1. Introduction
In the last decade, there has been a growing trend to replace traditional hydraulic actuation (HA) systems with electromechanical actuation (EMA) systems for aircraft nose wheel steering systems or flight control surfaces. This shift is motivated by the numerous advantages of EMA over HA, including better economy, energy efficiency, noise reduction, maintenance, and downsizing [
1]. Additionally, to enhance aircraft safety, most aircraft components, including actuators, require system redundancy [
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13].
Unlike other components, redundant actuation systems must consider the effects of mechanical parameter differences, such as manufacturing differences, assembly tolerances, backlash, friction, and payload, when creating system redundancy. These differences make it impossible for the mechanical control outputs of two or more actuators to move to the same position. Consequently, during operation, the actuators may generate forces that push and pull against each other, which is commonly referred to as the force-fight phenomenon. This phenomenon can lead to serious issues, such as fatigue failure and degraded control performance during flight, as discussed in [
2]. Therefore, it is crucial to either eliminate or mitigate the force-fight to ensure safe and efficient aircraft operation.
In the past, a physical method of manually tightening the bolts of the actuation systems before takeoff was used to improve the position error and mitigate the force-fight. However, this physical method has limitations in eliminating the force-fight because fundamental causes, such as manufacturing errors and assembly tolerances, are not eliminated. Therefore, several studies have been conducted to reduce or eliminate the force-fight using various control approaches, such as the multi-variable control approach [
3,
4], decoupling method [
5,
6], motion synchronization approach [
7], pressure differential equalization method [
8,
9,
10,
11], redundant current-sum feedback approach [
12], and precise model-based approach [
13]. However, these existing methods have limitations when applied to a redundant system with only EMAs because they are designed for a redundant system with only HAs or a dissimilar redundant system that combines HA and EMA, and, thus, do not account for the differences in system characteristics. Furthermore, their approaches assume that all relevant system states are observable and/or measurable, or that the models used for force equalization closely match real systems.
This paper focuses on a dual redundant system that uses two EMAs, as illustrated in
Figure 1. Unlike previous studies, this system has only three measurement variables available for each EMA, namely two motor velocities and a final control axis angle, which limits the number of system states that can be used. Additionally, the force generated by the force-fight cannot be directly measured, making it necessary to accurately predict or estimate it using the limited system states in order to eliminate the phenomenon. To address this issue, we propose a novel control approach based on disturbance observers that can estimate and eliminate the force-fight, as the force generated by the force-fight can be regarded as an external and unknown disturbance for each EMA. By employing a disturbance observer, it is possible to remove external disturbance forces that are caused by the force-fight phenomenon. This approach can significantly enhance the system’s robustness and enable it to respond effectively to potential uncertainties [
14].
Disturbance observers are composed of several types including Q-filter-based Disturbance Observers (DOBs), binary disturbance observers, and state-space-based disturbance observers. In this paper, our intention is to utilize a Q-filter-based DOB due to its simple structure and flexibility in implementing the controller [
15]. The proposed method has been applied to an aircraft nose wheel steering system, as depicted in
Figure 1. This system is a dual-redundant actuation system consisting of two sets of EMA systems. Each EMA system employs a PMSM as its power source, and a gear reducer and a worm as power transmission devices, as illustrated in
Figure 2. The worm gear of each actuation system is connected to a single, common worm wheel, resulting in a final motion output that controls the angle direction of the aircraft’s nose wheel steering system.
The rest of this paper is organized as follows. In
Section 2, we describe the system model for the aircraft nose wheel steering system, which consists of a dual redundant actuation system with two PMSMs and worm–worm gear power transmission. In
Section 3, we present the proposed dual control architecture based on a Q-filter-based DOB, which aims to eliminate force-fighting.
Section 4 includes the simulation results used to verify the proposed methods. Finally, in
Section 5, we draw conclusions and provide an outlook on future work.
