Method for controlling preset performance of elastic aircraft with convergence in preset time

Abstract

The invention discloses an elastic aircraft preset performance control method with convergence in preset time. According to the method, the good robustness of the sliding mode controller is used, the state observer is combined to obtain the lumped disturbance to generate the elastic suppression compensation instruction, divergence of the elastic mode of the aircraft can be effectively reduced, the influence of elastic vibration on the structure and attitude control of the aircraft is reduced, and parameter adjustment is convenient; meanwhile, the actual attitude error is converted into a new error variable through preset performance constraint of preset time convergence and error conversion, it is guaranteed that a control instruction is tracked rapidly and accurately within preset convergence time, the variation amplitude of a sliding mode surface is effectively reduced, a smoother control signal is generated, and therefore buffeting is reduced. According to the invention, elastic suppression can be effectively realized, rapid and accurate tracking of a control instruction can be realized in a preset time, and overshoot and oscillation in a control process can be reduced. Compared with a traditional aircraft controller, the aircraft controller has more excellent dynamic performance.

Description

Technical Field

[0001] The present invention relates to the technical field of high-speed aircraft control, and in particular to a method for controlling the preset performance of an elastic aircraft with predetermined time convergence. Background Art

[0002] With the development of aerospace technology, people are extending their exploration into near-space. High-speed aircraft, as common payloads in this airspace, have become a hot topic of research for many scholars. High-speed aircraft have high flight speeds, large flight envelopes, and complex flight environments. They are characterized by strong nonlinearity, uncertainty, and strong coupling. These aircraft typically use lightweight materials, resulting in a low natural frequency of the aircraft structure. The elastic deformation of the body affects the flight stability and dynamic characteristics of the aircraft. These characteristics pose significant challenges to the design of control systems for high-speed aircraft. To adapt to the elastic effects, parameter perturbations, and uncertainties caused by external interference during the flight of elastic high-speed aircraft, the control system needs to be more robust and adaptable to achieve stable attitude tracking.

[0003] Sliding mode control (SMC) is considered an effective method for mitigating model uncertainty and external disturbances and has become a key control approach for flexible aircraft. However, while terminal sliding mode controllers can guarantee steady-state control performance, they often only guarantee asymptotic stability and fail to limit the transient response of the control process. Given the need for aircraft to quickly reach their desired attitude, designing fast-converging controllers is of significant engineering importance.

[0004] Preset performance control, a control method proposed by Bechlioulis et al., ensures that the convergence rate and overshoot meet pre-defined conditions by limiting the tracking error of the system state to within the bounds of a preset performance function. This control method balances both transient and steady-state performance and is widely used in flight control system design. However, existing preset performance control methods are designed for rigid objects and do not consider elasticity. Furthermore, while existing fixed-time convergence attitude controllers can predetermine the convergence time, the results are unintuitive and difficult to adjust parameters in practical applications. Summary of the Invention

[0005] In view of this, the present invention provides a preset performance control method for an elastic aircraft with predetermined time convergence, which can simultaneously achieve elastic suppression and predetermined time convergence, and effectively improve the accuracy and stability of the elastic aircraft's attitude control.

[0006] The method for controlling the preset performance of an elastic aircraft with predetermined time convergence of the present invention comprises:

[0007] Taking the difference between the pitch angle and pitch velocity of the elastic aircraft and their expected values ​​as an attitude tracking error, and constraining the attitude tracking error using a preset performance function that converges in a predetermined fixed time;

[0008] The error conversion method is used to convert the constrained posture tracking error into the unconstrained posture tracking conversion error;

[0009] The total disturbance of the elastic aircraft is estimated using a state observer;

[0010] A sliding mode controller is constructed to control the unconstrained attitude tracking transition error and is compensated for the sliding mode controller based on the total disturbance estimated by the state observer.

[0011] Preferably, the preset performance function for the predetermined fixed time convergence is:

[0012]

[0013] Among them, γ, l and v are parameters, γ>1, l>0, v>0; ρ ∞ represents ρ(t) t→∞ Upper bound of steady-state value; T f is the predetermined convergence time, which is a fixed value; t is the time.

