Stratosphere airship timing flight control method based on event triggering

Abstract

The application discloses a stratosphere airship timing flight control method based on event triggering and belongs to the technical field of automatic control, and comprises the following steps: step one, giving a stratosphere airship model and an expected trajectory; step two, designing an observer, establishing a fixed-time convergent observer, and eliminating the influence of unknown airspeed and other error terms by using an adaptive term; step three, trajectory tracking, designing a fixed-time convergent control rate to make the trajectory of the airship reach the expected trajectory; and step four, event triggering, designing an event triggering mechanism to calculate the control quantity. The stratosphere airship timing flight control method based on event triggering can minimize the energy consumption while effectively tracking the trajectory of the stratosphere airship, and realizes the flight control of the stratosphere airship under unknown wind field to reach the fast convergence index.

Description

Technical Field

[0001] This invention relates to the field of automatic control and monitoring technology, and in particular to a timed flight control method for stratospheric airships based on event triggering. Background Technology

[0002] A stratospheric airship is a lighter-than-air aircraft. Its biggest difference from a balloon is that it has a propulsion and flight control system.

[0003] Stratospheric airships have the following application prospects:

[0004] 1) Communication Terminal. When a stratospheric airship platform is at a fixed altitude of 20 kilometers, its effective ground coverage area can reach tens of thousands of square kilometers, providing high-speed communication services to a wide area.

[0005] 2) Area surveillance. Stratospheric airships combine the advantages of near-Earth flight of aircraft with the fixed-point surveillance of geostationary satellites, enabling fixed-point, high-resolution surveillance of a large designated area.

[0006] 3) Meteorological observation. Stratospheric airships fly above the cloud layer and can be used to observe extreme weather phenomena such as typhoons.

[0007] Currently, there is no intellectual property in the field of automatic flight control for stratospheric airships that can simultaneously address unknown environmental factors and unpredictable wind fields, conserve computational resources, and achieve rapid error convergence. Most current patents only achieve one of these three aspects. For example, the invention patent CN113419431A, entitled "An Event-Triggered Stratospheric Airship Trajectory Tracking Control Method and System," does not consider that wind fields are unpredictable in the actual engineering applications of stratospheric airships; the invention patent CN113552902A, entitled "A Three-Dimensional Trajectory Tracking Control Method and System for Stratospheric Airships," achieves trajectory tracking control of the airship without computational resource limitations; and the invention patent CN112180961B, entitled "A Full-State Constrained Stratospheric Airship Trajectory Tracking Control Method and System," also does not consider the wind field problem, treating wind speed as a known quantity in the control design. However, in practical engineering applications and given current technological capabilities, stratospheric airships must employ a spatiotemporal energy storage strategy to achieve day-night cycles. Furthermore, traditional airborne wind speed measurement equipment uses pitot tubes: for stratospheric flight with low air density and low power, pressure changes caused by dynamic pressure cannot be accurately measured. Therefore, to meet mission requirements, this invention develops a control method that minimizes energy consumption while enabling stratospheric airships to effectively track their trajectory, in the absence of airspeed measurement. Summary of the Invention

[0008] The purpose of this invention is to provide an event-triggered timed flight control method for stratospheric airships. Addressing the limitations of computational resources and the unmeasurable airspeed of stratospheric airships in practical applications, this invention proposes a control method that minimizes energy consumption while effectively tracking the trajectory of the stratospheric airship. This method enables stratospheric airships to achieve rapid convergence in flight control under unknown wind fields.

[0009] To achieve the above objectives, the present invention provides an event-triggered timed flight control method for stratospheric airships, comprising the following steps:

[0010] Step 1: Given a stratospheric airship model and the desired trajectory;

[0011] Step 2: Design an observer. Establish a fixed-time convergent observer and use adaptive terms to eliminate the effects of unknown airspeed and other error terms.

[0012] Step 3: Trajectory tracking. Design a control law with fixed-time convergence to ensure the airship's trajectory reaches the desired trajectory.

[0013] Step 4: Event Triggering. Following Step 3, a time-triggered mechanism is designed to calculate the control variables.

