Fixed-wing automatic landing method based on inverse dynamics planning and time-varying LQR

Abstract

The application discloses a fixed-wing automatic landing method based on inverse dynamics planning and time-varying LQR, and relates to the technical field of aerospace control. The method is aimed at the nonlinear dynamic characteristics of the landing stage of a fixed-wing aircraft, and proposes a control scheme combining inverse dynamics trajectory planning and a time-varying linear quadratic regulator. According to the initial conditions of landing and the ideal landing site, an exponential function is used to plan the height and descent rate trajectory, and the ideal pitch angle and pitch angle velocity reference trajectory is inversely solved by using the longitudinal inverse dynamics model of the aircraft to establish consistent physical constraints. A state deviation-based augmented objective function is constructed, and a time-varying feedback gain matrix and a feedforward compensation vector are obtained by solving the Riccati equation of the time-varying matrix. The method proposed by the application can more smoothly track the ideal landing trajectory, significantly reduce the vertical velocity and attitude error during landing, and improve the safety and comfort of the automatic landing process.

Description

Technical Field

[0001] This invention relates to the field of aerospace control technology, and in particular to a fixed-wing automatic landing method based on inverse dynamics planning and time-varying LQR. Background Technology

[0002] Automatic landing of fixed-wing aircraft is one of the most critical and challenging phases in flight control systems. During landing, the aircraft needs to complete a series of maneuvers, including descent, leveling off, and touchdown, within a short time and altitude, while ensuring passenger comfort and structural safety. Traditional automatic landing control often employs proportional-integral-derivative (PID) control or linear quadratic regulator (LQR) control based on fixed weights. In many engineering implementations, traditional LQR methods typically design a reference trajectory only for altitude or vertical velocity, setting the pitch angle reference to a constant or simple setpoint.

[0003] However, there is a strong coupling between aircraft altitude changes and pitch attitude: to change the rate of descent, the aircraft must first change its pitch angle in order to change lift and vertical velocity through aerodynamics. If only the altitude channel planning reference is used, while ignoring the corresponding pitch angle and pitch rate changes, the controller will experience a "tug-of-war" phenomenon when attempting to simultaneously reduce altitude error and maintain attitude stability. This incoordination can lead to overshoot in glide path tracking, and even significant pitch oscillations before touchdown, reducing landing safety and passenger comfort. Furthermore, traditional steady-state LQR typically uses a constant gain matrix, which makes it difficult to fully consider the characteristic of "finite arrival time at touchdown" and lacks predictability for future trajectory changes.

[0004] Therefore, there is an urgent need for an automatic landing controller design that can simultaneously plan altitude and attitude reference trajectories based on a unified physical model and combine time-varying optimal control methods. Summary of the Invention

[0005] To address the aforementioned technical problems, this application provides a fixed-wing automatic landing method based on inverse dynamics planning and time-varying LQR, which solves problems such as the incoordination between trajectory planning and attitude control and the inability of steady gain to adapt to terminal constraints in traditional methods. The aim is to achieve accurate tracking of the landing trajectory and smooth landing, thereby improving the safety and comfort of automatic landing.

[0006] To achieve the above objectives, this invention provides a fixed-wing automatic landing method based on inverse dynamics planning and time-varying LQR, comprising the following steps: S1. Establish a longitudinal linearized state-space model for the landing phase of a fixed-wing aircraft. The state-space model describes the dynamic relationship between the aircraft's altitude, vertical velocity, pitch angle, and pitch rate. S2. Based on the initial altitude, initial descent rate, and predetermined touchdown point of the aircraft landing, design an ideal altitude reference trajectory and an ideal descent rate reference trajectory based on an exponential function; S3. Using the longitudinal inverse dynamics model of the aircraft, based on the ideal descent rate reference trajectory and its derivative, the ideal pitch angle reference trajectory and the ideal pitch angular velocity reference trajectory are solved in reverse, thereby constructing a complete full-state reference trajectory vector. S4. Construct a quadratic performance index function that includes state tracking error and control input, where the state weighting matrix sets weights for altitude, rate of descent, pitch angle and pitch rate respectively. S5. Solve the time-varying matrix Riccati differential equation to obtain the optimal feedback gain matrix and feedforward compensation vector. S6. Calculate the optimal control law based on the real-time measured aircraft state vector and control the elevator deflection.