[0014] Preferably, the attitude tracking error e1(t) is subject to the following inequality constraints:

[0015]

[0016] Where λ is a parameter, 0<λ≤1; ρ(t) is a preset performance function that converges in a predetermined fixed time; λρ(t) is the maximum overshoot allowed by e1(t);

[0017] The ET function Γ(ε(t)) is used to transform the inequality constraint (5) into the following system:

[0018] e1(t)=ρ(t)Γ(ε(t)) (9)

[0019] Where ε(t) is the unconstrained attitude tracking conversion error; Γ(ε(t)) is the error conversion function, and satisfies the following properties:

[0020] 1) Γ(ε(t)) is smooth and strictly increasing;

[0021] 2)Γ(ε(t)) satisfies the following inequality:

[0022]

[0023] 3) Γ(ε(t)) satisfies the following equation:

[0024]

[0025] Performing an inverse transformation on the ET function, the unconstrained posture tracking conversion error ε is:

[0026]

[0027] Preferably, the state observer is a nonlinear extended state observer, a linear extended state observer, a nonlinear dynamic observer or a sliding mode observer.

[0028] The optimal, nonlinear extended state observer is:

[0029]

[0030] Where z1, z2, and z3 are the pitch angle, pitch velocity, and total disturbance estimated by the nonlinear extended state observer, respectively; θ is the pitch angle; β i is the observer gain; b is the control torque coefficient, u is the control input; e1(t) is the attitude tracking error; is a nonlinear function,

[0031]

[0032] Among them, α i , δ are observer parameters and are constants.

[0033] Preferably, the attitude tracking control law u of the sliding mode controller is:

[0034]

[0035] Where G = ψρ, Where ρ(t) is a preset performance function that converges in a predetermined fixed time; 0<λ≤1, λρ(t) is the maximum overshoot allowed by e1(t); k1, k2 are parameters greater than 0; sgn is the sign function; c>0 is the control parameter; ε(t) is the unconstrained posture tracking conversion error; is the desired pitch angular velocity; z3 is the total disturbance estimated by the state observer.

[0036] It is better to switch the sign function sgn to the saturation function sat:

[0037]

[0038] Then the attitude tracking control law u of the sliding mode controller is:

[0039]

[0040] Preferably, the elastic aircraft is any hypersonic or ordinary aircraft that has a slender shape or is designed with lightweight materials and is prone to elastic deformation during flight.

[0041] Beneficial effects:

[0042] In response to the impact of elasticity on the control system during aircraft flight, the present invention leverages the good robustness of the sliding mode controller itself and combines it with a state observer to obtain lumped disturbances to generate elastic suppression compensation instructions, which can effectively reduce the divergence of the aircraft's elastic modes and the impact of elastic vibrations on the aircraft's structure and attitude control, and is easy to adjust parameters. At the same time, through preset performance constraints and error conversion with predetermined time convergence, the actual attitude error is converted into a new error variable, ensuring that the control instructions are tracked quickly and accurately within the predetermined convergence time, and effectively reducing the amplitude of the sliding mode surface change, generating a smoother control signal, thereby reducing vibration.

[0043] The present invention can effectively achieve elastic suppression, quickly and accurately track control instructions within a predetermined time, and reduce overshoot and oscillation during the control process. Compared with traditional aircraft controllers, it has better dynamic performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is the basic principle of preset performance control method.

[0045] Figure 2 Schematic diagram of the control method of the present invention.

[0046] Figure 3 The performance function designed for the present invention is compared with the traditional performance function.

[0047] Figure 4 These are reference control instructions that serve as examples of control effects.

[0048] Figure 5 This is the pitch angle tracking effect of the controller designed by the present invention.

[0049] Figure 6 This is the rudder angle response of the controller designed by the present invention.

[0050] Figure 7 This is the suppression effect of the elastic suppression control algorithm based on disturbance observer designed by the present invention on the first-order elastic mode and its derivative. DETAILED DESCRIPTION

[0051] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0052] The present invention provides a preset performance control method for an elastic aircraft with a predetermined time convergence. The method adopts a sliding mode controller and combines it with a preset performance control algorithm with a predefined time convergence to reduce the amplitude of the sliding membrane surface change, thereby generating a smoother control signal and reducing vibration. At the same time, considering the influence of the elastic characteristics of the aircraft on the attitude control, a state observer is added to the sliding mode controller design to observe the elastic influence, and the observation results are compensated into the controller design to achieve elastic suppression and fast and accurate tracking of control instructions, thereby completing the attitude control of the elastic aircraft.

