Parawing system flight path tracking and anti-interference control method based on constant period sliding mode control

Abstract

The invention discloses a parafoil system flight path tracking and anti-interference control method based on constant period sliding mode control, and the method comprises the steps: carrying out the stress analysis of a parafoil system, building a translation three-degree-of-freedom model and a rotation three-degree-of-freedom model of the parafoil system according to a Newton-Euler equation, and taking the models as a flight path tracking control basis; based on a sliding mode control principle, designing a basic sliding mode controller of the parafoil system, and obtaining a sliding mode control law by constructing a sliding mode surface and designing an approaching law so as to realize finite time stable tracking of a system state variable; for the inherent buffeting and overshoot problems of sliding mode control, a saturation function is introduced to replace a sign function, and a continuous and smooth switching law is designed in a sliding mode surface neighborhood to realize sliding mode control law optimization; and designing a constant period disturbance observer, estimating and compensating the total disturbance of the system in real time, and performing feedforward compensation on an observation value to a sliding mode control law, thereby enhancing the robustness and anti-interference performance of the system. The method has good trajectory tracking performance and anti-interference capability.

Description

Technical Field

[0001] This invention belongs to the field of trajectory tracking and control technology for paraglider systems, specifically relating to a method for trajectory tracking and disturbance rejection control of paraglider systems based on constant period sliding mode control. Background Technology

[0002] As a high-performance, high-glide-ratio parachute, the winged parachute system plays an irreplaceable role in precision airdrops, spacecraft recovery, and drone landings due to its excellent aerodynamic performance and controllability. Compared to traditional circular parachutes, the winged parachute system can achieve gliding, turning, and rappelling maneuvers by manipulating the left and right parachute lines, thereby significantly improving landing accuracy and safety.

[0003] Currently, various technical approaches have emerged in the field of trajectory tracking control for paraglider systems, primarily including traditional PID control, fuzzy logic-based adaptive control, model predictive control based on linearized approximation, and robust sliding mode control. A comprehensive analysis of existing control architectures reveals that most studies still employ a single control strategy to achieve paraglider trajectory tracking. However, as an unpowered high-altitude flight platform, the paraglider system exhibits significant slow dynamic characteristics, strong nonlinearity, and lag in maneuver response. When faced with complex wind field disturbances, traditional control methods often struggle to achieve an ideal balance between dynamic performance and robustness. In contrast, sliding mode control, with its strong invariance to parameter perturbations and external disturbances, offers a highly promising solution for such nonlinear systems. However, traditional sliding mode control faces significant challenges in paraglider system applications: its inherent high-frequency chattering phenomenon excites unmodeled dynamics of the system, adversely affecting the flexible structure of the paraglider and potentially reducing control accuracy and system stability.

[0004] This shows that, when faced with the stringent requirements for control quality of paraglider systems in complex environments, a single control strategy has inherent limitations in balancing disturbance rejection, dynamic performance, and flutter suppression. Summary of the Invention

[0005] The technical problem to be solved by this invention is to address the shortcomings of the prior art by providing a trajectory tracking and disturbance rejection control method for a paraglider system based on constant-period sliding mode control. An innovative control architecture is proposed, combining a constant-period disturbance observer with sliding mode control. This fully utilizes the strong robustness of sliding mode control while simultaneously achieving rapid and accurate estimation and feedforward compensation of uncertainties such as wind disturbances through the constant-period observer. Combined with an improved reaching law design, this effectively suppresses control chattering while maintaining the system's finite-time convergence performance, comprehensively improving the trajectory tracking accuracy and robustness of the paraglider system in complex environments.

[0006] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for trajectory tracking and disturbance rejection control of a paraglider system based on constant period sliding mode control, characterized by comprising:

[0008] Step 1: Perform force analysis on the parachute system and establish translational and rotational three-degree-of-freedom models of the parachute system based on the Newton-Euler equations, which serve as the basis for trajectory tracking control.