[0007] In some embodiments of this application, the specific steps for establishing the longitudinally linearized state-space model in S1 are as follows: Establish the nonlinear dynamic equations of a fixed-wing aircraft in the longitudinal plane: ; Among them, above the parameters The derivative of this parameter. Vacuum speed, The trajectory angle is the angle between the velocity vector and the horizontal plane. For the angle of attack, The pitch angle, For height, It is the pitch angular velocity; For thrust, As resistance, For lift, For pitching moment, For aircraft quality, It is the acceleration due to gravity. It is the longitudinal moment of inertia; Near the landing equilibrium state, assume small perturbations and neglect velocity. The changes in ... Control input This yields the state-space form: ; Among them, the parameters in the matrix and parameters Closely related to the aerodynamic derivative of an aircraft, its physical meaning and expression relationship are as follows: : Represents the vertical velocity damping derivative, reflecting the stability of the aircraft's vertical motion; : Indicates the response characteristics of lift to pitch angle; : Indicates the coupled effect of altitude change on pitch moment; : Represents the derivative of pitch static stability; : Represents the pitch damping derivative; : Represents the derivative of elevator control effectiveness; Of the parameters mentioned above, These are all aerodynamic derivatives of the aircraft, determined by the aircraft's aerodynamic configuration and flight status.

[0008] In some embodiments of this application, in S2, the design formula for the ideal height reference trajectory is: ; in, The initial height, The time constant is adjusted by... The convergence speed of the descent can be controlled; The corresponding reference trajectory for the rate of decline is: .

[0009] In some embodiments of this application, in S3, the specific formula for solving the pitch angle reference trajectory using the inverse dynamics model is as follows: ; in, For ideal descent acceleration, These are the corresponding elements in the system matrix of S1, representing the vertical velocity damping characteristics and the influence coefficient of the pitch angle on lift, respectively. The ideal pitch angular velocity reference trajectory is: .

[0010] In some embodiments of this application, in S4, the specific expression of the quadratic performance index function is as follows: ; in, The landing end time, For terminal weighting matrix, and These are the process state weighting matrix and the control weighting matrix, respectively.

[0011] In some embodiments of this application, in step S5, the specific steps for solving the time-varying matrix Riccati differential equation and the feedforward compensation vector are as follows: By inverse integration of the following two differential equations, we obtain Moment and : ; ; Boundary conditions are and The feedback gain matrix .

[0012] In some embodiments of this application, in step S6, the formula for calculating the optimal control law is: ; The control law consists of two parts: the first part State feedback is used to stabilize the system and eliminate errors; Part Two For feedforward compensation, reference trajectory information is introduced to improve tracking accuracy.

[0013] The advantages and beneficial effects of this invention compared to the prior art are: The fixed-wing automatic landing method based on inverse dynamics programming and time-varying LQR proposed in this application, compared with the traditional steady LQR control method, solves the problem of incoordination between altitude and attitude control by introducing inverse dynamics and time-varying optimal control, significantly reducing landing error. In particular, it controls the touchdown vertical velocity and altitude error within a very small range, achieving high-precision and high-safety automatic landing.

[0014] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0015] Figure 1 This is a flowchart of the fixed-wing automatic landing method based on inverse dynamics planning and time-varying LQR in an embodiment of the present invention; Figure 2 This is a detailed flowchart of the inverse dynamics trajectory planning in an embodiment of the present invention; Figure 3 This is a detailed flowchart of the time-varying LQR optimal control calculation in an embodiment of the present invention; Figure 4 This is a simulation comparison diagram of the high-level tracking effect in an embodiment of the present invention; Figure 5 This is a simulation comparison diagram of vertical velocity changes in an embodiment of the present invention; Figure 6 This is a simulation comparison diagram of pitch angle changes in an embodiment of the present invention; Figure 7 This is a simulation comparison diagram of pitch angular velocity changes in an embodiment of the present invention; Figure 8This is a simulation comparison diagram of the elevator deflection angle in an embodiment of the present invention; Figure 9 This is a simulation comparison chart of high tracking error in an embodiment of the present invention. Detailed Implementation

[0016] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product is in use. These terms are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," and "connect" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0017] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0018] The overall flowchart of the fixed-wing automatic landing method based on inverse dynamics programming and time-varying LQR of this invention is as follows: Figure 1 As shown; a detailed flowchart of inverse dynamics trajectory planning in this embodiment of the invention is shown below. Figure 2 As shown; the detailed flowchart of the time-varying LQR optimal control calculation in this embodiment of the invention is as follows. Figure 3 As shown; simulation comparison diagrams of the high-level tracking effect in embodiments of the present invention are as follows. Figure 4 As shown; the simulation comparison diagram of vertical velocity change in the embodiments of the present invention is as follows. Figure 5 As shown; the simulation comparison diagram of pitch angle change in the embodiment of the present invention is as follows. Figure 6 As shown; the simulation comparison diagram of pitch angular velocity change in the embodiment of the present invention is as follows. Figure 7 As shown; the simulation comparison diagram of the elevator deflection angle in the embodiment of the present invention is as follows. Figure 8 As shown; simulation comparison diagrams of high tracking error in embodiments of the present invention are as follows. Figure 9 As shown.

