A morphing aircraft deformation control method based on an interference observer

Abstract

This invention discloses a morphing control method for a conventional aircraft based on a disturbance observer. A longitudinal model of the aircraft is established, and variable parameters related to airfoil camber are introduced into the aerodynamic parameters. The relationship between the aircraft's aerodynamic parameters and airfoil camber is fitted, followed by small-disturbance linearization. Using the fitted functional relationship between the aircraft's longitudinal aerodynamic parameters and airfoil camber, a variable-parameter model of the aircraft is established, i.e., a specific state-space model. Based on the constructed state-space model, a disturbance observer is constructed to estimate disturbance dynamics. Combining the disturbance estimate and a PI-type state feedback controller, the controlled model is effectively controlled, improving stability. By combining the Lyapunov stability method and convex optimization methods, the controller gain and observer gain are calculated, thereby ensuring good dynamic performance of the controlled morphing aircraft system.

Description

Technical Field

[0001] This invention relates to the field of aircraft anti-interference control technology, specifically to a variant aircraft deformation control method based on an interference observer. Background Technology

[0002] In traditional modeling methods for morphing aircraft, the most common methods are multibody modeling, analytical mechanics modeling, and vector mechanics modeling. Due to the influence of the design factors of the morphing aircraft itself, it has a relatively complex deformation structure and actuation mechanical structure, which makes the modeling using common methods quite complicated. When the aerodynamic shape of the aircraft changes, its own aerodynamic parameters will also change accordingly, thus making the aerodynamic parameters not fixed and the accuracy low.

[0003] Currently, almost all systems suffer from external interference, such as motion control systems, robot manipulation systems, complex chemical processes, terminal sliding mode systems, and flight control systems. Existing reaction systems exhibit poor stability and control effectiveness during deformation when subjected to input interference. Therefore, the problem of interference-resistant control has attracted widespread attention from academia and engineering.

[0004] Therefore, a morphing control method for a morphing aircraft based on a disturbance observer is needed. To reduce the complexity of the system model problem, a theoretical model of the morphing aircraft with variable airfoil camber is constructed here, addressing its longitudinal characteristics and control problem. A longitudinal model of a conventional aircraft is established, and variable parameters related to airfoil camber are introduced into the aerodynamic parameters. This involves fitting the aerodynamic parameters of the aircraft to the airfoil camber relationship, followed by small disturbance linearization. Using the fitted functional relationship between the longitudinal aerodynamic parameters and airfoil camber, a variable parameter model of the aircraft is established, i.e., a specific state-space model. Then, based on disturbance observer theory, an algorithm is designed to solve the system control problem with external disturbances. A switching signal is constructed based on the average dwell time method, and combined with state feedback information and disturbance estimation information, a PI-type anti-disturbance composite controller is designed. Subsequently, the stability of the designed closed-loop system is proved using Lyapunov stability analysis. Summary of the Invention

[0005] The purpose of this invention is to provide a variant aircraft deformation control method based on an interference observer, which solves the problems of complex and low accuracy of conventional aircraft modeling methods, and poor stability of the aircraft during deformation when there is input interference in the existing reaction system.

[0006] To achieve the above objectives, the specific technical solution of the morphing control method for a morphing aircraft based on an interference observer according to the present invention is as follows:

[0007] A method for controlling the morphing of a morphing aircraft based on an interference observer includes the following steps:

[0008] Step (1): Based on the conventional dynamics modeling of a general aircraft, obtain its dynamic equations and kinematic equations; according to the dynamic equations and kinematic equations of the aircraft, obtain the model equations of the aircraft in different coordinate systems; decouple the motion equations of the aircraft model to obtain the longitudinal motion equations that are independent of the lateral state variables.

[0009] Step (2): Based on the longitudinal motion equation and the wing switching principle, the aerodynamic parameters of the wing with camber relationship are fitted and then substituted into the longitudinal model of the morphing aircraft and balanced to obtain the equilibrium point as the airfoil camber changes. Combine the equilibrium point to construct the longitudinal small disturbance linearization equation and parameter model of the morphing aircraft, that is, to establish a specific state space model.