[0009] Step 2: Based on the translational three-degree-of-freedom and rotational three-degree-of-freedom model of the paraglider system, and based on the sliding mode control principle, design the basic sliding mode controller of the paraglider system. By constructing the sliding surface and designing the reaching law, the sliding mode control law is obtained to achieve finite-time stable tracking of the system state variables.

[0010] Step 3: Based on the basic sliding mode controller, to address the inherent chattering and overshoot problems of sliding mode control, a saturation function is introduced to replace the sign function, and a continuous and smooth switching law is designed in the neighborhood of the sliding surface to optimize the sliding mode control law.

[0011] Step 4: Design a constant period disturbance observer to estimate and compensate for the total system disturbance in real time, and feed the observed values ​​forward to the sliding mode control law to enhance the robustness and disturbance rejection performance of the system.

[0012] To optimize the above technical solution, the specific measures also include:

[0013] Step 1 above establishes the translational three degrees of freedom of the parachute system as follows:

[0014] ;

[0015] in, The three-dimensional coordinates of the parachute are given. For parachute ground speed; and These are the tilt angle and deflection angle of the flight trajectory, respectively.

[0016] The three-degree-of-freedom rotational model of the parachute system established in step 1 above is as follows:

[0017] ;

[0018] in, , and It is the component of the rotational angular velocity along each axis of the body coordinate system;

[0019] pitch angle Yaw angle and roll angle The derivative of .

[0020] Step 2 above, which designs the basic sliding mode controller, includes:

[0021] Define position error and speed error : , ;

[0022] in, The actual three-dimensional coordinates of the parachute's position. These are the three-dimensional coordinates of the predetermined trajectory points. These are the three-dimensional error values ​​between the actual position of the parachute and the predetermined trajectory point;

[0023] The actual velocities of the paraglider in the three axial directions, These are the predetermined velocities in the three axial directions of the parachute. These are the differences between the actual speed and the predetermined speed of the parachute in the three axial directions;

[0024] The derivative of velocity is obtained by the following formula: ;

[0025] in, Yaw angle The derivative; For horizontal velocity, For horizontal acceleration, Vertical velocity; for The derivative;

[0026] The sliding surface is designed as follows: ,right Differentiating, we get: ,in For sliding surface, This is the sliding mode scaling factor;

[0027] Define the law of exponential convergence: ;in, It is the linear convergence rate parameter. It's about switching the gain. >0, >0;

[0028] Define Lyapunov functions Differentiating it, we get: ,in It is a Lyapunov function;

[0029] According to the above formula, the designed sliding surface satisfies the Lyapunov stability criterion;

[0030] The control law is composed of the equations for the sliding surface and the exponential reaching law, resulting in:

[0031] Among them, parameters , , , , , , These are coefficients obtained from system modeling; It is a nonlinear term in parachute dynamics; It is the input gain matrix. They are equivalent control input variables. For symbolic functions, This represents the ideal dynamics of the target system.

[0032] Step 3 above is specifically as follows:

[0033] By replacing the symbolic function with a saturation function The optimization of the convergence law is as follows: ;in, It is the linear convergence rate parameter. It's about switching the gain. >0, >0;

[0034] Define Lyapunov functions Differentiating it, we get: ;

[0035] According to the above formula, the designed sliding surface satisfies the Lyapunov stability criterion;

[0036] The control law is composed of the equations for the sliding surface and the exponential reaching law, resulting in: ;

[0037] Among them, parameters , , , , , , These are coefficients obtained from system modeling. It is a nonlinear term in parachute dynamics; It is the input gain matrix. They are equivalent control input variables. This represents the ideal dynamics of the target system.