[0019] The following sections, in conjunction with steps S1 to S6, describe the specific implementation process of the automatic landing control method for fixed-wing aircraft based on optimal control according to the present invention.

[0020] In S1, a longitudinally linearized state-space model for the landing phase of a fixed-wing aircraft is established.

[0021] During the landing phase, the aircraft mainly moves along the runway direction while moving up and down in the vertical direction. The changes in roll angle and yaw angle are relatively small, and the aircraft's motion can be approximated as motion in the longitudinal plane.

[0022] Furthermore, this method employs a "constant thrust / idle" control strategy, assuming that during the short period of leveling off during landing, engine thrust remains constant (e.g., in idle mode) and is not considered an active control variable in the closed loop. The aircraft utilizes the kinetic energy accumulated during the landing approach phase to adjust lift and drag by changing the pitch angle, thereby achieving a natural coupling between trajectory tracking and velocity decay. This strategy avoids complex thrust-attitude coupling control, simplifies the controller structure, and aligns with the landing operation habits of most small and medium-sized UAVs.

[0023] Based on this assumption, near the equilibrium flight state, the nonlinear equations of motion describing the aircraft's altitude, velocity, and attitude are linearized with small perturbations, and short-period changes in velocity are ignored, resulting in the form: The state-space model.

[0024] Wherein, the state vector These represent altitude, vertical velocity, pitch angle, and pitch rate, respectively, and are the control inputs. This indicates the elevator deflection.

[0025] matrix coefficients in , These parameters reflect the coupling relationship between vertical velocity, pitch angle, and aerodynamic derivatives; the matrix... The elements reflect the effect of elevator deflection on pitch angle and vertical speed.

[0026] By linearizing the aircraft's aerodynamic and moment equations and retaining the first-order terms of the Taylor expansion, we can obtain the equations of motion in the vertical direction and the equations of rotation in the pitch direction, and then rearrange them into the state-space form described above.

[0027] In S2, an ideal altitude reference trajectory based on an exponential function is designed based on the aircraft's initial landing altitude, initial descent rate, and predetermined touchdown point. and the reference trajectory of the rate of decline .

[0028] To achieve a smooth landing, this embodiment selects an initial altitude. Initial rate of decline Landing time corresponding to the predetermined landing point As boundary conditions for trajectory planning.

[0029] To avoid a significant height "step" change before grounding, an exponential height reference trajectory is used. ,in This is a time constant tuned based on the landing distance and the allowable descent rate.

[0030] Through the By taking the first and second derivatives, we can obtain the reference trajectory of the rate of descent. and descent acceleration reference trajectory This allows the height and vertical speed to be within the range of [missing information]. to Throughout the process, it gradually converges along the smooth curve to zero or a predetermined safety threshold.

[0031] In S3, using the aircraft's longitudinal inverse dynamics model, the ideal pitch angle reference trajectory is derived from the ideal rate of descent reference trajectory and its derivative. and ideal pitch angular velocity reference trajectory Thus, a complete full-state reference trajectory vector is constructed. .

[0032] In longitudinal dynamics, there is a clear physical relationship between altitude change and pitch angle. Under small perturbation conditions, the second derivative of altitude can be approximated as... The linear relationship.

[0033] in, Self-feedback characteristics reflecting vertical velocity It reflects the effect of pitch angle on vertical acceleration.

[0034] The above-mentioned and Substituting into this relationship, the pitch angle reference trajectory can be obtained. .

[0035] To obtain the pitch angular velocity reference trajectory, this embodiment utilizes kinematic relationships. ,right Taking the derivative, we get .

[0036] Therefore, this invention expands the reference trajectory, which was originally defined only in the altitude channel, into a full-state reference trajectory that includes altitude, vertical velocity, pitch angle, and pitch angular velocity. .

[0037] The above derivation process ensures the consistency and feasibility of each state component, so that the controller no longer encounters the contradiction of "desiring to descend in altitude but not in attitude" during the tracking process.

[0038] In S4, a quadratic performance index function is constructed that includes state tracking error and control input.

[0039] To balance tracking accuracy and control smoothness within a limited landing time, this embodiment adopts the following performance indicators: .

