Keywords
aircraft control, sliding mode control, landing gear failure, autonomous landing, mobile platform, Lyapunov stability
Emergency landing procedures during landing gear malfunction necessitate quick thinking and precise execution to ensure the safety of passengers and crew. A common strategy involves executing a "wheels-up" landing. This paper examines a unique emergency landing scenario where an aircraft lands on a mobile platform moving along the runway. This method requires coordination and control between the aircraft and the platform to match their velocities during the landing process.
A Boeing 747 was performed as a 3-D point mass simulation in MATLAB. The mobile platform was modeled as a first-order system having throttle as an input and the mobile platform velocity as an output. The methods Proportional integral derivative controller (PID) and sliding mode control (SMC) were utilized to achieve the velocity synchronization amid the aircraft and the platform. For examining the stability of the mobile platform model, Lyapunov’s Theorem for stability was employed. and sliding mode control (SMC) were utilized to achieve the velocity synchronization amid the aircraft and the platform. For examining the stability of the mobile platform model, Lyapunov’s Theorem for stability was employed.
Simulation results show that both PID and SMC controllers successfully controlled the platform velocity to match the aircraft velocity during the emergency landing. However, the SMC controller demonstrated superior performance with faster convergence to the desired velocity reference compared to the PID controller.
The analysis demonstrated that the most suitable control strategy for the mobile platform velocity in relation to aircraft velocity is SMC during emergency landings. The inherent robustness of SMC to disturbances and uncertainties, coupled with its rapid convergence capabilities, makes it well-suited for this application.
aircraft control, sliding mode control, landing gear failure, autonomous landing, mobile platform, Lyapunov stability
This study has been restructured along STARD (Standards for Reporting Diagnostic Accuracy Studies) framework to provide transparent and high quality reporting of the findings and facilitate reproducibility. The STARD checklist was implemented so as to increase the clarity of reporting, give adequate methodological details, and increase the dependability of the reported work.
Effective execution of emergency landing procedures when the nose landing gear mechanism fails, mandates proper coordination and timing, in order to protect the passengers and the rescue team. Such scenarios are mostly dependent on the level of training and experience the pilots possess. (Fahmi, Gatot, & Sutami, 2022) studied the factors which integrate into the decision making processes of aviation pilots such as expertise level, roles undertaken, self-confidence, safety perception, pressure exerted and the pre-acquired training. In the same way, (Neigel & Priest, 2017) focused on the quality of training resources available to U.S. Naval aviators generating particularly among the Landing Signal Officers (LSOs) whose role is very crucial in the safe retrieval of planes flying from the aircrafts.
One standard practice when there is a nose gear failure mechanism is to conduct a wheels-up landing while the main gear is lowered, allowing the nose to ‘sway’ sideways on the runway to reduce the impact. This technique reduces damage to the aircraft by allowing it to safely taxi on the runway surface. (Abdi, et al., 2018) presented a scenario based constructive course certification strategy to evaluate situational circumstances of wheels-up landings through the use of multi scale progressive failure dynamic analysis (MS-PFDA) to encourage forecasting of the deformation behaviour and damage to occur concurrently with the large scale structural models.
Aerodynamic braking and differential braking are other ways that pilots might use in order to control the aircrafts trajectory towards the desired point during the landing rollout apart from the physical techniques. (Guidi, Borgarelli, & Malleret, 2021) have consulted the comprehensive coverage of actuation opportunities within the ATA32 chapter on landing and braking systems, stating the alternating patterns of research and serial developments for fixed and rotary too aircrafts as well as urban and regional air mobility systems which are coming up.
Pilots and emergency services personnel must retain strong lines of communication in the event of an emergency landing so that they can devise a coordinated course of action that reduces safety risks. Regardless of regulated and prescribed maintenance schedules, the failure of landing gear systems still does occur and therefore there is a need for out of the box ideas. (Chuang & Peng, 2024) have described design and specification of a decision-aid landing system for micro fixed wing aircrafts with the aid of computer vision technologies such as robust plane-fitting algorithms as well as orb-slam2 for improved landings.
Other exciting contributions of the Czech scientists’ work include, for example, the cost-effective trajectories for safe concentrating target points across the globe. An RRT* algorithm was proposed by (Fallast & Messnarz, 2017) to create a new automated scenario during emergency events. A dual automated control was provided in (Brukarczyk, Nowak, Kot, Rogalski, & Rzucidło, 2021) which integrated visual landing systems and automation based on fuzzy logic algorithms, imitating the operation of a pilot during landing. Evidently, (Zhang, Zhai, He, Wen, & Niu, 2019) disclosed a method to improve the accuracy of an aircraft landing in a near zero visibility condition without the use of GPS employing Square – root Unscented Kalman Filters (SR-UKF) for the fusion of inertial, infrared and geographical data.