[0010] Step (3): Based on the established state-space model and considering the existence of disturbances, design a PI controller and a disturbance observer to estimate unknown disturbances and effectively control the output.

[0011] Step (4): Combine the Lyapunov stability analysis method to obtain the corresponding controller gain and observer gain, and then apply them to the state space model to complete the anti-interference control of the aircraft deformation.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0013] (1) The present invention uses the variable parameter modeling method, which is simpler and more accurate than conventional aircraft modeling methods, providing another approach for the research of variant aircraft control.

[0014] (2) This invention analyzes the control of variable wing camber of aircraft and designs a reasonable average dwell time to improve the control of deformation process.

[0015] (3) By estimating and compensating for the presence of interference using the interference observer method of the present invention, interference can be effectively suppressed and the stability of the variant process can be improved. Attached Figure Description

[0016] Figure 1 This is a flowchart of the present invention. Detailed Implementation

[0017] like Figure 1 The method for controlling the deformation of a variator based on an interference observer, as shown, includes the following steps:

[0018] Step (1) Based on the conventional dynamics modeling of a general aircraft, obtain its dynamic equations and kinematic equations; according to the dynamic equations and kinematic equations of the aircraft, obtain the model equations of the aircraft in different coordinate systems; decouple the motion equations of the aircraft model to obtain the longitudinal motion equations that are independent of the lateral state variables, specifically: according to Newton's laws of motion, the dynamic equations and kinematic equations of the aircraft body coordinate system are given below, the process is as follows:

[0019] Force equations

[0020]

[0021] system of equations of motion

[0022]

[0023] Torque Equations

[0024]

[0025] Navigation Equations

[0026]

[0027] Based on the above dynamic equations and kinematic equations of the aircraft, the model equations for different coordinate systems of the aircraft can be obtained:

[0028] (1) Model equations of the body coordinate system

[0029] Assume the engine thrust offset angle is α T =β T =0, meaning the thrust is on the x-axis of the body coordinate system, T = T x The body coordinate system can be converted to the airflow coordinate system in the following way:

[0030]

[0031] Wherein, the transformation matrix Defined as follows:

[0032]

[0033] Substituting the forces into the above equation yields:

[0034]

[0035] Expanding the above equation, we get:

[0036]

[0037] Substituting the above equation into the force equation set, we obtain the equations for the body coordinate system model:

[0038]

[0039] Where α represents the angle of attack of the aircraft, and β represents the sideslip angle.

[0040] (2) Airflow coordinate system model equations

[0041] Assume the total external force on the aircraft is F W This includes engine thrust T and total aerodynamic force R. ∑ The components of gravity G on each axis of the airflow coordinate system, namely:

[0042]

[0043] Substituting the force equations of the aircraft into the equations, we can obtain the airflow coordinate system model equations:

[0044]

[0045] In this paper, we assume that the aircraft is in an ideal flight environment, that is, under ideal flight conditions with no horizontal slip and no sideslip (φ=β≡0, p=r≡0, and Based on the model equations of each coordinate system obtained above, the motion equations of the aircraft model are decoupled to obtain the longitudinal motion equations, which are independent of the lateral state variables:

[0046]

[0047] In the formula, V is the aircraft velocity, α represents the aircraft angle of attack, m is the aircraft mass, and g is the gravitational acceleration; θ and q are the pitch angle and pitch rate, respectively; I y Let L be the moment of inertia about the axis; and let L be the lift, D be the drag, M be the pitching moment, and T be the thrust, respectively.

[0048]

[0049]

[0050]

[0051]

[0052] Among them, C L C is the lift coefficient. D C is the drag coefficient. M T is the torque coefficient. δt δ is the engine thrust coefficient. t This refers to the throttle opening of the aircraft.