[0040] Among them, the terminal weighting matrix Used to emphasize the impact of the state deviation at the time of grounding. This is the weighting matrix for the components of altitude, vertical velocity, pitch angle, and pitch angular velocity. This is the weight matrix for the control input.

[0041] By making appropriate choices and The relative size can be balanced between "strictly tracking the trajectory" and "controlling the movement smoothly".

[0042] In S5, the time-varying matrix Riccati differential equation is solved to obtain the optimal feedback gain matrix. and feedforward compensation vector .

[0043] In a given linear system and the above performance indicators Under these conditions, this embodiment uses the variational method from optimal control theory for derivation.

[0044] First, we introduce the co-state vector. And construct the Hamiltonian function. .

[0045] Control quantity Taking the partial derivative and setting it to zero yields the optimality condition. Thus obtain ,Right now .

[0046] For ease of solution, this embodiment assumes that the co-state vector can be written as In the form of, It is a symmetric matrix. This is a time-dependent vector.

[0047] Substituting this form into the co-state equation After rearranging, we can obtain the matrix Riccati differential equation. and feedforward vector differential equations ,in .

[0048] By setting boundary conditions at the terminal time , For the two equations above, from Integrating in reverse This allows us to obtain the changes over time. , and .

[0049] In S6, based on the real-time measured aircraft state vector Calculate the optimal control law It controls the aircraft's pitch attitude by deflecting the elevator.

[0050] During simulation or test flight, state variables such as altitude, vertical velocity, pitch angle, and pitch angular velocity are collected and substituted into the above control law to calculate the elevator command.

[0051] Through this control law, the aircraft can gradually reduce its descent rate during the glide phase and automatically "level off" before touchdown, causing its vertical speed to decrease slowly to near zero.

[0052] In this embodiment, the initial height is selected to be approximately The initial vertical velocity is approximately The landing conditions were determined, and the time constant of the exponential trajectory was determined based on the runway length and safe landing requirements. and terminal time .

[0053] Under the same aircraft model and initial conditions, simulations were conducted using the traditional steady reference plus conventional LQR method and the method of this invention, respectively. The results show that, under the traditional method, the aircraft needs a large pitch angle change before touchdown to correct the altitude error, resulting in a significant lag in attitude adjustment and an excessively high vertical velocity at the moment of touchdown. However, when using the method of this invention, the vertical velocity at touchdown is significantly reduced, the pitch angle change process is smoother, and the control input waveform is more continuous, demonstrating better ride comfort and structural safety margin.

[0054] Table 1 Comparison of Landing Performance Indicators

[0055] As shown in Table 1 and the simulation results, the traditional steady-state LQR method often struggles to achieve stable control of both altitude and attitude at the end of the landing process, resulting in a relatively large vertical landing velocity and significant altitude error. In contrast, the method proposed in this invention, which combines inverse dynamics trajectory planning with time-varying LQR, can precisely control the vertical landing velocity within a safe range (close to -0.2 m / s), with near-zero altitude and mean square errors, achieving a safer and more precise automatic landing.

[0056] The fixed-wing automatic landing method based on inverse dynamics programming and time-varying LQR proposed in this application, compared with the traditional steady LQR control method, solves the problem of incoordination between altitude and attitude control by introducing inverse dynamics and time-varying optimal control, significantly reducing landing error. In particular, it controls the touchdown vertical velocity and altitude error within a very small range, achieving high-precision and high-safety automatic landing.

[0057] In another aspect of this application, a fixed-wing automatic landing method system based on inverse dynamics planning and time-varying LQR can also be provided.

[0058] The system may include a trajectory planning module, an optimal control calculation module, and an execution control module.

[0059] The trajectory planning module generates an exponential altitude reference trajectory based on the aircraft's initial landing altitude, initial rate of descent, and predetermined touchdown point. And its derivative, and further generate pitch angle and pitch velocity reference trajectories. .

[0060] The optimal control calculation module is used to solve the matrix Riccati differential equation and the feedforward vector differential equation based on the longitudinal linearized state-space model and the preset performance index function, to obtain the time-varying feedback gain matrix. and feedforward compensation vector And calculate the elevator control law in real time during flight. .

[0061] The execution control module receives elevator commands from the optimal control calculation module and drives the servo motors to execute them, thereby completing the automatic control of the aircraft's pitch attitude and altitude.

[0062] The aforementioned system can be deployed in the aircraft's flight control computer or ground simulation platform to support the design, verification, and application of automatic landing functions.