[0038] Step 4 above specifically refers to:

[0039] Write the second-order error dynamics in a compact form: ;

[0040] in, The total disturbance is obtained by combining all unknowns with the disturbance: ; Represents the ideal dynamics of the target system. for , is a nonlinear term in parachute dynamics. for , is the matrix showing the influence of control inputs on system dynamics. It is the input gain matrix. It is a control input. These are equivalent control input variables;

[0041] Define the equivalent quantity of the disturbance measurement: In ideal circumstances ;

[0042] Based on the above definition, a constant-period observer is designed as follows:

[0043] Observer Dynamically retrieved: ;

[0044] in , To ensure the parameters for constant periodic convergence, , It is the observer gain. , , , , This is the disturbance estimate. for , is the estimated total disturbance. for ;

[0045] make And assume If the surface is sufficiently smooth or the change is slow, then the error kinetics are:

[0046]

[0047] in, for This is the estimation error; The derivative of the estimation error;

[0048] For any initial value, It converges to 0 within a constant period, and the convergence time is bounded above and independent of the initial value:

[0049]

[0050] in, For convergence time.

[0051] The present invention has the following beneficial effects:

[0052] This invention addresses the problems of paraglider systems being susceptible to external wind field interference and inaccurate aerodynamics. It adopts a sliding mode control strategy that integrates a constant-period observer. This strategy combines the advantages of a constant-period observer in estimating disturbances within a finite time with the strong robustness and fast response speed of sliding mode control. Furthermore, it uses a saturation function to replace the sign function in traditional sliding mode control, thereby improving the inherent defect of chattering in sliding mode control. This allows for tracking control of the paraglider system's homing trajectory, which not only improves the response speed of the paraglider system but also reduces high-frequency vibrations in the control input and enhances its resistance to external wind field interference.

[0053] Simulation results demonstrate that this invention exhibits excellent trajectory tracking performance and anti-interference capability in paraglider systems. The saturation function effectively suppresses chattering, and the sliding mode control combined with a constant-period disturbance observer significantly improves the system's control quality under disturbance conditions. Attached Figure Description

[0054] Figure 1 This is a flowchart illustrating the principle of the constant period sliding mode control method for the paraglider system disclosed in this invention.

[0055] Figure 2 This is a block diagram of a sliding mode controller according to a specific embodiment of the present invention;

[0056] Figure 3 This is a block diagram of a sliding mode controller based on a constant-period observer, according to a specific embodiment of the present invention.

[0057] Figure 4 The target homing trajectory is shown in a specific embodiment of the present invention;

[0058] Figure 5 A comparison diagram of the expected straight-line tracking effect under windless conditions;

[0059] Figure 6 This is a comparison diagram of the expected straight-line tracking effect under windy conditions.

[0060] Figure 7 A comparison image showing the effect of horizontal trajectory tracking of the expected circular arc under windless conditions;

[0061] Figure 8 A comparison diagram showing the effect of horizontal trajectory tracking of the expected circular arc under windy conditions;

[0062] Figure 9 The image shows a comparison of the tracking performance of PID and FTO-based sliding mode control under windy conditions. Detailed Implementation

[0063] The embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0064] This invention presents a trajectory tracking and disturbance rejection control method for a paraglider system based on constant-period sliding mode control. It performs trajectory tracking control during the gliding and energy control phases of the paraglider system. By integrating a constant-period observer with sliding mode control, it further improves disturbance rejection performance and control accuracy while retaining the strong robustness of sliding mode control, thus improving the system's dynamic response and overcoming the control challenges caused by the nonlinearity, coupling, and time delay of the paraglider system. Figure 1 As shown, the method includes:

[0065] Step 1: Perform force analysis on the parachute system and establish a six-degree-of-freedom dynamic model of the parachute system's translation and rotation based on the Newton-Euler equations, which serves as the basis for trajectory tracking control.

[0066] This invention ignores the relative motion between the parachute body and the load, treats the parachute system as a whole, and establishes a 6-DOF nonlinear dynamic model of the parachute system.

[0067] Based on the Newton-Euler equations, a six-degree-of-freedom model of the parachute system for translation and rotation can be obtained:

[0068] (1) Translational three-degree-of-freedom equations:

[0069]

[0070] (2) Equations for the three degrees of freedom of rotation:

[0071]

[0072] in, and These are the tilt angle and deflection angle of the flight trajectory, respectively. , and These are pitch angle, yaw angle, and roll angle. , and It is the component of the rotational angular velocity on each axis of the body coordinate system.