This work presents the solution of a problem by introducing a helicopter, deemed an aircraft, which can perform an emergency landing with few injuries as it plans and executes an emergency landing with the help of a mobile platform which is situated along the length of the runway. This approach focuses on the aviation control systems as well as the risks of the passengers and the rest of the crew members. Multi-Agent Systems and leader-follower control methods, plus reliable landing protocols are necessary for the coordination of ground and aerial craft to mochican during emergencies.
This literature review shows the airports as Licensing Compliance Assurance Systems, analysis of landing gear failures, and synchronization strategies of the leader and follower as high-end control systems and management. The results are envisioned to motivate creative approaches that would mitigate risks in emergency landings and form development objectives of future research in this crucial area.
Failure of the landing gear is a significant safety concern, particularly for the nose landing gear, which can cause catastrophic consequences if it malfunctions. In their study, (Jeevanantham, Vadivelu, & Manigandan, 2017) established that the capability of the landing gear to offer structural safety is very important and especially in models like Boeing 747. (Freitas, Infante, & Baptista, 2019) also presented an extensive laboratory study on the nose landing gear axle of a commercial aircraft. Applying material analysis reinforced with optical and scanning electron microscopies it was determined that the main cause of failure resultant from overload conditions resulting from both shear and bending stresses. Studies of this kind highlights the suitability of using the micro level to decipher the dimensions and enhancing the dependability of the landing gears.
Because of these risks, researchers have directed efforts towards new autonomous landing systems. (Santa Cruz & Shoukry, 2022) presented NNLander-VeriF, a neural network-based method to control air- craft during autonomous landing with vision-based controllers. It showed that a vision-based autonomous landing system is capable both of verifying a safe landing and of doing so in a mechanical failure condition. (Oszust, et al., 2018) also developed a vision-based landing system based on the realistic methodology that onboard cameras could suffice to estimate position of the aircraft during landing. The authors determined that it is possible to safely steer an aircraft in conditions when a part of the landing gear is jammed or nonoperational by using specific visual signals, like the lights on the runway.
Leader-follower control methods have emerged as a promising solution for managing autonomous systems during landings. (Dai, He, Cai, & Yang, 2022) explored leader-follower formation control in underactuated vehicles, which can be adapted to aircraft scenarios where a ground vehicle supports landing operations by synchronizing with the aircraft's motion. Their method, which is based on adaptive backstepping and Lyapunov functions, ensures that the follower (ground vehicle) maintains a safe distance and alignment with aircraft. Furthermore, (Darling, 2014) demonstrated a decentralized leader-follower control strategy using small UAVs. His work showed how visual-based localization can be employed to maintain formation, suggesting its application to nose landing gear malfunctions when a supporting vehicle is used to ensure safe landing.
This study aims to investigate how a control system can efficiently coordinate the velocity of a mobile platform with an aircraft's velocity in order to facilitate a secure and regulated emergency landing. The research question focuses on the effectiveness of synchronizing the velocity of the mobile platform with the velocity of the aircraft during emergency situations to ensure a safe and controlled maneuver.
The successful completion of an emergency landing, where an aircraft lands on a platform, relies heavily on coordination and control between the aircraft and the supporting platform. This part outlines the challenges and goals of creating a control system for matching velocities between the aircraft and the platform.
The main hurdle involves dynamically coordinating the velocity of the moving platform with the aircraft during landing. This necessitates a control algorithm that can adjust the platform's velocity in time to align with the desired approach velocity of the aircraft. The control system must include a feedback mechanism to monitor and assess the aircraft and platform velocities continually. This feedback is crucial for adjusting the platform's velocity, ensuring it aligns optimally and stays in sync with descending aircraft.
We aim to create a framework for emergency landing procedures involving aircraft and mobile support platforms by tackling these aspects in designing a control system for matching velocities between platforms. Through simulations and theoretical analyses, we aim to validate our proposed approach and pinpoint opportunities for improvement in real-world scenarios.
This study suggests two advanced control strategies, Proportional integral derivative controller (PID) and sliding mode control (SMC), to obtain accurate velocity synchronization between the aircraft and the support platform. This section explains the mathematical expressions of the proposed control strategies.