[0063] In this application, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. In case of any inconsistency, the meaning set forth in this specification or derived from the content described herein shall prevail. Furthermore, the terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit the scope of this application.

[0064] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A fixed-wing automatic landing method based on inverse dynamics programming and time-varying LQR, characterized in that, Includes the following steps: S1. Establish a longitudinal linearized state-space model for the landing phase of a fixed-wing aircraft. The state-space model describes the dynamic relationship between the aircraft's altitude, vertical velocity, pitch angle, and pitch rate. S2. Based on the initial altitude, initial descent rate, and predetermined touchdown point of the aircraft landing, design an ideal altitude reference trajectory and an ideal descent rate reference trajectory based on an exponential function; S3. Using the longitudinal inverse dynamics model of the aircraft, based on the ideal descent rate reference trajectory and its derivative, the ideal pitch angle reference trajectory and the ideal pitch angular velocity reference trajectory are solved in reverse, thereby constructing a complete full-state reference trajectory vector. S4. Construct a quadratic performance index function that includes state tracking error and control input, where the state weighting matrix sets weights for altitude, rate of descent, pitch angle and pitch rate respectively. S5. Solve the time-varying matrix Riccati differential equation to obtain the optimal feedback gain matrix and feedforward compensation vector. S6. Calculate the optimal control law based on the real-time measured aircraft state vector and control the elevator deflection.

2. The fixed-wing automatic landing method based on inverse dynamics programming and time-varying LQR as described in claim 1, characterized in that, In S1, the specific steps for establishing the longitudinally linearized state-space model are as follows: Establish the nonlinear dynamic equations of a fixed-wing aircraft in the longitudinal plane: ； Among them, above the parameters The derivative of this parameter. Vacuum speed, The trajectory angle is the angle between the velocity vector and the horizontal plane. For the angle of attack, The pitch angle, For height, It is the pitch angular velocity; For thrust, As resistance, For lift, For pitching moment, For aircraft quality, It is the acceleration due to gravity. It is the longitudinal moment of inertia; Near the landing equilibrium state, assume small perturbations and neglect velocity. The changes in the equations are linearized and rearranged, and the state vector is selected. Control input This yields the state-space form: ； Among them, the parameters in the matrix and parameters Closely related to the aerodynamic derivative of an aircraft, its physical meaning and expression relationship are as follows: : Represents the vertical velocity damping derivative, reflecting the stability of the aircraft's vertical motion; : Indicates the response characteristics of lift to pitch angle; : Indicates the coupled effect of altitude change on pitch moment; : Represents the derivative of pitch static stability; : Represents the pitch damping derivative; : Represents the derivative of elevator control effectiveness; Of the parameters mentioned above, These are all aerodynamic derivatives of the aircraft, determined by the aircraft's aerodynamic configuration and flight status.

3. The fixed-wing automatic landing method based on inverse dynamics programming and time-varying LQR as described in claim 2, characterized in that, In S2, the design formula for the ideal height reference trajectory is: ； in, The initial height, The time constant is adjusted by... The convergence speed of the descent can be controlled; The corresponding reference trajectory for the rate of decline is: .

4. The fixed-wing automatic landing method based on inverse dynamics programming and time-varying LQR as described in claim 3, characterized in that, In S3, the specific formula for solving the pitch angle reference trajectory using the inverse dynamics model is as follows: ； in, For ideal descent acceleration, These are the corresponding elements in the system matrix of S1, representing the vertical velocity damping characteristics and the influence coefficient of the pitch angle on lift, respectively. The ideal pitch angular velocity reference trajectory is: 。 5. The fixed-wing automatic landing method based on inverse dynamics programming and time-varying LQR according to claim 4, characterized in that, In S4, the specific expression of the quadratic performance index function is as follows: ； in, The landing end time, For terminal weighting matrix, and These are the process state weighting matrix and the control weighting matrix, respectively.

6. The fixed-wing automatic landing method based on inverse dynamics programming and time-varying LQR according to claim 5, characterized in that, In S5, the specific steps for solving the time-varying matrix Riccati differential equation and the feedforward compensation vector are as follows: By inverse integration of the following two differential equations, we obtain Moment and : ； ； Boundary conditions are and The feedback gain matrix .

7. The fixed-wing automatic landing method based on inverse dynamics programming and time-varying LQR as described in claim 6, characterized in that, In S6, the formula for calculating the optimal control law is: ； The control law consists of two parts: the first part State feedback is used to stabilize the system and eliminate errors; Part Two For feedforward compensation, reference trajectory information is introduced to improve tracking accuracy.

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