[0053] Step (2) Based on the longitudinal motion equation and the wing switching principle, the aerodynamic parameters of the wing with camber relationship are fitted and then substituted into the longitudinal model of the morphing aircraft and balanced to obtain the equilibrium point as the airfoil camber changes. Combining the equilibrium point, the longitudinal small disturbance linearization equation and parameterized model of the morphing aircraft are constructed, that is, the specific state space model is established. The specific process is as follows:

[0054] First, the aerodynamic parameters of the wing are given:

[0055] (1) Aircraft lift parameters

[0056] Aircraft fly by relying on lift generated by their movement through atmospheric currents. The lift of an aircraft primarily comes from the lift generated by its wings, L. ω Fuselage lift L b Horizontal tail lift L t ,Right now:

[0057] L = L ω +L b +L t

[0058] Substituting the lift forces of each component into the equation, we obtain:

[0059]

[0060] Lift mainly comes from the wings. The all-moving horizontal stabilizer control surface aircraft model used in this chapter has a very small lift from the fuselage compared to the aerodynamic force generated by the control surface. Therefore, its influence on the overall torque of the aircraft can be ignored. Next, we will optimize the lift formula and simplify it into the sum of the lift from the wings and the lift from the all-moving horizontal stabilizer control surface.

[0061] Based on the above analysis, the lift coefficient of the aircraft can be modified as follows:

[0062]

[0063] Here, the zero angle-of-attack lift coefficient C of the entire aircraft is defined. L0 The zero angle-of-attack lift coefficient C is directly taken from the fitted deformable wing. l0 Overall lift aerodynamic derivative C Lα Take the aerodynamic derivative of lift of the deformable wing, C lα Then we have:

[0064] C L0 =0.1044f + 0.02036

[0065] C Lα =5.73 / rad

[0066] (2) Aircraft drag parameters

[0067] The drag factors that make up an aircraft are quite complex. Generally, it consists of zero-lift drag D. L0 and rise to resistance D t These factors constitute the drag of an aircraft. Zero-lift drag includes frictional drag, pressure drag, and zero-lift wave drag; lift-induced drag includes induced drag and lift-induced wave drag. Therefore, the overall drag coefficient of the aircraft is:

[0068]

[0069] Wherein, the zero-lift drag coefficient is defined. Define the lift-induced drag coefficient When an aircraft enters subsonic flight, induced drag becomes the main component of lift drag.

[0070]

[0071] Where ε is the downwash angle of the aircraft. When the aircraft is in supersonic flight, lift-induced wave drag is the main component of lift-induced drag:

[0072]

[0073] Based on the relationship between aircraft drag and angle of attack, its drag coefficient can be written as:

[0074] C D =C D0 +C Dα α

[0075] Based on the components of aircraft drag, it is known that the drag coefficient is related to the lift coefficient, and drag mainly originates from the effect of airflow on lift components and the fuselage. The relationship between fuselage drag and angle of attack can be approximated as linear. Db The drag coefficient is expressed as kα, where k is a suitable constant. The drag of an aircraft can be approximated as the sum of the drag from the fuselage and the wings. The overall zero-angle-of-attack drag coefficient C of the aircraft is... D0 and the overall drag aerodynamic derivative C Dα for:

[0076] C D0 =0.0008774f + 0.007328

[0077] C Dα =(-0.8634f+3.2506)α+k

[0078] (3) Aircraft longitudinal pitch moment parameters

[0079] Torque can affect the flight performance and attitude of an aircraft and is an important parameter in an aircraft. Under normal circumstances, torque is mainly generated by the lift and aerodynamic forces of the control surfaces of the aircraft, and can be described in the following form:

[0080] M a =C M QS ω c A =(C m +C mb +C mt QS ω c A

[0081] According to the above formula, the overall torque of the aircraft is composed of the torque generated by the wings, fuselage and horizontal stabilizer.

[0082] The aircraft used in this paper has an all-moving horizontal stabilizer, and the lift of the fuselage is ignored. Therefore, the total static pitch moment coefficient can be simplified to:

[0083]

[0084] in, and These are defined as the relative positions of the aircraft's aerodynamic focus and its center of gravity on the mean geometric chord, respectively. Then, the moment coefficient is simplified: the overall angle-of-attack moment coefficient C of the aircraft is... M0 Defined as the zero angle-of-attack moment coefficient C of a deformable airfoil m0 Overall torque aerodynamic derivative C Mα Defined as the moment initiation derivative C of the deformable wing mα Then we have:

[0085] C M0 =0.0166f + 0.0126

[0086] C Mα = -0.1962 / rad

[0087] In summary, by substituting these parameters into the functional relationship between the aerodynamic parameters and airfoil camber of the variator aircraft, the aerodynamic parameters of the wing with a camber relationship are obtained through fitting, as shown in the following specific expression:

[0088]

[0089] C D =C D0 +C Dα α=0.0008774f+(3.2506-0.8634f)α 2 +0.007328

[0090]

[0091] Among them, C L C is the lift coefficient. D C is the drag coefficient. M δ is the torque coefficient.e This refers to the elevator deflection angle.

