A method for lateral control of a micro ornithopter

Abstract

The present application relates to a kind of micro flapping wing aircraft lateral control method, unknown nonlinear disturbance of flapping wing aircraft is observed by first extended state observer, and desired input is introduced into first tracking differentiator and is filtered and adjusted;The disturbance of quasi-steady aerodynamic force of flapping wing aircraft is observed by second extended state observer, and the virtual control signal is filtered and adjusted by second tracking differentiator;According to virtual control signal, the lateral drive mechanism of flapping wing aircraft is controlled.The present application solves the problem that system model needs to accurately include uncertainty disturbance by introducing extended state observer technology in dynamic surface design process, and then introduces tracking differentiator to obtain the accurate differentiation of original stabilization function, which significantly improves the control performance of closed-loop system.Tracking differentiator is used to filter command signal, which essentially solves the calculation complexity problem of traditional backstepping method, reduces the calculation time of control algorithm, and facilitates the implementation of algorithm in actual control system.

Description

Technical Field

[0001] The invention belongs to the field of micro-miniature bionic robots, in particular to a lateral control method for a micro-miniature flapping-wing aircraft. Background Art

[0002] Micro flapping-wing aircraft generate thrust and lift through high-frequency flapping, representing a typical underactuated system. When the wingspan is less than 15 cm, flapping-wing flight offers significant advantages over traditional fixed-wing and rotary-wing aircraft in terms of flight efficiency and maneuverability. Their quietness, high efficiency, and maneuverability make them promising for civilian research.

[0003] From a motion mode perspective, lateral control of flapping-wing micro aircraft is highly complex, involving multiple state variables such as sideslip, roll, and heading. Furthermore, current research does not fully understand the aerodynamic model of flapping-wing aircraft, and the impact of the flow field on aerodynamic forces and torques is not fully understood. This presents significant challenges in controller design for flapping-wing aircraft. Managing the uncertainties and aerodynamic disturbances of flapping-wing aircraft is a crucial and unavoidable issue. Summary of the Invention

[0004] The present invention aims to provide a lateral control method for a micro-flapping-wing aircraft. This method addresses the model uncertainty arising from the quasi-steady-state aerodynamics of flapping-wing aircraft and designs a control method based on an extended state observer and an improved robust dynamic surface including a tracking differentiator. This method addresses the following tasks: heading control and track control for micro-flapping-wing aircraft.

[0005] The technical solution adopted by the present invention to achieve the above-mentioned object is: a lateral control method for a micro-flapping-wing aircraft, comprising the following steps:

[0006] Construct the attitude angle error model of flapping-wing aircraft;

[0007] The first extended state observer is used to observe the unknown nonlinear disturbance of the flapping-wing aircraft in the attitude angle error model of the flapping-wing aircraft, and the expected value of the attitude angular rate input to the attitude angle error model of the flapping-wing aircraft is introduced into the first tracking differentiator for filtering and tuning;

[0008] The second extended state observer is used to observe the disturbance of the quasi-steady aerodynamic force of the flapping-wing aircraft, and the second tracking differentiator is used to filter and adjust the virtual control signal.

[0009] The control quantity is output to the lateral drive mechanism of the flapping-wing aircraft according to the virtual control signal, so that the time-varying parameters in the control process conform to the parameter adaptive law.

[0010] The flapping-wing aircraft attitude angle error model is as follows:

[0011]

[0012] Its matrix form is:

[0013]

[0014] in,

[0015]

[0016] The aircraft attitude dynamics equation is obtained according to the momentum theorem and combined with equation (6) to obtain:

[0017]

[0018] in, is the attitude angle error, x2=[ω x ,ω y ,ω z ] T is the design constant, is the expected value of the attitude angle, is the expected value of attitude angular rate, ψ, γ are the pitch angle, roll angle, and heading angle, respectively; I is the unit matrix; u is the quasi-steady-state aerodynamic input value of the flapping-wing aircraft; F un (t) is the disturbance of the quasi-steady aerodynamic force of the flapping-wing aircraft, and A1 is the unknown nonlinear disturbance.

[0019] The method comprises the following steps: observing the unknown nonlinear disturbance of the flapping-wing aircraft in the attitude angle error model of the flapping-wing aircraft by a first extended state observer, and introducing the attitude angular rate expectation value input to the attitude angle error model of the flapping-wing aircraft into the first tracking differentiator for filtering and setting.