[0053] The design of the preset performance controller includes two parts: the preset performance function and the error transformation function. Its core principle is to constrain the convergence process of the system state by pre-designing the upper and lower bounds of the system state. Figure 1 The upper and lower bounds of the system state are collectively referred to as the preset performance function. By reasonably designing the convergence process of the preset performance function, the transient and steady-state performance of the system state can be constrained. The transient performance includes convergence speed, overshoot, etc., and the steady-state performance mainly refers to the steady-state error. The process of imposing upper and lower bounds on performance introduces additional nonlinear constraints to the system, which increases the complexity of controller design. In order to solve this problem, the preset performance control method maps the constrained state quantity to the unconstrained space by performing an unconstrained mapping, such as Figure 1 As shown on the right side of . By using a one-to-one mapping function to map the bounded interval to an infinite interval, the state quantity under the constraint will be mapped to the unconstrained state quantity. Therefore, as long as the controller is designed to ensure that the mapped state quantity is bounded, the original state quantity can be guaranteed to meet the preset performance upper and lower bounds ( Figure 1 Central).

[0054] The method of the present invention is as follows Figure 2 As shown, it includes elastic aircraft dynamics modeling and elastic aircraft control law design:

[0055] 1. Elastic Aircraft Dynamics Module

[0056] 1) Kinetic model

[0057] The longitudinal dynamics model of the elastic aircraft studied in this invention is as follows:

[0058]

[0059] Where S=[V x ,V y ,X,Y,θ,ω z ] T is the state of the aircraft, including the axial velocity V x , longitudinal speed V y , axial position x, longitudinal position y, pitch angle θ and pitch angular velocity ω z ; Fx 、F y and M z are the axial force, normal force and pitching moment respectively; are 6 elastic states, which are the generalized coordinates of the first three elastic modes and their derivatives; ξ i and ω i (i=1,2,3) are the damping and frequency of the first three elastic modes respectively. The damping values ​​of the first three elastic modes are all taken as 0.05, ω1=31.1788rad / s, ω2=85.9455rad / s, ω3=168.4875rad / s; m, g and I z They are respectively the mass of the aircraft, the acceleration of gravity and the moment of inertia in the pitch direction; N i It is a generalized force.

[0060] According to aerodynamic theory, the aerodynamic force, aerodynamic moment and generalized force N acting on the elastic aircraft are: i The polynomial expression of can be expressed as:

[0061]

[0062] Where: q, S, l are dynamic pressure, characteristic area and characteristic length respectively; α, L, D, M z ,N i are angle of attack, lift, drag, pitching moment and generalized force respectively; C L ,C D , They are lift, drag, pitching moment and generalized force coefficient, which are Mach number Ma, angle of attack α, pitch rudder deflection angle δ z and elastic modal generalized coordinates η i (i=1,2,3) polynomial function.

[0063] 2) Control-oriented model

[0064] The simplified dynamic equations can be used when designing control systems:

[0065]

[0066] Let the posture tracking error e = xx c ,in The desired pitch angle and pitch velocity command are: Then formula (3) can be rewritten as:

[0067]

[0068] in, M z0is the pitch moment other than the control moment caused by the aircraft shape and other parameters; d is the disturbance of the pitch angle channel, which includes the influence of the elastic effect on the pitch moment, parameter uncertainty and various possible external disturbances; u is the control quantity,

[0069] 2. Elastic Aircraft Control Law Design Module

[0070] This section first introduces a preset performance function with a predetermined convergence time and uses an error conversion function to transform the error system into an unconstrained system. A state observer is then designed to estimate the lumped disturbance in the system. A sliding mode controller with a predetermined convergence time and a predetermined performance is proposed to accurately and rapidly track the desired attitude command. Furthermore, the stability of the designed controller is demonstrated using the Lyapunov method.

[0071] 1) Introduce a preset performance function with a predetermined time convergence and error conversion

[0072] In order to ensure that the attitude control process meets the predetermined steady-state and transient performance, the following inequality constraint function is designed:

[0073]

[0074] Where: 0 < λ ≤ 1 represents the design parameter, which can be adjusted based on actual operating conditions to control the performance function boundaries; ρ(t) represents the preset performance function. Under the constraints of the constraints, the pitch angle tracking error e1(t) will converge rapidly within the specified limits. λρ(t) represents the maximum allowable overshoot of e1(t). The convergence rate of ρ(t) is the lower bound of the convergence rate of e1(t) and directly affects the settling time of e1(t). Therefore, by selecting an appropriate performance function, the transient and steady-state performance of the system can be planned in advance.

