂, n₃₂, n₃₃ are replaced by the coefficients n’₀, n’_B, n’_22, n’₃₂, n’₃₃. They are determined by formulas (4), (5) [7].

                                              (4)

In formula (4), the factor related to the aerodynamic characteristics of the aircraft is expressed by the aerodynamic constant t_a.

                                                                          (5)

Where: m is the weight of the plane, r is the air density, V is the speed of the plane, S is the wing area of the plane.

When analyzing the diagram of Figure 3, for light aircraft, the pitch angle channel, the control signal gain is determined according to (6) [5, 7].

                                                                 (6)

When analyzing the diagram of Figure 4, for light aircraft, the pitch angle channel, the gains is determined according to (7), (8).

                               (7)

            (8)

Materials and Methodology

Consider the case of a simple system

Analyze the diagram of Figure 3 with simulation data referenced from [1, 2, 3] as follows: Light aircraft (H = 15 km; M = 2,5; t_a = 2.5c); parameters n₀ = 0,7; n_B = 100; n₂₂ = 2,5; n₃₃ = 2,2; n₃₂ = 16; The input signal used is a step function (Step).

Conduct simulation by modeling and analysis software for automatic control system VISSIM. The result is the transition characteristic of Figure 5. When the system has no delay t = 0s; when the system has a delay with t = 0.3s and when the system has a delay with t = 1s. The detailed results of the kinetic parameters are shown in Table 1.

Figure 5. Simulation graph of the transient process of the automatic control system when considering the effect of delay

Table 1.

Kinetic parameters of the system when considering the effect of hysteresis

From the simulation results we see that in the control process, the presence of delay in the control channel will reduce the control quality. The larger the delay, the worse the dynamics of the automatic control system.

Consider the case that the system has added speed and acceleration feedback loops

Simulating the transition process of the automatic control system according to Figure 4, the simulation data remains unchanged (same case as above).

The simulation graph is shown in Figure 8. The detailed results of the kinematic parameters are shown in Table 4.

Figure 6. Graph simulating the transient process of the automatic control system when there are speed and acceleration feedback loops.

Table 4.

Kinetic parameters of the system when there are feedback loops

In this case we also see that in the control process, the presence of delay in the control channel will reduce the control quality, the larger the delay, the worse the dynamic quality of the automatic control system. However, when comparing Figures 5 and 7, Figures 6 and 8, comparing tables 1 and 3, 2 and 4, we see that the effect of hysteresis has been significantly reduced. The kinematic quality of the system with speed and acceleration feedback loops has been improved.

Conclusion

Thus, the research content presented in the paper has given the correct scientific basis to confirm the existence of delay time and its influence on the quality of kinematics of a aircraft's angular stability automatic control system. Since then, the paper presents research results with evidence by simulation on a solution to overcome the effects of delay and improve the kinematic quality of the automatic control system on the aircraft. With this solution, speed and acceleration feedback loops were used to attenuate the effect of delay. Therefore, the quality of the automatic control system has been improved significantly.

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