[0092] After obtaining the aerodynamic parameters of the aircraft, the functional relationships are substituted into the system model of the variant aircraft to further study the control problem.

[0093] Secondly, there's the aircraft trimming, which involves determining its equilibrium point. The basic principle is: using the Earth as a coordinate system, ensure the resultant force on the X and Z axes of the aircraft is zero. At this point, the forces are in equilibrium, and the longitudinal moments are balanced. This generally involves trimming the longitudinal direction. Therefore, trimming is performed on variant aircraft with different airfoil camber f to obtain the equilibrium angle of attack α and elevator deflection δ. e and the engine thrust T

[0094] Based on the above principle, the simplified equation for balancing is obtained:

[0095]

[0096] By substituting these parameters into the aerodynamic parameters under various curvature conditions, the equilibrium points under different curvatures can be obtained. Combining this with the physical parameter model of the variator aircraft, and substituting the relevant formulas for the lift L, drag D, torque M, and thrust T of the aircraft, the equilibrium points that vary with curvature can be obtained.

[0097] Furthermore, the functional relationship between the fitted equilibrium point and the curvature change can be derived:

[0098] α trim = -1.242f + 5.62

[0099]

[0100]

[0101] Where, α trim The aircraft's angle of attack equilibrium point, The elevator deflection angle equilibrium point, This is the balance point for the aircraft's throttle opening.

[0102] After obtaining the longitudinal model equations of the aircraft, the system model equations are linearized with small perturbations at the equilibrium point to obtain the state equations of the aircraft:

[0103]

[0104] In the above formula, State variable X = [ΔV Δα Δθ Δq] T Input variable (i.e., control variable) U = [△δ e △δ T ] T .

[0105] Linearizing the equilibrium point yields matrix E, state matrix A, and control matrix B:

[0106]

[0107]

[0108]

[0109] Next, the aircraft model is simplified. Considering that the aircraft is flying horizontally without sideslip, the aerodynamic derivatives in matrix E related to the rate of change of angle of attack are set to... If the value is 0, then matrix E becomes the identity matrix. Furthermore, we obtain the linearized form of the aircraft state equations:

[0110]

[0111] Similarly, the aerodynamic derivatives related to the pitch rate in state matrix A Aerodynamic derivative with respect to velocity V and thrust derivative If all values ​​are approximately 0, then matrix A can be simplified to:

[0112]

[0113] In addition, due to the angle of attack α at the equilibrium point trim The mass of the aircraft is relatively small, while the product of its mass and initial velocity is extremely large, therefore the mass of the aircraft in control matrix B is relatively small. This term can be approximated as 0, and matrix B can be simplified to:

[0114]

[0115] Now it's usable Represented as the equations of the simplified model of the variant aircraft after linearization, V0 and C in the state matrix A and control matrix B. L0 Q0, C M0 C D0 Each component represents the aircraft's flight speed, lift coefficient, dynamic pressure, pitching moment coefficient, and drag coefficient at the equilibrium point. Based on the fitted functional relationship between the aerodynamic parameters and camber, substituting these into state matrix A and control matrix B yields a variable parameter matrix model containing the varying parameter (camber f):

[0116]

[0117]

[0118] A(f) is the state matrix of a parametric model of a variant aircraft with an airfoil camber parameter f. This aircraft increases its camber f by increasing the thickness of the upper surface of the airfoil. The change in state variables caused by the camber f alters the flight state. The relative camber increment of this variant aircraft is 0.25%, and the relative camber ranges from 1% to 2.5%, meaning the value of f is between [1, 2.5]. Numerical simulations are performed on these variant airfoils to obtain the influence of camber variation on the aerodynamic characteristics of the morphing airfoil.