[0075] The present invention proposes a Figure 3 The new ρ(t) with predetermined time convergence characteristics is shown, namely

[0076]

[0077] Where: γ>1, l>0, v>0, which are the parameters to be designed and can be adjusted according to the actual working conditions; ρ ∞ represents ρ(t) t→∞ Upper bound of steady-state value; T f For this performance function, when designing the control system, it is not necessary to know the exact initial error in advance. According to the actual working conditions, the initial error can be included in the performance function boundary by simply adjusting γ, l, and v. At the same time, based on the convergence time T fThe performance function can ensure that the posture tracking converges within the expected time. Then Theorem 1 follows.

[0078] Theorem 1 Assumptions Figure 3 The preset performance function is shown in formula (6), and γ>1, T f >0, then at T f At this moment, ρ will be equal to ρ ∞ ,and and Equal to 0.

[0079] Proof First, when t=T f When ρ(T f )=ρ ∞ , and taking the derivative of formula (6) we can get:

[0080]

[0081] Where:

[0082] According to formula (7), it is easy to know that Ξ(T f )=0, and then Further deriving formula (7) again yields

[0083]

[0084] Where:

[0085]

[0086] When t = T f hour, And Ξ(T f )=0, then This completes the proof of Theorem 1.

[0087] However, the posture tracking error described by Equation (5) is a typical constrained problem. The error conversion method is used to convert it into an unconstrained problem. The ET function Γ(ε(t)) is introduced to transform the inequality constraint (5) into the following system:

[0088] e1(t)=ρ(t)Γ(ε(t)) (9)

[0089] Where: ε is the conversion error, Γ(ε(t)) is the ET function, and it satisfies the following properties:

[0090] 1) The ET function Γ(ε(t)) is smooth and strictly increasing;

[0091] 2)Γ(ε(t)) satisfies the following inequality:

[0092]

[0093] 3)Γ(ε(t)) satisfies the following equation

[0094]

[0095] According to the properties of the ET function, further inverse transformation of the ET function can be obtained:

[0096]

[0097] By taking the derivative of formula (12), we can get:

[0098]

[0099] Where:

[0100] Further derivation of formula (13) yields:

[0101]

[0102] 2) Disturbance observer design

[0103] Formula (4) contains uncertainties such as elasticity and external disturbances. To estimate and compensate for disturbances, a state observer is designed based on the principle of active disturbance rejection control. State observers can be nonlinear extended state observers (NLESO), linear extended state observers (LESO), nonlinear dynamic observers (NDO), and sliding mode observers (SMO).

[0104] This embodiment adopts a nonlinear extended state observer (NLESO):

[0105]

[0106] Where: nonlinear function where β i is the observer gain, α i , δ are constant observer parameters. The nonlinear function form is:

[0107]

[0108] The observer z1 is used to estimate the pitch angle θ, and z2 is used to estimate the pitch angular velocity ωz , z3 is used to estimate the total disturbance Δ. In a finite time, the state observation error will converge, then in A definable small quantity greater than 0.

[0109] 3) Attitude controller design and stability analysis

[0110] According to the new error variables and their derivatives established by equations (12) to (14), the sliding surface is designed as follows:

[0111]

[0112] Where: c>0 is the control parameter. Taking the derivative of the sliding surface, the result is as follows:

[0113]

[0114] Where: G = ψρ; Δ=f+d.

[0115] According to the observer shown in formula (15), the attitude tracking control law can be designed:

[0116]

[0117] Among them, k1, k2> 0. Therefore, Theorem 2 can be obtained.

[0118] Theorem 2: For the attitude error dynamics model (Equation (4)), based on the newly designed conversion error variable and its linear sliding surface (Equation (17)) and the NLESO (Equation (15)), a controller (Equation (19)) is designed. The controller is convergent. The detailed proof is given below.

[0119] Proof: First, the Lyapunov function is given as

[0120] V=|S| (20)

[0121] Derivative of the Lyapunov function:

[0122]

[0123] Substituting the controller shown in equation (19) into equation (21) yields

[0124]

[0125] Due to observation errors Then we only need to choose the parameters of k1 and k2 reasonably so that Then there is

[0126]

[0127] This completes the proof of Theorem 1.