[0073] Step 2: Based on the sliding mode control principle, design the basic sliding mode controller for the paraglider system. By constructing the sliding mode surface and designing the reaching law, achieve finite-time stable tracking of the system state variables and realize the accurate tracking of the target trajectory by the paraglider system.

[0074] Combination Figure 2 Based on sliding mode control, the basic idea is to design and optimize the sliding surface, and prove that the sliding surface is stable and usable in order to obtain a usable control law.

[0075] To design the sliding surface, this invention first defines position error and velocity error:

[0076] , ;

[0077] The derivative of velocity can be obtained from the following formula:

[0078]

[0079] The sliding surface is designed as follows: ;

[0080] right Differentiating, we get: ;

[0081] Define the law of exponential convergence: ;

[0082] in, >0, >0, It is a linear convergence rate parameter that guarantees asymptotic convergence. It involves switching the gain to enhance robustness against external disturbances and model uncertainties.

[0083] Define Lyapunov functions Differentiating it, we get:

[0084]

[0085] According to the above equation, the designed sliding surface satisfies the Lyapunov stability criterion, ensuring the asymptotic stability of the closed-loop system. The control law can be formed by combining the sliding surface and the exponential reaching law equation, and then we obtain:

[0086]

[0087]

[0088]

[0089]

[0090] in, , , , These are coefficients obtained from system modeling and are related to parachute aerodynamic parameters and control distribution.

[0091] Step 3: To address the inherent chattering and overshoot problems of sliding mode control, a saturation function is introduced to replace the sign function in traditional sliding mode control. A continuous and smooth switching law is designed in the neighborhood of the sliding surface, which effectively reduces the high-frequency chattering phenomenon of the control output and improves the structural stability of the system.

[0092] Traditional sliding mode control has the inherent defect of chattering, which easily leads to frequent switching of control input and frequent pulling of the control rope by the drive motor. This invention uses a saturated function to replace the sign function to reduce chattering.

[0093] As shown in step 2, the definitions of position error, velocity error, velocity derivative, and sliding surface are defined. In this step, the main focus is on optimizing the exponential reaching law and replacing the sign function with a saturation function. The optimized exponential reaching law is as follows:

[0094]

[0095] in, >0, >0, It is a linear convergence rate parameter that guarantees asymptotic convergence. It involves switching the gain to enhance robustness against external disturbances and model uncertainties.

[0096] Define Lyapunov functions Differentiating it, we get:

[0097]

[0098] According to the above equation, the designed sliding surface satisfies the Lyapunov stability criterion, ensuring the asymptotic stability of the closed-loop system. The control law can be formed by combining the sliding surface and the exponential reaching law equation, and then we obtain:

[0099]

[0100]

[0101]

[0102]

[0103] in, , , , These are coefficients obtained from system modeling and are related to parachute aerodynamic parameters and control distribution.

[0104] Step 4: To improve the system's anti-interference capability, a fixed-time observer (FTO) is designed to estimate and compensate for the system's lumped disturbances, including wind disturbances, in real time. The observed values ​​are then fed forward to compensate the sliding mode control law, thereby enhancing the system's robustness and anti-interference performance.

[0105] Specifically, a constant-period disturbance observer is designed to estimate the external disturbances such as wind disturbances affecting the system in real time, and the estimated values ​​are incorporated into the sliding mode control law to enhance the system's robustness; combined with Figure 3 Based on the reduction of chattering by sliding mode control, a constant period observer is designed to estimate wind disturbance and compensate for the impact of wind disturbance in advance in the control law design.

[0106] The second-order error dynamics can be written in a compact form from the derivation given in the previous steps: ;

[0107] This involves combining all unknowns and disturbances into a single total disturbance. :

[0108] ;

[0109] in The "ideal dynamics" representing the target system. It is a nonlinear term in parachute dynamics. It is the matrix showing the influence of control inputs on system dynamics. It is the input gain matrix. It is a control input. It is an equivalent control input variable.