[0119] Based on the calculated system matrix, the following state-space model is established:

[0120]

[0121]

[0122]

[0123] Where d(t) represents the unknown disturbance, and satisfies:

[0124]

[0125] Where w(t) represents the interference state, and H and Y represent parameters related to the interference type.

[0126] Step (3) Based on the established state-space model and considering the presence of disturbances, a PI controller and a disturbance observer are designed to estimate unknown disturbances and effectively control the output. Specifically, to obtain good tracking performance, new augmented variables are defined. Where z(t) represents the aircraft state, e y This is the difference between the system output and the expected output.

[0127] An augmentation system can be described as:

[0128]

[0129] in Next, an interference observer is constructed to estimate the interference, in the following form:

[0130]

[0131] In the formula This is an estimate of the interference; the interference estimation error is defined as:

[0132] Furthermore, the PI state feedback controller is designed based on disturbance estimation as follows:

[0133]

[0134] Step (4) Combine the Lyapunov stability analysis method to solve for the corresponding controller gain and observer gain, and then apply them to the state space model to complete the anti-interference control of the aircraft deformation.

[0135] The Lyapunov analysis method used to solve for the controller and observer gains is expressed as follows:

[0136] Theorem 1: For a given constant T f >0, α>0, μ≥1. Here, if there is a positive definite symmetric matrix P i ∈R m×m Q i ∈R k×k satisfy:

[0137]

[0138] P i ≤μP j Q i ≤μQ j , j∈Z, i≠j

[0139] This leads to the conclusion that the variant aircraft system is stable, the interference estimation error system is convergent, and it can achieve good tracking performance. The gains of the controller and interference observer can be determined by… V i =K i ρ i ,and The result was obtained through calculation.

[0140] Proof: Choose the following Lyapunov function: φ i =φ 1,i +φ 2,i , φ 2,i =e w T (t)Q i e w (t),

[0141] According to step (3), it is easy to obtain:

[0142]

[0143] Based on Schul complement lemma, multiply both sides of the first matrix inequality by diag{ρ} -1 i II}, we can obtain: When φ i =h and Sometimes, Therefore, when the initial condition φ σ(0) When =h, we have φ σ(t) ≤h, right Integrating over [0,t], we get:

[0144]

[0145] At this time, if there is φ σ(t) If (ζ(t))≥α / h, then we have Next, we will look at φ σ(t) We will discuss two cases of (ζ(t)):

[0146] (1) When the system is running, the system does not meet the conditions. That is, each subsystem satisfies the condition. At this point, the switching system is bounded.

[0147] (2) When the system is running, the system can meet the conditions. When the system is running, we can obtain From t k Integrating to t yields:

[0148]

[0149] After simplifying the above inequality, we get the following form:

[0150]

[0151] Assume that at the switching time t k ,exist When the inequalities in the theorem are satisfied

[0152] At that time, there were:

[0153]

[0154] Combining the above formula, we can obtain:

[0155]

[0156] Based on the above conditions and the iteration theorem, we can obtain:

[0157]

[0158] According to the theorem, Therefore, the switching system is bounded.

[0159] Combining the two situations above, we can conclude that φ σ(t) (ζ(t)) can eventually become bounded. And we can know that φ σ(t)(ζ(t)) eventually converges to a boundary π and reaches stability, where As φ σ(t) A component of (ζ(t)), It eventually converges to a boundary. Therefore, as t→∞, It exists and is bounded. The above proof demonstrates that the designed error tracking system is effective.

[0160] This invention is not limited to the above embodiments. Based on the technical solutions disclosed in this invention, those skilled in the art can make some substitutions and modifications to some of the technical features without creative effort, and all such substitutions and modifications are within the protection scope of this invention.