3. Force-Fighting and Disturbance Rejection Methodology in Dual EMA Systems
3.1. Control Architecture
The controller structure that integrates the Q-Filter-Based DOB for Dual EMA systems is illustrated in
Figure 5. The key elements comprise Q-Filter-based DOBs, a worm position controller, motor controllers, and a motor command generator. Among these components, the Q-Filter-based DOBs play a crucial role in estimating and mitigating the overall disturbance, denoted as
d1 and
d2, caused by unknown external disturbances, namely
TL, as well as torque differences Δ
Tw1 and Δ
Tw2 between the PMSM dynamics #1 and #2.
The primary input (Worm wheel position Ref.) to the system is derived from the position of the worm wheel, serving as an indicator of the intended action to be executed by the control system to achieve the desired performance. Simultaneously, the system’s output is characterized by the measurable response of the worm wheel position, θw, which is influenced by both the control signal and a multitude of disturbances and force-fighting phenomena.
Consequently, the controller responsible for regulating the worm wheel position, specifically referred to as the worm wheel position controller in
Figure 6, is employed to generate a control signal,
Rw, based on the system’s present state and the desired performance, as depicted in
Figure 6. To accomplish this, the controller adopts a PID control law, whereby the appropriate gains are determined iteratively through a trial-and-error process, optimizing their values to attain the desired control performance [
17,
18]. The control signal
Rw is subsequently employed within the motor command generator to bifurcate into two secondary reference inputs, namely Ref. #1 and Ref. #2, designated for the motor controller, as depicted in
Figure 6.
The Q-filter-based DOB is designed based on the desired disturbance and force-fighting rejection characteristics of the system. It is typically implemented as a low-pass filter with specific cut-off frequencies and attenuation properties. Hence, the Q-Filter-based DOB’s role is to filter out external disturbances and force-fighting phenomena that can negatively impact the performance of the EMA system, by estimating and compensating for the disturbances.
The compensation process is executed by the motor controllers, as illustrated in
Figure 7, specifically for the actuation system #1. It involves utilizing feedback of the motor velocity and comparing it with the reference input to determine the velocity error, which is subsequently compensated using a PID controller. Simultaneously, the DOB generates a compensation signal to counteract the effects of disturbances, with the objective of achieving precise control of the Dual EMA systems.
Subsequently, the output of the PID controller is combined with the observed disturbances using a feedforward controller. This integration serves the purpose of rejecting external disturbances and engaging in force-fighting measures. The resulting compensated output is then directly applied to the PMSM motor for implementation. The selection of the PID controller gain is typically determined through a process of trial and error, optimizing its value to achieve the desired control performance. On the other hand, the transfer function of the feedforward controller can be designed mathematically as follows:
3.2. Q-Filter-Based DOB Design and Structure
Essentially, the DOB provides a robust dynamic relationship between control inputs and desired plant outputs even in the presence of model uncertainties and disturbances. To this end, DOB leverages the inverse of the nominal model in combination with a low-pass Q-filter to estimate system disturbances, which can then be utilized as a cancellation signal.
Figure 8 illustrates the structure of DOB, where
Pn(
s) represents the nominal model from Equation (7),
Q(s) is the Q filter whose DC gain is one, and Δ(
s) corresponds to the model uncertainty from Equations (9) and (10). Hence, to attain behavior similar to Equation (2), the actual plant must be represented by
P(
s) =
Pn(
s) + Δ(
s) [
19].
Pn(
s) and Δ(
s) can be derived as in
To ensure that
is proper and implementable, it is necessary for the relative degree of
Q(
s) to be greater than or equal to the relative degree of
Pn(
s). With this requirement, the structure of the Q-filter DOB can be selected as follows:
where the damping ratio
ζ is typically set to 0.707, while the cutoff frequency
ωc is chosen so that it does not compromise the stability of the closed-loop system. The transfer function of the system in
Figure 8 can be expressed as
The Q-filter is a type of low-pass filter, as depicted in Equation (12), with the property that
Q(
jω) tends to be unity for
ω values much smaller than
ωc, and tends to be zero for
ω values much greater than
ωc. Consequently, Equation (13) indicates that for ω values much smaller than
ωc,
In other words, in the frequency domain, where Q(jω) equals one, external disturbances and model uncertainties are significantly attenuated, leading to the output of the actual system closely resembling that of the nominal system. This finding is especially useful for real-world applications, as most reference inputs and disturbances are low-frequency signals.