[0110] Define the "measurement equivalent of the disturbance": ;

[0111] In ideal circumstances Therefore, a simple and effective constant-period observer can be designed as follows: Define the estimated value. And estimation error. Observer Dynamically retrieved:

[0112]

[0113] Where the parameters satisfy , , , . , It is the observer gain, used to adjust the convergence speed and robustness. , Guarantee convergence with a constant period.

[0114] make And assume If the surface is sufficiently smooth or the change is slow, then the error dynamics are approximated as:

[0115]

[0116] For any initial value, It converges to 0 within a constant period, and the convergence time is bounded above and independent of the initial value:

[0117]

[0118] This is a design formula for an observer with a constant period (independent of initial conditions). In practice... A non-zero value will introduce modeling errors, but choosing a larger value is preferable. , A suitable index can achieve a balance between rapid convergence and robustness to noise in engineering.

[0119] Example 1

[0120] The geometric and mass characteristics of a parachute system mainly include: wingspan. String length Effective area of ​​umbrella canopy Installation corner Paracord length Effective area of ​​the load body Total system mass .

[0121] like Figure 4 As shown, the initial position of the paraglider system target homing trajectory is set to... , , The initial heading angle is .

[0122] Set the initial position for parachute system deployment as follows: , , The initial heading angle is Wind disturbance is introduced during the trajectory tracking process of the paraglider system: an amplitude of [value missing] is applied. Random wind: ,in, It is the standard deviation of wind speed disturbance. It is the time constant of the disturbance. It is the cutoff frequency of the disturbance.

[0123] Figure 5 This demonstrates the desired linear tracking performance of PID control, basic sliding mode control, improved sliding mode control, and sliding mode control with a constant period observer under windless conditions, including tracking position error and tracking control signal. Figure 6 The study demonstrates the desired linear tracking performance of PID control, basic sliding mode control, improved sliding mode control, and sliding mode control with a constant period observer under windy conditions, including tracking position error and tracking control signal. Figure 7The study demonstrates the desired circular arc tracking performance under windless conditions using PID control, basic sliding mode control, improved sliding mode control, and sliding mode control with a constant period observer, including tracking position error and tracking control signal. Figure 8 This demonstrates the desired circular tracking performance of PID control, basic sliding mode control, improved sliding mode control, and sliding mode control with a constant period observer under windy conditions, including tracking position error and tracking control signal. Figure 9 The simulation demonstrates the overall expected flight path tracking performance under windy conditions. Compared to PID control, the sliding mode control incorporating a constant-period observer significantly smooths the position error and control variable curves, resulting in better tracking performance. Simulation curves show that, compared to traditional sliding mode control, the constant-period sliding mode control method of this invention exhibits better control accuracy, stronger anti-interference capability, and superior dynamic performance.

[0124] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principle of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for trajectory tracking and disturbance rejection control of a paraglider system based on constant period sliding mode control, characterized in that, include: Step 1: Perform force analysis on the parachute system and establish translational and rotational three-degree-of-freedom models of the parachute system based on the Newton-Euler equations, which serve as the basis for trajectory tracking control. Step 2: Based on the translational three-degree-of-freedom and rotational three-degree-of-freedom model of the paraglider system, and based on the sliding mode control principle, design the basic sliding mode controller of the paraglider system. By constructing the sliding surface and designing the reaching law, the sliding mode control law is obtained to achieve finite-time stable tracking of the system state variables. Step 3: Based on the basic sliding mode controller, to address the inherent chattering and overshoot problems of sliding mode control, a saturation function is introduced to replace the sign function, and a continuous and smooth switching law is designed in the neighborhood of the sliding surface to optimize the sliding mode control law. Step 4: Design a constant period disturbance observer to estimate and compensate for the total system disturbance in real time, and feed the observed values ​​forward to the sliding mode control law to enhance the robustness and disturbance rejection performance of the system.

