Data-driven non-uniform sampling controller design method based on aircraft model

Abstract

The present invention discloses a design method of a data-driven non-uniform sampling controller based on an aircraft model. The steps of the present invention are as follows: Step 1: Modeling the aircraft model as a Markov jump system, including model analysis, decomposition model, simplified equations, equilibrium state transformation, and linear state simplification; Step 2: Proposing an unknown system matrix representation method for a data-based Markov jump system; Step 3: Establishing a data-based stability condition for the Markov jump system by constructing a Lyapunov bilateral loop functional; Step 4: Verifying that the designed data-driven non-uniform sampling data controller can not only smoothly realize control when the system is subjected to noise disturbance, but also save communication resources; Step 5: Demonstrating the effectiveness of the proposed control scheme through flight test data of longitudinal and lateral models.

Description

Technical Field

[0001] The present invention relates to the field of aircraft model control, in particular to a method for designing a data-driven non-uniform sampling controller for an aircraft model with bounded noise that is modeled as a Markov jump system. Background Art

[0002] The evolution of modern control systems has played an important role in the development of civil and military aviation. Modern aircraft are composed of various automatic control systems to assist the crew in navigation, flight management and enhance the stability characteristics of the aircraft. Flight control method design technology mainly adopts linear control theory to linearize the aircraft dynamics and conduct a comprehensive and in-depth analysis of the designed controller under various flight conditions. Markov jump system is a special type of switching system, which is modeled by a set of linear or nonlinear systems, in which Markov chains are used to determine the transition between system modes. Markov jump system not only plays a prominent role in control theory, such as sliding mode control, dissipative control, and fault-tolerant control, but also has a wide range of applications in practical engineering systems, such as communication systems, economic systems, networked control systems, power systems, aircraft engine systems, etc. The present invention models the aircraft model system as a Markov jump system, so as to specifically study the flight stability conditions of the aircraft model. In recent years, with the widespread application of embedded control and network control, non-uniform sampling control systems have gradually received attention. On the one hand, sampled data control has been deeply studied in various practical control systems, such as mass-spring-damper systems, single-link robotic arm systems, satellite control systems, etc. On the other hand, compared with uniform sampling, non-uniform sampling obtains more valuable signals, which helps to reduce the average frequency of sampled data and improve the efficiency of the processor. Therefore, for the aircraft model modeled as a Markov jump system, it is particularly important to study the sampling control of the system. Model-based control is a major research method and plays a huge role in control theory. Since obtaining the system matrix of the model is a thorny problem, data-driven control methods have become a research hotspot, and the control rules are directly obtained from the data without relying on the explicit or implicit information of the mathematical model of the communication process. There are many specific methods to solve data-driven control problems, such as state and output feedback methods (Journal: IEEE Transactions on Automatic Control; Author: Claudio De Persis and Pietro Tesi; Publication Date: 2020; Article Title: Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness; Pages: 909-924), robust control methods (Journal: Information Sciences; Author: Honggui Han, Jiacheng Zhang, Hongyan Yang, Ying Hou and Junfei Qiao; Publication Date: 2022;Article title: Data-driven robust optimal control for nonlinear system with uncertain disturbances; Pages: 248-264), stochastic optimal control method (Journal: IEEE Transactions on Neural Networks and Learning Systems; Authors: Guoliang Chen, Jianwei Xia, Ju H. Park, Hao Shen and Guangming Zhuang; Publication date: 2021; Article title: Sampled-Data Synchronization of Stochastic Markovian Jump Neural Networks With Time-Varying Delay; Pages: 3829-3841), model predictive control method (Journal: IEEE Transactions on Automatic Control; Authors: Wenjie Liu, Jian Sun, Gang Wang, Francesco Bullo and Jie Chen; Publication date: 2022; Article title: Data-Driven Resilient Predictive Control Under Denial-of-Service; Pages: 1-16) and sliding mode control method (Journal: IEEE Transactions on Aerospace and Electronic Systems; Author: EM Jafarov and R. Tasaltin; Publication Date: 2000; Article Title: Robust sliding-mode control for the uncertain MIMO aircraft model F-18; Pages: 1127-1141). In summary, based on the mathematical model of the aircraft modeled as a Markov jump system, the present invention considers the core problem of how to design a data-driven non-uniform sampling controller so that the system can achieve stability while saving communication resources and improving robustness under bounded noise. ; Summary of the invention

[0003] The purpose of the present invention is to propose a data-driven non-uniform sampling controller design method for an aircraft model with bounded noise in response to the hot issues in existing research. First, this method models the aircraft model into a more practical system based on the aircraft model while considering bounded noise. Secondly, with the help of data-driven methods and the stability theory in the sense of Lyapunov, using the free weight matrix method, the scaling method of integral inequalities and the dual-loop functional technology, a data-driven non-uniform sampling controller is designed for the system under consideration, so that when subjected to bounded noise, the system can achieve stability while saving communication resources and improving the core problem of robustness. Not only can the control be smoothly achieved when the system is subjected to bounded noise, but also communication resources can be saved and the communication burden can be reduced.