The control architecture also transmits the aircraft's velocity to the mobile platform, which adjusts its throttle output following the aircraft's velocity. Its closed-loop configuration enables communication between the aircraft and the platform needed for a controlled landing operation.
An aircraft's 3-DOF model was simulated using MATLAB 2021b, Simulink version 9.5. Aerodynamic coefficients CL, CD, CY are interpolated from lookup tables generated by Computational Fluid Dynamics simulations. Angles of attack range between a minimum of -10° and a maximum of 20°, Mach between 0.3 and 1.2 (Vinuesa, 2021); however, the aerodynamic coefficient lookup table is based on subsonic tests and therefore cannot capture some crucial effects during high-velocity flight, hence its limited applicability in supersonic regimes. In this work, linear interpolation was performed in order to make the movement of points smooth. The wind gusts were simulated as a short-duration disturbance within a magnitude of 10 to 20 m/s applied for a duration of 2 seconds. In the simulation of turbulence, Gaussian white noise with a standard deviation of 0.05 m/s was used on all axes: x, y, and z. The random seed was controlled in order to make sure that results are repeatable. PID controller was tuned by trial and error while SMC controller has been designed with a sliding surface defined as:
Proportional Integral Derivative Control
More control actions and a quicker reaction are offered by the PID controller approach than by the P and PI controller systems. Control lessens the impact of the disturbance, and PID cuts down on the time needed to archive the set point. Calculating the values of gain Kp, Ki, and Kd is necessary prior to starting the system's tuning procedure. In order to optimize the PID curve's responsiveness, trial and error is employed in the tuning process. Equation (2) is utilized for the computation of all the parameters.
Where:
represents the control signal (throttle setting).
e(τ) is the error between the desired value (aircraft's velocity) and the actual value (platform's velocity) at a previous time points τ.
indicates the error of the difference in velocity between the aircraft and the platform, defined as
Kp, Ki, and Kd are the proportional, integral, and derivative gains, respectively.
PID controllers are used to operate most control systems in most industries. In order to reduce mistake, proportional mode will expedite the process, enhance the manipulating variable more quickly, and provide dynamic response. There is no steady state error when the integral mode reaches zero offset. The derivatives mode alters the pace at which the controlled variable changes. The entire system, which includes the P, I, and D terms, commits to a minimum overshoot, a quick rising time increase in stability, and a reduction in steady state error. The characteristic changes for each controller are displayed in Table 1.
Term | Rise time | Overshoot | Setting time | Steady state error |
---|---|---|---|---|
Proportional | Decrease | Increase | Small changes | Decrease |
Integral | Decrease | Increase | Increase | eliminate |
Derivative | Decrease | Decrease | Decrease | No changes |
When the output is measured by a precise input signal, the control system is depicted by a crude mathematical model through system description. The P, I, and D parameters are gained using an auto-tuning technique, which is often carried out using MATLAB, and a PID controller is created. The identification system's PID closed-loop control is implemented using a Simulink model.
Sliding Mode Control
The sliding mode control (SMC) provides a sliding mode to make the error dynamics reside on a sliding surface to handle the system uncertainties and disturbances. It is very well suited for systems where the controlled quantities are perturbed; moreover, the system's parameters are uncertain or change. The central concept in sliding mode control is to create a control law that forces the system's state to the desired sliding surface, where the system is simplified and more convenient to handle. This forces the system to stay on this surface, giving robustness against disturbances and uncertainties.
The sliding mode control synthesis is done in three steps (Slotine & Li, 1991):
We consider a nonlinear system presented in the equation as follow:
Where f and g are two nonlinear functions continuous supposed bounded.
The goal is to guide an aircraft (Boeing 747) towards a mobile platform, ensuring that both the aircraft and the platform arrive at the landing position simultaneously. This requires precise path tracking and velocity matching between the two systems:
• Aircraft Path Tracking: The SMC strategy focuses on guiding the aircraft along a specific trajectory.
• Platform Velocity Control: The mobile platform adjusts its velocity to ensure that the target landing point matches the aircraft's final position and velocity.
Define Sliding Surface: The sliding surface is designed to ensure that the error between the platform's velocity and the aircraft's velocity converges to zero over time. The sliding surface can be defined as Eq. (1):
Where:
is the velocity error between the aircraft and platform.
λ > 0 is a positive constant that affects the convergence rate of the system.
is the time derivative of the error.