[0014] Preferably, the desired trajectory in step one is X. 1d =[x d ,y d ,z d ,φ d ,θ d ,ψ d ]:

[0015]

[0016] Where X1 = [x, y, z, φ, θ, ψ] T For the position / attitude data of the stratospheric airship, T = diag[R a ,R p [x] is the coordinate transformation matrix, X2 = [u, v, w, p, q, r] T The data represents the velocity / attitude angular velocity of the stratospheric airship, Y is the moment of inertia matrix, τ is the control input, and f is the interference caused by the error between the predicted wind field and the actual wind field.

[0017] Where x is the airship's northward position; y is the airship's eastward distance; z is the airship's vertical position, pointing downwards; φ is the airship's roll angle; θ is the airship's pitch angle; and ψ is the airship's yaw angle.

[0018] Preferably, in step two, the external disturbance, airspeed term, and event-triggered measurement error are first combined to obtain a new state-space equation. An observer is then set up, and the error of the observer is subjected to stability analysis to determine whether the observer is stable.

[0019] Preferably, in step two, the new state-space equation is:

[0020]

[0021] Where, δ * This is a combined measurement error that includes external disturbances, airspeed, and event-triggered measurements.

[0022] Preferably, the observer is designed as follows:

[0023]

[0024] in It is an adaptive term, α i ∈(0,1),β i >1, i = 1, 2, 3, 4, μ i ,ε i ,γ i ,k i It is a positive number. These are observations of pose, velocity, airspeed, and other unknown disturbances;

[0025] The observer error is defined as:

[0026]

[0027] Differentiation yields:

[0028]

[0029] Observer parameters Where l1 and l2 are small constants greater than zero. Extracting the observer gain coefficients yields two Herwitz matrices:

[0030]

[0031] Then, a stability analysis was performed on the observer error.

[0032] Preferably, in the trajectory tracking calculation method in step three, two sliding surfaces are first defined, new virtual state variables are introduced, derivative calculations are performed, and the control target is comprehensively considered to obtain the control law.

[0033] Preferably, in step three, the two sliding surfaces s1 and s2 are respectively:

[0034]

[0035] in C1 and C2 are synovial variables, α, β, γ i ,β i ,k i ,η i It is a positive real number and satisfies 0 < α < 1, β > 1.

[0036] Preferably, in step three, the control rate expression is:

[0037]

[0038] Where λ 21 , λ 22 This is a normal amount.

[0039] Preferably, in step four, after obtaining the control rate in step three, an event triggering mechanism is designed to calculate the airship control quantity when the event triggering conditions are met.

[0040] The event triggering mechanism is designed as follows:

[0041] And there are

[0042]

[0043] in This is the measurement error. 0 < ζ i <1 and These are control parameters.

[0044] definition Then, based on the triggering condition, for any t∈[t k ,t k+1 ),exist and If t0 is defined as 0, then the above conclusion applies; the controller error caused by event-driven mechanisms is...

[0045] Therefore, the event-triggered timed flight control method for stratospheric airships of the present invention has the following beneficial effects:

[0046] (1) This invention takes into account the actual application requirements of stratospheric airships and designs an event-triggered fixed-time stratospheric airship trajectory tracking control method by designing an efficient trajectory tracking control law, a fixed-time observer and an event-triggered adaptive trajectory tracking controller, thus filling the technical gap in this field.

[0047] (2) This invention solves the problems of unknown interference and unmeasurable airspeed by using a timed state expansion observer, uses a first-order filter to solve the problem of difficulty in solving the desired attitude derivative, reduces the driving frequency of the actuator when tracking the desired trajectory by adding an event triggering mechanism, and designs a fixed-time trajectory tracking controller based on event triggering and a timed observer to achieve accurate trajectory tracking.

[0048] (3) This invention combines a fixed-time backstepping controller, a fixed-time convergent observer and an adaptive event-driven control method. The closed-loop system of the control is converged in a fixed time, and the designed event-driven controller can effectively save computing resources. This provides an effective design means for the automatic flight engineering realization of stratospheric airships.