2. The method for trajectory tracking and disturbance rejection control of a paraglider system based on constant period sliding mode control according to claim 1, characterized in that, Step 1 establishes the translational three degrees of freedom of the parachute system as follows: ； in, The three-dimensional coordinates of the parachute. For parachute ground speed; and These are the tilt angle and deflection angle of the flight trajectory, respectively.

3. The method for trajectory tracking and disturbance rejection control of a paraglider system based on constant period sliding mode control according to claim 1, characterized in that, The three-degree-of-freedom rotational model of the parachute system established in step 1 is as follows: ； in, , and It is the component of the rotational angular velocity along each axis of the body coordinate system; pitch angle Yaw angle and roll angle The derivative of .

4. The method for trajectory tracking and disturbance rejection control of a paraglider system based on constant period sliding mode control according to claim 1, characterized in that, Step 2, designing the basic sliding mode controller, includes: Define position error and speed error : , ; in, The actual three-dimensional coordinates of the parachute's position. These are the three-dimensional coordinates of the predetermined trajectory points. These are the three-dimensional error values ​​between the actual position of the parachute and the predetermined trajectory point; The actual velocities of the paraglider in the three axial directions, These are the predetermined velocities in the three axial directions of the parachute. These are the differences between the actual speed and the predetermined speed of the parachute in the three axial directions; The derivative of velocity is obtained by the following formula: ; in, Yaw angle The derivative; For horizontal velocity, For horizontal acceleration, Vertical velocity; for The derivative; The sliding surface is designed as follows: ,right Differentiating, we get: ,in For sliding surface, This is the sliding mode scaling factor; Define the law of exponential convergence: ;in, It is the linear convergence rate parameter. It's about switching the gain. >0, >0; Define Lyapunov functions Taking its derivative, we get: ,in It is a Lyapunov function; According to the above formula, the designed sliding surface satisfies the Lyapunov stability criterion; The control law is composed of the equations for the sliding surface and the exponential reaching law, resulting in:

5. Among them, parameters , , , , , , These are coefficients obtained from system modeling; It is a nonlinear term in parachute dynamics; It is the input gain matrix. They are equivalent control input variables. For symbolic functions, This represents the ideal dynamics of the target system.

6. The method for trajectory tracking and disturbance rejection control of a paraglider system based on constant period sliding mode control according to claim 1, characterized in that, Step 3 specifically involves: By replacing the symbolic function with a saturation function The optimization of the convergence law is as follows: ;in, It is the linear convergence rate parameter. It's about switching the gain. >0, >0; Define Lyapunov functions Taking its derivative, we get: ; According to the above formula, the designed sliding surface satisfies the Lyapunov stability criterion; The control law is composed of the equations for the sliding surface and the exponential reaching law, resulting in: ; Among them, parameters , , , , , , These are coefficients obtained from system modeling. It is a nonlinear term in parachute dynamics; It is the input gain matrix. They are equivalent control input variables. This represents the ideal dynamics of the target system.

7. The method for trajectory tracking and disturbance rejection control of a paraglider system based on constant period sliding mode control according to claim 1, characterized in that, Step 4 specifically involves: Write the second-order error dynamics in a compact form: ; in, The total disturbance is obtained by combining all unknowns with the disturbance: ; Represents the ideal dynamics of the target system. for , is a nonlinear term in parachute dynamics. for , is the matrix showing the influence of control inputs on system dynamics. It is the input gain matrix. It is a control input. They are equivalent control input variables; Define the equivalent quantity of the disturbance measurement: In ideal circumstances ; Based on the above definition, a constant-period observer is designed as follows: Observer Dynamically retrieved: ; in , To ensure the parameters for constant periodic convergence, , It is the observer gain. , , , , This is the disturbance estimate. for , is the estimated total disturbance. for ; make And assume If the surface is sufficiently smooth or the change is slow, then the error kinetics are: ； in, for This is the estimation error; The derivative of the estimation error; For any initial value, It converges to 0 within a constant period, and the convergence time is bounded above and independent of the initial value: ； in, For convergence time.

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