The SMC control input is designed to drive the sliding surface S(t) to zero. The control law of SMC allows to converge very rapidly to the velocity reference even in the presence of changes in the operating conditions. The objective of this control law is to limit the state trajectories of the system so that they not only reach the sliding surface but also remain on it, even in the presence of uncertainties within the system. In essence, the control law must render the sliding surface locally appealing. Consequently, the control law should be determined by verifying a condition that guarantees the sliding variable S(t) to converge to 0. This condition is referred to as the reachability condition. Since platform velocity was to be controlled relative to aircraft velocity, the stability of the mobile platform model is a mandatory check before implementing a controller. The Lyapunov stability theorem has been used to check the stability of the mobile platform model.
Zhou et al. (Zhou, Hu, Zhu, & Ma, 2021) [11] claim Hamilton energy can be the most suitable Lyapunov function. The Hamiltonian energy refers to a system's total energy (sum of kinetic and potential energy), which is a fundamental concept in classical mechanics. Potential energy can be ignored when moving a vehicle on a straight runway. The stability analysis of the proposed control is proved using the Lyapunov candidate function approach given by:
The derivative of Lyapunov function must be negative and the asymptotic stability is therefore guaranteed using sliding mode control. The necessary and sufficient condition to satisfy the reachability condition is expressed as (Edwards & Spurgeon, 1998):
For a convergence in finite time, we replace the condition of reachability (Eq. (6)) which only guarantees an asymptotic convergence towards the sliding surface by a more restrictive condition called η-reachability and it is defined by:
The control variable U is the sum of the equivalent control , which can be interpreted as the continuous control law that would maintain , and a discontinuous component which presents the dynamic response providing the convergence and the sliding mode.
is the discontinuous command usually adopted as:
Where:
k is a positive gain that controls the strength of the sliding action.
is the sign function that switches the control input based on the sliding surface's value
The sliding mode control law can be expressed as (Liu, Gao, Yunfei, Jiahui, Wensheng, & Guanghui, 2020):
k1 and k2 are a positive constant, tuned to ensure robustness against disturbances.
In order to describe the motion of the aircraft and mobile platform, a fixed inertial frame is defined in a north-west-up (NWU) reference coordinate frame and a velocity frame is placed at the center of mass of each vehicle in a forward-left-up coordinate frame. This simulation model, which focuses on an aircraft's primary motion axes (pitch, roll, and yaw), provides a fundamental understanding of aircraft dynamics and behaviour. In this paper, a Boeing-747 is considered as a point mass, and its three-dimensional equations of motion in the presence of wind disturbances are shown below (Rucco, Sujit, Pedro Aguiar, Sousa, & Lobo, 2018):
Where defines the position of the aircraft in the inertial frame. The velocity vector is determined by the airspeed , flight-path angle , and heading angle . The wind components within the inertial frame are represented as , , and . In the trajectory optimization problems addressed in this study, a constant wind velocity is presumed. The method we propose seeks to create trajectories that will act as reference trajectories, enabling the design of closed-loop control systems capable of adhering to these nominal trajectories despite uncertainties and disturbances caused by wind gusts and turbulence during actual flight. The lift, drag, and side forces are computed as follows:
Where is the atmospheric density, and S is the reference surface area of the aircraft. The lift ( ), drag ( ), and side force ( ) coefficients are assumed to be from Table 2, which shows the aerodynamic parameters of the Boeing-747 used to implement the aircraft mathematical model in simulation (McLean, 1990).
The motion of the mobile platform is confined to a two-dimensional plane on the ground, and its equations of motion in this context are as follows:
Mobile Platform has been modelled as a SISO system where the throttle is the input, and Mobile Platform velocity is the output. The platform has been modelled as single order system:
Where defines the position of the mobile platform in the inertial frame, and due to the planar-motion assumption. The velocity vector is determined by the ground velocity and the heading angle . We assume that the path of the mobile platform is predetermined by the runway, which doesn’t have curvature ( ), and we control the longitudinal acceleration of the mobile platform to accelerate or decelerate along the fixed path.
By choosing the velocity frame of the aircraft as the reference frame, the motion of the mobile platform can be defined with respect to the aircraft, and a coupled dynamic system is formulated below (Wang & McDonald, 2020):
This section shows the results of the complete simulation. Simulation results show that the Lypunov function and its derivative fulfill Lyapunov stability criteria, as shown in Figure 1.
Figure 2 shows the 3D trajectory followed by the aircraft during the emergency landing. The figure shows that the aircraft follows the predefined trajectory for an emergency landing.