Claims

1. A morphing control method for a morphing aircraft based on an interference observer, characterized in that, Includes the following steps: Step (1): Based on the conventional dynamics modeling of the aircraft, obtain its dynamic equations and kinematic equations; according to the dynamic equations and kinematic equations of the aircraft, obtain the model equations of the aircraft in different coordinate systems; decouple the motion equations of the aircraft model to obtain the longitudinal motion equations that are independent of the lateral state variables. Step (2): Based on the longitudinal motion equation and the wing switching principle, the aerodynamic parameters of the wing with camber relationship are fitted and then substituted into the longitudinal model of the morphing aircraft and balanced to obtain the equilibrium point as the airfoil camber changes. Combine the equilibrium point to construct the longitudinal small disturbance linearization equation and parameterized model of the morphing aircraft, that is, to establish a specific state space model. Step (3): Based on the established state-space model and considering the existence of disturbances, design a PI controller and a disturbance observer to estimate unknown disturbances and effectively control the output. Step (4): Combine the Lyapunov stability analysis method to obtain the corresponding controller gain and observer gain, and then apply them to the state space model to complete the anti-interference control of the aircraft deformation. In step (2), based on the longitudinal motion equation and the wing switching principle, the aerodynamic parameters of the wing with camber relationship are fitted, and the specific expression is as follows: ； ； ； in, The lift coefficient, The drag coefficient, This is the torque coefficient. Elevator deflection angle; The specific expression for the equilibrium point of the airfoil camber change in step (2) is as follows: ； When the balancing equation is satisfied, the equilibrium points under different curvatures can be obtained, and thus the functional relationship between the equilibrium points and the curvature can be derived: ； ； ； in, The aircraft's angle of attack equilibrium point, The elevator deflection angle equilibrium point, The balance point for the aircraft's throttle opening; In step (2), based on the functional relationship of the airfoil corresponding to the aerodynamic parameters of the aircraft, and combined with the equilibrium point, the linearized equations and parameterized models of the longitudinal small disturbance of the variant aircraft are constructed as follows: ； in Indicates the flight status of the aircraft. This represents the control input, specifically the aircraft's elevator deflection angle. and This represents the system's parameter model matrix containing the curvature function; Based on the calculated system matrix, establish a state-space model: ； ； ； For parameters with airfoil camber variation The state matrix of the parametric model of the variant aircraft. The value of is in between, This represents an unknown disturbance and satisfies: ； in In a state of interference, This indicates parameters related to the type of interference.

2. The morphing control method for a morphing aircraft based on an interference observer according to claim 1, characterized in that, In step (1), the model equations of the aircraft in different coordinate systems are the body coordinate system model equation and the airflow coordinate system model equation, respectively.

3. The morphing control method for a morphing aircraft based on an interference observer according to claim 1, characterized in that, In step (1), the motion equations of the aircraft model are decoupled, and the longitudinal motion equations, which are independent of the lateral state variables, are obtained as follows: ； In the formula, , These are pitch angle and pitch angular velocity, respectively. For the mass of the aircraft, It is the acceleration due to gravity; Moment of inertia about the axis; lift Pitch moment ,thrust They are respectively: ； ； ； ； in, The lift coefficient, The drag coefficient, This is the torque coefficient. This is the engine thrust coefficient. This refers to the throttle opening of the aircraft.

4. The morphing control method for a morphing aircraft based on an interference observer according to claim 1, characterized in that, The specific steps in step (3) are as follows: Define new augmentation variables ,in In aircraft status, The augmented system is described as the difference between the system output and the desired output: ； in , , The desired output is given; next, an interference observer is proposed to estimate the interference, in the following form: ； In the formula It is an estimate of the interference. It is an auxiliary variable that is set. It is the observer gain; the disturbance estimation error is defined as: The PI state feedback controller is designed by combining disturbance estimation as follows: ； in This represents the controller gain that needs to be solved.

5. The morphing control method for a morphing aircraft based on an interference observer according to claim 1, characterized in that, The Lyapunov analysis method used in step (4) to solve for the controller and observer gains is expressed as follows: For a given constant , , Here, if there is a positive definite symmetric matrix , satisfy: ； ， ， ， ； ； This leads to the derivation that the variant aircraft system is stable, the interference estimation error system is convergent, and it achieves good tracking performance. The gain of the controller and interference observer is determined by... , ,and The result was obtained through calculation.

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