[0049] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of an embodiment of an event-triggered stratospheric airship timed flight control method according to the present invention;

[0051] Figure 2 This is a flowchart of an embodiment of an event-triggered stratospheric airship timed flight control method according to the present invention. Detailed Implementation

[0052] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0054] Example

[0055] like Figure 1-2 As shown, this invention provides an event-triggered timed flight control method for stratospheric airships, comprising the following steps:

[0056] Step 1: Given a stratospheric airship model and the desired trajectory X 1d =[x d ,y d ,z d ,φ d ,θ d ,ψ d ]:

[0057]

[0058] Where X1 = [x, y, z, φ, θ, ψ] T For the position / attitude data of the stratospheric airship, T = diag[R a ,R p [x] is the coordinate transformation matrix, X2 = [u, v, w, p, q, r] T The data represents the velocity / attitude angular velocity of the stratospheric airship, Y is the moment of inertia matrix, τ is the control input, and f is the interference caused by the error between the predicted wind field and the actual wind field.

[0059]

[0060]

[0061]

[0062]

[0063]

[0064] Where x is the airship's northward position; y is the airship's eastward distance; z is the airship's vertical position, pointing downwards; φ is the airship's roll angle; θ is the airship's pitch angle; v is the airship's yaw angle; u is the airship's forward velocity, pointing forward; v is the airship's lateral velocity, pointing to the right; w is the airship's vertical velocity, pointing downwards; p is the airship's roll rate; q is the airship's pitch rate; and r is the airship's yaw rate. ρ is the volume of the airship; ρ is the atmospheric density; x g ,y g ,z g The location of the airship's center of gravity; I x ,I y ,I z Airship moment of inertia; I xz B is the airship's inertial product; k1, k2, k3 are the airship's inertial factors; f ρ is the buoyancy of the airship; m is the mass of the airship; g is the acceleration due to gravity; F a M a Aerodynamics and aerodynamic torque of an airship.

[0065] Step 2: Design the observer. First, combine the external disturbances, airspeed term, and event-triggered measurement errors into δ. * The expression for the measurement error triggered by the event will be given in step four.

[0066] At this point, the new state-space equation is:

[0067]

[0068] The observer is designed as follows:

[0069]

[0070] in It is an adaptive term, α i ∈(0,1),β i >1, i = 1, 2, 3, 4, μ i ,ε i ,γ i ,k i It is a positive number. These are observations of pose, velocity, airspeed, and other unknown disturbances;

[0071] The observer error is defined as:

[0072]

[0073] Differentiation yields:

[0074]

[0075] Observer parameters Where l1 and l2 are small constants greater than zero. Extracting the observer gain coefficients yields two Herwitz matrices:

[0076]

[0077] Then, a stability analysis was performed on the observer error;

[0078] First, consider a partial form of the observer:

[0079]

[0080] Two Lyapunov functions are given for the error:

[0081] V1(β1,e)=κ T P1κ and

[0082] in, Differentiating V1 with respect to parameter β1 = 1 yields:

[0083]

[0084] If e i =0, then we have and Additionally, it should be noted that if β1∈(1,1+ξ), and ξ is a small quantity, then we have Therefore, the error system corresponding to V1 is asymptotically stable.

[0085]

[0086] Similarly, for V2(α1,e), we can also obtain

[0087]

[0088] According to Rayleigh's inequality When ||κ||=1:

[0089] There exists a real number Ω such that Differentiation over the entire system with respect to all time has

[0090]

[0091] Where γ2=λ min Q2 / λ max P2, it is easy to see that the time for V2 to converge to Ω will not exceed [the specified time]. And it is independent of the initial conditions of the system.

[0092] Similarly, the full-time derivative over the entire system also has

[0093]

[0094] Where γ1=λ min Q1 / λ max P1.

[0095] When α is sufficiently close to 1, the influence of the initial error can be ignored, that is, the effect of the initial error can be eliminated. The impact of the item.

[0096] At this point, according to Lyapunov's theorem, the observer is stable.

[0097] Where P1, P2, Q1, Q2 are positive definite non-singular symmetric matrices and satisfy...

[0098]

[0099] Step 3: Trajectory tracking, the calculation method is as follows:

[0100] First, define two sliding surfaces s1 and s2 as follows:

[0101]

[0102] in C1 and C2 are synovial variables, α, β, γ i ,β i ,k i ,η i X is a positive real number that satisfies 0 < α < 1, β > 1. 3dThese are newly introduced virtual state variables, and their expressions will be derived using backstepping:

[0103] Differentiating with respect to the sliding surface yields

[0104]

[0105]

[0106] Where X c It is a virtual control input, expressed as follows; λ 11 ,λ 12 This is a normal amount.