[0128] Note 1: To avoid system chattering, the sign function in equation (19) can be switched to a saturation function:

[0129]

[0130] Where h is the boundary layer thickness.

[0131] Then formula (19) can be rewritten as

[0132]

[0133] Using the elastic suppression control algorithm designed by the present invention, a single case simulation is performed:

[0134] Figure 4 For reference control instructions. Figure 4 The algorithm designed by the present invention is compared with the traditional sliding mode algorithm with NLESO. The controller pitch angle tracking effect and rudder angle response are shown in the following figure. Figure 5 and Figure 6 As shown. Further, the elastic suppression method of the designed lumped disturbance compensation controller including elasticity is studied by estimating the elasticity through the observer, and the first-order elastic mode and its derivative change curves before and after the introduction of the elastic suppression framework of the present invention are compared. The simulation results are shown in Figure 7 shown.

[0135] It can be seen that under the action of the elastic suppression attitude control algorithm designed by the present invention, which uses the interference observer to estimate the lumped disturbance and compensate the controller, the aircraft can effectively reduce the divergence of the elastic mode and its derivatives while ensuring the attitude control accuracy, thereby achieving the effect of elastic suppression attitude control.

[0136] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for controlling the preset performance of an elastic aircraft with a predetermined time convergence, characterized in that: include: Taking the difference between the pitch angle and pitch velocity of the elastic aircraft and their expected values ​​as an attitude tracking error, and constraining the attitude tracking error using a preset performance function that converges in a predetermined fixed time; The error conversion method is used to convert the constrained posture tracking error into the unconstrained posture tracking conversion error; The total disturbance of the elastic aircraft is estimated using a state observer; A sliding mode controller is constructed to control the unconstrained attitude tracking transition error and is compensated for the sliding mode controller based on the total disturbance estimated by the state observer.

2. The method according to claim 1, wherein The preset performance function for the predetermined fixed time convergence is: Among them, γ, l and v are parameters, γ>1, l>0, v>0; ρ ∞ represents ρ(t) t→∞ Upper bound of steady-state value; T f is the predetermined convergence time, which is a fixed value; t is the time.

3. The method according to claim 1 or 2, wherein: The attitude tracking error e1(t) is subject to the following inequality constraints: Where λ is a parameter, 0<λ≤1; ρ(t) is a preset performance function that converges in a predetermined fixed time; λρ(t) is the maximum overshoot allowed by e1(t); The ET function Γ(ε(t)) is used to transform the inequality constraint (5) into the following system: e1(t)=ρ(t)Γ(ε(t)) (9) Where ε(t) is the unconstrained attitude tracking conversion error; Γ(ε(t)) is the error conversion function, and satisfies the following properties: 1) Γ(ε(t)) is smooth and strictly increasing; 2)Γ(ε(t)) satisfies the following inequality: 3) Γ(ε(t)) satisfies the following equation: Performing an inverse transformation on the ET function, the unconstrained posture tracking conversion error ε is:

4. The method according to claim 1 or 2, wherein: The state observer is a nonlinear extended state observer, a linear extended state observer, a nonlinear dynamic observer or a sliding mode observer.

5. The method according to claim 4, wherein The nonlinear extended state observer is: Where z1, z2, and z3 are the pitch angle, pitch velocity, and total disturbance estimated by the nonlinear extended state observer, respectively; θ is the pitch angle; β i is the observer gain; b is the control torque coefficient, u is the control input; e1(t) is the attitude tracking error; is a nonlinear function, Among them, α i , δ are observer parameters and are constants.

6. The method according to claim 5, wherein The attitude tracking control law u of the sliding mode controller is: Where G = ψρ, Where ρ(t) is a preset performance function that converges in a predetermined fixed time; 0<λ≤1, λρ(t) is the maximum overshoot allowed by e1(t); k1, k2 are parameters greater than 0; sgn is the sign function; c>0 is the control parameter; ε(t) is the unconstrained posture tracking conversion error; is the desired pitch angular velocity; z3 is the total disturbance estimated by the state observer.

7. The method according to claim 6, wherein Switch the sign function sgn to the saturation function sat: Then the attitude tracking control law u of the sliding mode controller is:

8. The method according to claim 1, wherein An elastic aircraft is any hypersonic or ordinary aircraft that has a slender shape or is designed with lightweight materials and is prone to elastic deformation during flight.

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