[0020] Construct the first extended state observer to observe the unknown nonlinear disturbance A1 of the flapping-wing aircraft in the flapping-wing aircraft attitude angle error model:

[0021]

[0022] Among them, the error x1 is the state variable of the observed system, is an expansion variable used for observing nonlinear disturbances, b1 and b2 are proportional coefficients, a1 is a constant, and δ1 is a constant that affects the filtering effect; fal(e1, a1, δ1) is a nonlinear function;

[0023] The expected input attitude angular rate ν in the flapping-wing aircraft attitude angle error model d1 Introduce the first tracking differentiator for filter tuning:

[0024]

[0025] Wherein, χ1 and χ2 are tracking variables, sign represents the sign function, and r1 represents the maximum feedback gain of the first tracking differentiator.

[0026] The method of observing the disturbance of the quasi-steady-state aerodynamic force of the flapping-wing aircraft by the second extended state observer and filtering and adjusting the virtual control signal by the second tracking differentiator comprises the following steps:

[0027] Construct the second extended state observer to deal with the nonlinear disturbance F of the quasi-steady aerodynamic force of the flapping-wing aircraft. un (t) Conduct observations:

[0028]

[0029] Among them, the error x2 is the state variable of aerodynamic nonlinear disturbance, is an expansion variable used for observing nonlinear disturbances, b3 and b4 are proportional coefficients, a2 is a constant, and δ2 is a constant that affects the filtering effect; fal(e2, a2, δ2) is a nonlinear function;

[0030] Introducing the second tracking differentiator to obtain

[0031]

[0032] Wherein, χ3 and χ4 are tracking variables respectively; sign represents the sign function, and r2 represents the maximum feedback gain of the second tracking differentiator;

[0033] Among them, the virtual control signal

[0034] ο is a positive constant, the first dynamic surface S1=x1, k1 is a positive constant, is the error estimate of the first augmented observer.

[0035] The control quantities are as follows:

[0036]

[0037] in, is the estimated value of the nonlinear interference error of the quasi-steady-state aerodynamic force of the flapping-wing aircraft, ο is a positive constant, is the error estimate of the first extended observer, k1 is a positive definite constant;

[0038] The parameter adaptation law is as follows:

[0039]

[0040] in, is the error estimate of the second extended observer, σ2 is a positive constant, and the second dynamic surface S2 = x2-h z , x2 is the state variable of aerodynamic nonlinear disturbance, and π2 is a positive definite constant.

[0041] The present invention has the following beneficial effects and advantages:

[0042] 1. This invention thoroughly analyzes the existing aerodynamic modeling issues for micro-flapping-wing aircraft. Leveraging dynamic surface technology, it introduces an estimate of the quasi-steady aerodynamic disturbances for micro-flapping-wing aircraft, expanding the application of nonlinear robust attitude controllers for attitude tracking. The resulting adaptive robust controller for flapping-wing aircraft can locally compensate for the effects of aircraft uncertainties on system stability.

[0043] 2. To address the uncertainty of flapping-wing aircraft, an early idea was to design a mechanism that could estimate and compensate for uncertainty online, similar to the use of function approximation, often using a function estimator. However, a function estimator requires precise knowledge of the system model and the characteristics of the uncertainty. The order of the estimator cannot be too high, otherwise it would consume a large amount of computation. The present invention uses the extended state observer technology to address system uncertainty, constructing a dual model of the original system. The state variables of the dual model are used to observe changes in the original system state, avoiding the disadvantage of requiring precise knowledge of the system uncertainty characteristics.

[0044] 3. This invention utilizes the Extended State Observer (ESO) technology in the dynamic surface design process to specifically address the need for the system model to accurately incorporate uncertain perturbations. Furthermore, by introducing a tracking differentiator to obtain the precise differential of the original stabilization function, this significantly improves the control performance of the closed-loop system. Using the tracking differentiator to filter the command signal fundamentally addresses the computational complexity of traditional backstepping methods, reducing the computational time of the control algorithm and facilitating its implementation in practical control systems.

[0045] 4. The micro flapping-wing aircraft control in the present invention adopts a nonlinear control strategy. Through the back-stepping derivation process, a multivariable, strongly coupled nonlinear system is gradually degraded into a set of simple models, and the calculation process is differentiated into various stability analyses, thereby simplifying the overall control process. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Schematic diagram of the definition of attitude angle of the present invention;

[0047] Figure 2 Overall structural diagram of the control method of the present invention. DETAILED DESCRIPTION

[0048] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0049] like Figure 1 、 Figure 2 As shown, the present invention specifically includes the following steps:

[0050] Extended Observer Design

[0051] The structure of the extended state observer is a set of differential dynamic equations, including observer state variables, nonlinear negative feedback terms, and extended variables. The negative feedback term accelerates the convergence of the observer, and the extended variables are used to observe the quasi-steady aerodynamic disturbances of the flapping-wing aircraft. Its structure is as follows:

[0052]