[0107]

[0108] To reduce the complex calculations caused by directly differentiating dummy variables, a state variable X is introduced. 2d , which represents X c The filtered value of a first-order low-pass filter with a time constant σ is expressed as:

[0109]

[0110] Based on the control objective, the expression for the control rate can be derived as follows:

[0111]

[0112] Where λ 21 , λ 22 This is a normal amount.

[0113] Step 4, Event Triggering, the calculation method is as follows:

[0114] After obtaining the control rate in step three, an event triggering mechanism is designed to calculate the airship control quantity when the event triggering condition is met.

[0115] The event triggering mechanism is designed as follows:

[0116] And there are

[0117]

[0118]

[0119] in This is the measurement error. 0 < ζ i <1 and These are control parameters.

[0120] definition Then, based on the triggering condition, for any t∈[t k ,t k+1 ),exist and If t0 is defined as 0, then the above conclusion applies; the controller error caused by event-driven mechanisms is...

[0121] The error term mentioned in step two is Furthermore, it can be seen from the above event triggering mechanism that Bounded, since the disturbances in the stratospheric environment are significantly smaller than those in the troposphere, and the initial state and motor power are finite, the changes in disturbances will not be large. Therefore, there exists a constant C such that... Established.

[0122] This achieves efficient overall trajectory tracking.

[0123] Therefore, this invention provides an event-triggered timed flight control method for stratospheric airships. Addressing the limitations of computational resources and the unmeasurable airspeed of stratospheric airships in practical applications, this method proposes a control approach that minimizes energy consumption while effectively tracking the trajectory of the stratospheric airship. It can achieve rapid convergence flight control for stratospheric airships under unknown wind fields.

[0124] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A stratospheric airship timing flight control method based on event triggering, characterized in that, Includes the following steps: Step one, given a stratosphere airship model and a desired trajectory; the desired trajectory is : ； wherein is the position / attitude data of the stratospheric airship, is the coordinate system transformation matrix, is the velocity / attitude angular velocity data of the stratospheric airship, is the inertia matrix, is the control input, is the disturbance caused by the error between the predicted wind field and the actual wind field; in, The airship's northward position; The distance eastward from the airship; This indicates the vertical position of the airship, pointing downwards. To determine the roll angle of the airship; The pitch angle of the airship; This refers to the yaw angle of the airship; The forward velocity of the airship is in the direction of forward movement. This is the lateral velocity of the airship, directed to the right; This represents the vertical velocity of the airship, directed downwards. This refers to the airship's roll angular velocity; The pitch rate of the airship; airship yaw rate; The volume of the airship; Atmospheric density; The location of the airship's center of gravity; Airship moment of inertia; For the inertial product of the airship; The inertial factor of the airship; For the buoyancy of the airship; For the mass of the airship; It is the acceleration due to gravity; , Airship aerodynamics and aerodynamic torque; Step 2: Design the observer. Establish a fixed-time convergent observer and use adaptive terms to eliminate the influence of unknown airspeed and other error terms. First, combine the external disturbances, airspeed terms, and event-triggered measurement errors to obtain a new state-space equation. Set up an observer, and then perform stability analysis on the observer's errors to determine whether the observer is stable. The new state-space equation is: ； in, This is to combine the measurement errors caused by external disturbances, airspeed, and events. The observer is designed as follows: ； in It is an adaptive term. , It is a positive number. These are observations of pose, velocity, airspeed, and other unknown perturbations. Step 3: Trajectory tracking. Design a control law with fixed-time convergence to make the airship's trajectory reach the desired trajectory. In the trajectory tracking calculation method, first define two sliding surfaces, introduce new virtual state variables, perform derivative calculations, and synthesize the control objectives to obtain the control law. Two sliding surfaces They are respectively: in , and It is a synovial variable. It is a positive real number and satisfies ; The expression for the control rate is: in This is a normal amount; Step 4: Event Triggering. Following Step 3, an event triggering mechanism is designed to calculate the control variables. The event triggering mechanism is designed as follows: And there are in It is a measurement error; and These are control parameters; definition Then, based on the triggering condition, for any ,exist and .

2. The event-triggered timed flight control method for stratospheric airships according to claim 1, characterized in that: In step four, after obtaining the control rate in step three, an event triggering mechanism is designed to calculate the airship control quantity when the event triggering conditions are met.

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