Figure 3 shows the altitude landing profile along the distance from the runway endpoint.
When an aircraft approaches the runway for an emergency landing, the Mobile Platform tries to match its velocity with the aircraft. Aircraft velocity is taken as input, and a throttle command is generated based on an error between the desired/commanded velocity and the Platform velocity. Figures 4 and 5 show the Platform velocity control for the PID and SMC controllers, respectively.
Figure 5 shows the ground platform's velocity nearly sharply shoots over the desired velocity. Oscillatory behavior is less dominant in this strategy than in the PID control method. The ground platform matches the aircraft's velocity reduction, indicating higher stability during desired trajectory.
The comparison between the PID and SMC controllers reveals that the SMC performs much better than the PID controller. While the desired steady-state velocity was finally achieved thanks to the PID controller, persistent and substantial deviations around the actual velocity were evident during the transient period. This period was highly oscillatory, as overshoot and undershoot for a time resulted in large discrepancies from the required velocity.
In Figure 6, the relative position error over time which exhibits level of oscillations with time which reduce gradually, this means that the control strategy within the system is working to provide the necessary adjustments for the error as time advances. The system reaches a steady state accuracy also at one particular point, which has a position error of zero.
Figure 7 represents the control effort for a system controlled using a Sliding Mode Controller (SMC). After the oscillations reduce significantly, and the control effort stabilizes. The amplitude of the control effort initially varies significantly, showing the controller's aggressiveness in reducing the error and maintaining robustness. Over time, the control effort decreases, which is typical as the system approaches the desired trajectory.
This study's results highlight the crucial role precise velocity management plays in successful emergency aircraft landings on a mobile platform. Both Proportional Integral Derivative (PID) control and Sliding Mode Control (SMC) achieved synchronization between platform velocity and the aircraft during flight but SMC demonstrated better performance outcomes. SMC shows superior performance because it maintains strong stability in the presence of disturbances and uncertainties while quickly reaching the target velocity reference.
Sliding mode control demonstrates strong potential for achieving optimal aircraft-to-platform velocity matching during emergency landing situations. The study results indicate that future research should focus on improving control strategies for better reliability and adaptability through the adoption of advanced adaptive or intelligent control methods. Research should investigate multi-agent coordination methodologies and execute real-time trials on experimental testbeds to determine the controller's performance under actual conditions.
In conclusion, our comparative analysis between Proportional Integral Derivative (PID) and Sliding Mode Control (SMC) methodologies for controlling the velocity of a Mobile Platform concerning aircraft velocity during emergency landings reveals that SMC offers superior performance. The inherent robustness of SMC to disturbances and uncertainties, coupled with its ability to ensure rapid convergence to the desired velocity reference, renders it particularly well-suited for dynamic emergency landing scenarios. Furthermore, SMC's simplicity and effectiveness make it a viable choice for real-time implementation in aerospace systems. As such, our findings advocate adopting sliding mode control as the preferred control strategy for facilitating velocity matching between aircraft and mobile platforms during emergency landing operations, thereby enhancing the safety and efficiency of such critical manoeuvres.
All simulation codes used in this study have been fully adapted for compatibility with GNU Octave, an open-source alternative to MATLAB. To ensure smooth execution in the GNU Octave environment, MATLAB-specific functions have been replaced with equivalent alternatives, and plotting and data processing commands have been adjusted accordingly. This compatibility allows for the reproducibility of results without reliance on proprietary software, enhancing accessibility and broadening the potential user base within the academic and research communities.
No data are associated with this article.
GitHub Repository: CONTROL-STRATEGY-FOR-AIRCRAFT-LANDING-ON-MOBILE-PLATFORM (since 31/12/2024).
Zenodo Repository: DOI: 10.5281/ZENODO.14887222 (since 18/2/2025).
License: OSI approved open license software: Creative Commons Attribution 4.0 International
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Is the rationale for developing the new method (or application) clearly explained?
Partly
Is the description of the method technically sound?
Partly
Are sufficient details provided to allow replication of the method development and its use by others?
Partly
If any results are presented, are all the source data underlying the results available to ensure full reproducibility?
Yes
Are the conclusions about the method and its performance adequately supported by the findings presented in the article?
No
Competing Interests: No competing interests were disclosed.
Reviewer Expertise: Control & stability, Artificial Intelligence, Avionics Aeronautics, Aircraft Flight Control Systems, Anomaly Detection
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Version 1 14 Apr 25 |
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