[0053] Among them, x is the state variable of the observed system, is an expansion variable used to observe nonlinear disturbances, k is a proportional coefficient, a is a constant between 0 and 1, and δ is a constant that affects the filtering effect. The disturbance here is caused by the quasi-steady aerodynamic force acting on the body of the flapping-wing aircraft. fal(e, a, δ) is a nonlinear function:

[0054]

[0055] Tracking Differentiator Design

[0056] In each step of dynamic surface control, a tracking differentiator is added to solve the computational complexity problem. The tracking differentiator is used to filter the command signal, which essentially solves the computational complexity problem of the traditional backstepping method, reduces the calculation time of the control algorithm, and facilitates the implementation of the algorithm in the actual control system. The continuous time tracking differentiator is designed as:

[0057]

[0058] The symbol function sign(·) is defined as

[0059]

[0060] r represents the maximum feedback gain of the filter, α r It is the input signal of the tracking differentiator, which will be replaced by the virtual control signal in each step of the dynamic surface design process to eliminate the "complexity explosion" problem in the backstepping method.

[0061] Design of robust adaptive attitude controller based on extended observer

[0062] The dynamic surface control method is to define the error sliding surface, introduce an observer to estimate the aerodynamic uncertainty in the model, and add a tracking differentiator in the process of dynamic surface control to solve the computational complexity problem. According to the Lyapunov stability principle, the controller output value is found to satisfy the Lyapunov first-order derivative is negative, the error model converges to 0, that is, the system is stable; the control law design is completed.

[0063] The flapping-wing aircraft attitude error equation is used to define the variables: is the attitude angle error, x2=[ω x ,ω y ,ω z ] T is the design constant, is the expected value of the attitude angle, is the expected value of attitude angular rate.

[0064] Construct the attitude angle error equation of flapping-wing aircraft:

[0065]

[0066] Its matrix form is:

[0067]

[0068] in,

[0069]

[0070] The aircraft attitude dynamics equation is obtained according to the momentum theorem and combined with equation (6) to obtain:

[0071]

[0072] u is the quasi-steady-state aerodynamic force input value of the flapping-wing aircraft, F un (t) is the disturbance of the quasi-steady aerodynamic force of the flapping-wing aircraft.

[0073] In the following design, an improved robust dynamic surface design process including tracking differentiator is proposed for systems with uncertainties and disturbances based on nonlinear extended state observer.

[0074] 1. Constructing the first dynamic surface, the first extended state observer, and the first tracking differentiator

[0075] Define the first dynamic surface:

[0076] S1=x1 (9)

[0077] Define the Lyapunov function as:

[0078]

[0079] Among them, ε1 is a positive definite constant, is the evaluation error of the first extended state observer, θ1 is an unknown positive constant, is an estimated value.

[0080] Differentiating Equation V1 yields:

[0081]

[0082] Where ε1 is a positive definite constant.

[0083] In order to observe the unknown nonlinear disturbance A1 of the flapping-wing aircraft in Equation (6), an extended state observer is designed:

[0084]

[0085] use Observe the unknown nonlinear disturbance A1.

[0086] The expected input ν in the flapping-wing aircraft model d1 Introducing tracking differentiator filtering to obtain

[0087]

[0088] 2. Constructing the Second Dynamic Surface, the Second Extended State Observer, and the Second Tracking Differentiator

[0089] Design virtual control signals:

[0090]

[0091] Parameter update law of virtual control signal:

[0092]

[0093] σ1 is a positive constant, design value; k1 is a positive constant.

[0094] Define the second dynamic surface S2 = x2-h z , substituting formula (14) into (6) we obtain:

[0095]

[0096] Represents the estimation error of the unknown nonlinear perturbation.

[0097] Substituting equations (15) and (16) into equation (11), we obtain:

[0098]

[0099] π1 is a positive constant, γ1 is a positive constant, and is a set value; the above formula satisfies:

[0100]

[0101] According to Young's inequality:

[0102]

[0103] According to the properties of the inverse tangent function:

[0104]

[0105] get:

[0106]

[0107] Assume that the quasi-steady aerodynamic disturbance F of the flapping-wing aircraft is un (t) has no singular changes during the flapping period and is smooth, including the interference and filter errors into the system Lyapunov function:

[0108]

[0109] in, As the boundary of the estimation error of the second extended observer, ε2 is a positive definite constant, k2 is a positive definite constant, represents the estimation error of the quasi-steady aerodynamic disturbance.

[0110] Derivative of V2:

[0111]

[0112] Design the extended state observer:

[0113]

[0114] It is an expansion variable used for observing nonlinear disturbances, b3 and b4 are proportional coefficients, a2 is a constant, and δ2 is a constant that affects the filtering effect; fal(e2,a2,δ2) is a nonlinear function.

