Transverse and lateral control method of microminiature ornithopter

Abstract

The invention relates to a transverse and lateral control method of a microminiature ornithopter, which comprises the following steps of: observing unknown nonlinear disturbance of the ornithopter through a first extended state observer, and introducing expected input into a first tracking differentiator for filtering and setting; observing the interference of the quasi-steady-state aerodynamic force of the flapping-wing aircraft through a second expansion state observer, and carrying out filtering setting on the virtual control signal through a second tracking differentiator; and controlling a transverse driving mechanism of the ornithopter according to the virtual control signal. According to the method, the problem that a system model needs to accurately contain uncertainty disturbance is solved in a targeted manner by introducing an extended state observer technology in a dynamic surface design process, and accurate differentiation of an original stabilization function is obtained by introducing a tracking differentiator, so that the control performance of a closed-loop system is remarkably improved. The tracking differentiator is used for filtering instruction signals, the problem of calculation complexity of a traditional backstepping method is essentially solved, the calculation time of a control algorithm is shortened, and the algorithm can be conveniently achieved in an actual control system.

Description

Technical Field

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

[0002] Micro flapping-wing aircraft generate thrust and lift through high-frequency flapping, which is a typical underactuated system. When the wingspan of the aircraft is less than 15cm, flapping-wing flight has significant advantages over traditional fixed-wing and rotary-wing aircraft in terms of flight efficiency and maneuverability. High quietness, high efficiency, and maneuverability make micro flapping-wing aircraft have broad prospects for civilian research.

[0003] From the perspective of motion mode, the lateral control of micro flapping-wing aircraft is very complex, involving multiple state variables, such as sideslip, roll, heading, etc. At the same time, since current research cannot fully reveal the aerodynamic model of flapping-wing aircraft, the influence of flow field on aerodynamic force and torque has not been fully studied, which brings a lot of difficulties to the controller design of flapping-wing aircraft. How to deal with the uncertainty of flapping-wing aircraft and the interference caused by aerodynamic force is an extremely important problem that must be solved. Summary of the invention

[0004] The purpose of the present invention is to provide a lateral control method for a micro-flapping-wing aircraft. Aiming at the model uncertainty generated by the quasi-steady-state aerodynamics of the flapping-wing aircraft, the present invention designs a control method based on an extended state observer and an improved robust dynamic surface including a tracking differentiator to solve the tasks of heading keeping control and track control of the micro-flapping-wing aircraft.

[0005] The technical solution adopted by the present invention to achieve the above-mentioned purpose 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 into the attitude angle error model of the flapping-wing aircraft is introduced into the first tracking differentiator for filtering and setting;

[0008] The disturbance of the quasi-steady aerodynamic force of the flapping-wing aircraft is observed by the second extended state observer, and the virtual control signal is filtered and adjusted by the second tracking differentiator;

[0009] The control quantity is output to the lateral driving 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 pitch angle, roll angle, and heading angle respectively, I is the unit array; 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 the first extended state observer, and introducing the attitude angular rate expectation value input into 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 expected value 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 respectively, sign represents the sign function; 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 of the quasi-steady aerodynamic force of the flapping-wing aircraft F 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 extended observer.

[0035] The control quantities are as follows:

[0036]

[0037] in, is the estimated value of the nonlinear disturbance 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. The invention fully analyzes the problems existing in the aerodynamic model of micro flapping-wing aircraft, uses dynamic surface technology, introduces the estimation of quasi-steady aerodynamic disturbance of micro flapping-wing aircraft, and expands the application of nonlinear robust attitude controller in flapping-wing aircraft attitude tracking. The designed adaptive robust controller of flapping-wing aircraft can compensate the influence of aircraft uncertainty on system stability in a local range.

[0043] 2. In view of the uncertainty of flapping-wing aircraft, the early idea was to design a mechanism that can estimate and compensate for uncertainty online, similar to the way of using function approximation, mostly function estimators. However, the function estimator needs to know the model of the system accurately and the characteristics of the uncertainty. The order of the estimator cannot be too high, otherwise it will consume a lot of calculations. The extended state observer technology is used in this invention to construct a dual model of the original system for system uncertainty. The state variables of the dual model are used to observe the changes in the state of the original system, avoiding the disadvantage of needing to know the characteristics of system uncertainty accurately.

[0044] 3. The present invention solves the problem that the system model needs to accurately include uncertain disturbances by using the extended state observer technology in the dynamic surface design process, and then obtains the accurate differential of the original stabilization function by introducing the tracking differentiator, which significantly improves the control performance of the closed-loop system. The tracking differentiator is used to filter the command signal, which essentially solves the computational complexity problem of the traditional backstepping method, reduces the computational time of the control algorithm, and facilitates the implementation of the algorithm in the actual control system.

[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 The definition principle diagram of the attitude angle of the present invention;

[0047] Figure 2 The overall structure diagram of the control method of the present invention. DETAILED DESCRIPTION

[0048] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

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

[0050] Expanded 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. Among them, the negative feedback term accelerates the convergence of the observer, and the extended variable is used to observe the disturbance of the quasi-steady aerodynamic force 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 for observing 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 of the flapping-wing aircraft acting on the body. fal(e,a,δ) is a nonlinear function:

[0054]

[0055] Tracking Differentiator Design

[0056] Adding a tracking differentiator to each step of the dynamic surface control to solve the problem of computational complexity, and using the tracking differentiator to filter the command signal, 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. Design the continuous time tracking differentiator 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 a virtual control signal at 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 problem of complex calculations. According to the Lyapunov stability principle, the controller output value is found to satisfy the negative value of Lyapunov's first-order derivative, and 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. Construct 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 formula V1 yields:

[0081]

[0082] Among them, 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] Desired input ν in the flapping-wing aircraft model d1 Introduce tracking differentiator filtering to obtain

[0087]

[0088] 2. Construct 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 equation (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, which 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. Introduce 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 expected value of the attitude angle 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 lateral control method for 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 into the attitude angle error model of the flapping-wing aircraft is introduced into the first tracking differentiator for filtering and setting; The disturbance of the quasi-steady aerodynamic force of the flapping-wing aircraft is observed by the second extended state observer, and the virtual control signal is filtered and adjusted by the second tracking differentiator; The control quantity is output to the lateral driving 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.

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, 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 pitch angle, roll angle, and heading angle respectively, I is the unit array; 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.

3. The lateral control method of a micro flapping-wing aircraft according to claim 1, characterized in that: 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 the first extended state observer, and introducing the attitude angular rate expectation value input into 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, error e1 = ζ1-x1, x1 is the state variable of the observed system, ζ1 and ζ2 are expansion variables 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 expected value ν in the attitude angle error model of flapping-wing aircraft d1 Introduce the first tracking differentiator for filter tuning: Wherein, χ1 and χ2 are tracking variables respectively, sign represents the sign function; r1 represents the maximum feedback gain of the first tracking differentiator.

4. The lateral control method of a micro flapping-wing aircraft according to claim 1, characterized in that: 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 of the quasi-steady aerodynamic force of the flapping-wing aircraft F 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 extended observer.

5. The lateral control method of a micro flapping-wing aircraft according to claim 1, characterized in that: The control quantities are as follows: in, is the estimated value of the nonlinear disturbance 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.

Images