Therefore, to design a Q-filter DOB in this paper, the following requirements should be met:
- ①
The structure of the DOB must follow Equation (13).
- ②
The damping ratio ζ is commonly set to 0.707.
- ③
The cutoff frequency ωc must be selected in a way that maintains the stability of the closed-loop system.
- ④
The frequencies ω of all inputs should be significantly lower than ωc.
3.3. Stability Analysis for Motor Control Systems
Based on
Figure 5,
Figure 6,
Figure 7 and
Figure 8 and the equations pertaining to PMSM and Q-filter DOB, the closed-loop transfer function of the motor control system with disturbances can be derived as follows:
where
Gc(
s) represents the PID controller,
r(
s) denotes the reference input of Ref. #1 or Ref. #2, and
ω(
s) represents the motor velocity output of
ωm1 or
ωm2, as indicated in
Figure 7.
Since, for
ω values much smaller than
ωc,
Q(
jω) tends to be unity due to the property of the Q-filter DOB, Equation (16) indicates that the closed-loop system becomes
Now, the stability of the control system depends on how PID control gains are chosen. As mentioned in
Section 3.1, PID gains are determined iteratively through a trial-and-error process, optimizing their values to achieve the desired control performance. This implies that the poles of the system (17) should be placed on the left-hand side of the s-plane. Consequently, the control system can be stable regardless of the stability of PMSM and/or Q-filter DOB.
5. Conclusions
This paper presents a robust control system that addresses two key challenges in redundant actuators for an aircraft nose wheel steering system: the elimination of force-fighting phenomena and the ability to respond effectively to unexpected disturbances. In detail, a control method was devised to enhance the mitigation of force-fighting and disturbances by accurately observing and compensating for the torque-induced load applied to the PMSM. This was achieved through the utilization of a Q-filter-based DOB. The proposed control approach was implemented and evaluated on a redundant system consisting of the PMSM and the nose wheel steering system.
To facilitate the development of the control methodology, a comprehensive mathematical model was established for both the redundant system in the PMSM and the nose wheel steering system. This model served as the foundation for conducting in-depth analysis and investigation. The key objective of this research was to effectively address the force-fighting phenomenon and disturbances by incorporating the Q-filter-based DOB. This approach enabled the precise observation and compensation of the load exerted on the PMSM as a result of force-fighting and disturbances. The subsequent analysis and evaluation provided valuable insights into the performance and efficacy of the proposed control method in the context of the redundant system and its application to the nose wheel steering system. The performance of the proposed method was verified through extensive simulation studies. The simulation results confirmed the effectiveness and reliability of the method in accurately observing and responding to the force-fighting phenomenon that occurs in the redundant driving device.
By subjecting the system to various scenarios and disturbances, the simulation provided a comprehensive evaluation of the proposed method’s ability to handle force-fighting phenomena. The results demonstrated that the method successfully observed and responded to the force-fighting phenomenon, thereby mitigating its adverse effects on the system’s performance. Therefore, these outcomes serve as empirical evidence supporting the validity and efficiency of the proposed method in addressing the force-fighting phenomenon encountered in the redundant driving device. These findings substantiate the effectiveness of the proposed approach and its potential for practical implementation in real-world systems.
For future works, we need to consider inevitable time delays, as depicted in
Figure 4, since all electromechanical systems controlled with a digital controller face such delays. However, these delays were neglected in this paper. Interested readers regarding this topic can refer to the relevant topic in reference [
21]. Another aspect to be taken into account is the influence of aerodynamic forces. The landing gear is deployed above the landing speed, and the hyper sustainer elements are also deployed within the speed range of 170 to 240 knots. However, this particular effect was not addressed in this paper as it falls outside the scope of our study. Nonetheless, it is worth noting that the proposed method in this paper demonstrated its capability to effectively handle unknown disturbances, as shown in the verification section. As a result, we can speculate that the method presented in this paper has the potential to manage aerodynamic forces as a disturbance as well. Further research and investigation in this direction could prove beneficial for future applications in flight control systems.