[0115] use For the nonlinear term F un (t) is observed. Introducing the tracking differentiator to obtain

[0116]

[0117] 3. Steps 1 and 2 form an adaptive attitude controller, and the controller output is:

[0118] Finally, the actual controller is given:

[0119]

[0120] And the parameter adaptation law:

[0121]

[0122] Among them, σ2 is a positive constant and a design value.

[0123] like Figure 2 As shown, the input of the adaptive attitude controller constructed by the present invention is the attitude angle expected value The controller quantity u is output to the lateral drive mechanism of the flapping-wing robot through the adaptive posture controller, and the parameter adaptive law is used to adjust the time-varying parameters, including the positive definite parameters of σ2, ο, and π2.

Claims

1. A method for lateral control of a micro flapping-wing aircraft, characterized in that: The following steps are involved: Construct the attitude angle error model of flapping-wing aircraft; The first extended state observer is used to observe the unknown nonlinear disturbance of the flapping-wing aircraft in the attitude angle error model of the flapping-wing aircraft, and the expected value of the attitude angular rate input to the attitude angle error model of the flapping-wing aircraft is introduced into the first tracking differentiator for filtering and tuning; The second extended state observer is used to observe the disturbance of the quasi-steady aerodynamic force of the flapping-wing aircraft, and the second tracking differentiator is used to filter and adjust the virtual control signal. Outputting a control variable to a lateral drive mechanism of a flapping-wing aircraft according to a virtual control signal so that the time-varying parameters in the control process conform to a parameter adaptive law; The method comprises the following steps: observing the unknown nonlinear disturbance of the flapping-wing aircraft in the attitude angle error model of the flapping-wing aircraft by a first extended state observer, and introducing the attitude angular rate expectation value input to the attitude angle error model of the flapping-wing aircraft into the first tracking differentiator for filtering and setting. Construct the first extended state observer to observe the unknown nonlinear disturbance A1 of the flapping-wing aircraft in the flapping-wing aircraft attitude angle error model: Among them, the error x1 is the state variable of the observed system, is an expansion variable used for observing nonlinear disturbances, b1 and b2 are proportional coefficients, a1 is a constant, and δ1 is a constant that affects the filtering effect; fal(e1, a1, δ1) is a nonlinear function; The expected input attitude angular rate ν in the flapping-wing aircraft attitude angle error model d1 Introduce the first tracking differentiator for filter tuning: Where χ1 and χ2 are tracking variables, sign represents the sign function; r1 represents the maximum feedback gain of the first tracking differentiator; The method of observing the disturbance of the quasi-steady-state aerodynamic force of the flapping-wing aircraft by the second extended state observer and filtering and adjusting the virtual control signal by the second tracking differentiator comprises the following steps: Construct the second extended state observer to deal with the nonlinear disturbance F of the quasi-steady aerodynamic force of the flapping-wing aircraft. un (t) Conduct observations: Among them, the error x2 is the state variable of aerodynamic nonlinear disturbance, is an expansion variable used for observing nonlinear disturbances, b3 and b4 are proportional coefficients, a2 is a constant, and δ2 is a constant that affects the filtering effect; fal(e2, a2, δ2) is a nonlinear function; Introducing the second tracking differentiator to obtain Wherein, χ3 and χ4 are tracking variables respectively; sign represents the sign function, and r2 represents the maximum feedback gain of the second tracking differentiator; Among them, the virtual control signal ο is a positive constant, the first dynamic surface S1=x1, k1 is a positive constant, is the error estimate of the first augmented observer; The control quantities are as follows: in, is the estimated value of the nonlinear interference error of the quasi-steady-state aerodynamic force of the flapping-wing aircraft, ο is a positive constant, is the error estimate of the first extended observer, k1 is a positive definite constant; The parameter adaptation law is as follows: in, is the error estimate of the second extended observer, σ2 is a positive constant, and the second dynamic surface S2 = x2-h z , x2 is the state variable of aerodynamic nonlinear disturbance, and π2 is a positive definite constant.

2. The lateral control method of a micro flapping-wing aircraft according to claim 1, characterized in that: The flapping-wing aircraft attitude angle error model is as follows: Its matrix form is: in, The aircraft attitude dynamics equation is obtained according to the momentum theorem and combined with equation (6) to obtain: in, x1=[e θ ,e ψ ,e r ] T is the attitude angle error, x2=[ω x ,ω y ,ω z ] T is the design constant, x d =[θ d ,ψ d ,γ d ] T is the expected value of the attitude angle, is the expected value of the attitude angular rate, θ, ψ, and γ are the pitch angle, roll angle, and heading angle, respectively, and I is the unit matrix; u is the quasi-steady-state aerodynamic force input value of the flapping-wing aircraft, and F un (t) is the disturbance of the quasi-steady aerodynamic force of the flapping-wing aircraft, and A1 is the unknown nonlinear disturbance.

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