[0004] The present invention provides a data-driven non-uniform sampling controller design method based on an aircraft model with bounded noise, comprising the following steps:

[0005] (a) Establish a state space model of the aircraft system; use Newton's second law of motion to establish a nonlinear model of the aircraft model, where the translational motion equation is:

[0006]

[0007]

[0008]

[0009] The rotational motion equation is:

[0010]

[0011]

[0012]

[0013] When the aircraft flies horizontally and straight, these six equations are decomposed into three longitudinal equations and three lateral equations. First, consider the longitudinal motion equation of the aircraft model. For this system, only the interference of X, Z and M is considered. Since V = P = R = Φ = 0, the remaining equations are simplified, and the longitudinal motion equation of the aircraft model is obtained as follows:

[0014]

[0015]

[0016]

[0017] Assuming the aircraft is in equilibrium, the total external forces and moments are written as the sum of their equilibrium values ​​and perturbation values: U = U0 + u, Z = Z0 + dZ, W = W0 + w, X = X0 + dX, Θ = Θ0 + θ, M = M0 + dM, Q = Q0 + q, where W0 = 0, Q0 = 0, M0 = 0, then we have:

[0018]

[0019]

[0020]

[0021] Therefore, the longitudinal linear equation of the aircraft model is simplified to:

[0022]

[0023] in,

[0024] In addition, only disturbances Y, L and N are considered. Therefore, the three equations of the lateral motion equation are:

[0025]

[0026]

[0027]

[0028] Assuming that the aircraft is in a straight horizontal equilibrium state, the total bus speed and angular velocity, Euler angle, total external force and torque are all expressed as the sum of their equilibrium point and perturbation value: P = P0 + p, R = R0 + r, V = V0 + v, Y = Y0 + dY, L = L0 + dL, N = N0 + dN, Φ = Φ0 + φ, Ψ = Ψ0 + ψ, and the lateral motion equation of the aircraft model is:

[0029]

[0030]

[0031]

[0032] Therefore, the lateral linear equation of the aircraft model is simplified to:

[0033]

[0034] in, Where g is gravity, I X is the inertia of the aircraft about the x-axis, I Y is the inertia of the aircraft about the y-axis, I Z is the inertia of the aircraft about the z-axis, IXZ is the inertia cross product, L is the rolling moment, L β is the derivative of the rolling moment with respect to the sideslip angle, L p is the derivative of the roll moment with respect to the roll angular velocity, L r is the derivative of the rolling moment with respect to the yaw rate, M is the pitching moment, and M α is the derivative of the pitching moment with respect to the angle of attack, M q is the derivative of the pitch moment with respect to the pitch rate, m is the mass, N is the yaw moment, N β is the derivative of the yaw moment with respect to the sideslip angle, N p is the derivative of the yaw moment with respect to the roll angular velocity, N r is the derivative of the yaw moment with respect to the yaw rate, P is the total roll rate, p is the perturbed total roll rate, Q is the total pitch rate, q is the perturbed pitch rate, R is the total yaw rate, r is the perturbed yaw rate, U is the total velocity along the x-axis, u is the perturbed velocity along the x-axis, V is the total velocity along the y-axis, v is the perturbed velocity along the y-axis, W is the total velocity along the z-axis, w is the perturbed velocity along the z-axis, X is the total force along the x-axis, Y is the total force along the y-axis, Y β is the derivative of the force along the y-axis with respect to the sideslip angle, Z is the total force along the z-axis, and Z α is the derivative of the force along the z-axis with respect to the angle of attack, Z q is the derivative of the force along the z-axis with respect to the pitch rate, α is the angle of attack, β is the bank angle, Φ is the roll Euler angle, φ is the perturbation roll Euler angle, Ψ is the yaw Euler angle, is the perturbed yaw Euler angle, θ is the perturbed pitch Euler angle, δ A is the aileron deflection, δ DT is the differential horizontal tail deflection, δ E is the differential horizontal tail deflection, δ PTV is the pitch thrust vector nozzle deflection, δ R is the rudder deflection, δ RTV is the differential pitch moment thrust vectoring nozzle deflection, δ YTV is the yaw thrust vector nozzle deflection T < 0;

[0035] Due to the different speeds and altitudes of the aircraft, the parameters of the system are also different; based on the flight test data, the lateral model and longitudinal model of the aircraft are modeled as Markov jump systems, in which the jumps between different flight speeds and altitudes obey the Markov chain; the aircraft model is expressed as:

[0036]

[0037] in is the state vector, is the input vector, r(t) is a right-continuous Markov chain defined on a complete probability space, in a finite set The transfer rate matrix With the following transition probabilities: Among them, σ>0, If i≠j, χ ij ≥0 is the transition rate from mode i at time t to mode j at time t+σ;

[0038] (b) Set sampling conditions:

[0039] t=t k is the system sampling time and satisfies Control input u(t) = K r(t) x(t k ), t∈[t k ,t k+1 ); sampling period t k+1 -t k =h k ∈[h min ,h max ], where h min represents the lower bound of the sampling data period, h max Indicates the upper bound of the sampling data period;

[0040] (c) Design feedback input to transform the system model into a closed-loop system:

[0041] Define the control input u(t) = K r(t) x(t k ), t∈[t k ,t k+1 ), where K r(t) is a mode-dependent state feedback controller. r(t) , B r(t) and C r(t) Abbreviated as A i , B i and C i Then we get the closed-loop system:

[0042]

[0043] Lemma 1: Let is a differentiable signal. Given a vector Symmetric Matrix The following inequality is obtained:

[0044]

[0045] Lemma 2: (Dual Lemma) Let P be is a non-singular symmetric matrix, let are two complementary subspaces whose sum is equal to Then we have:

[0046] For all There is x T Px<0, for all There is x T Px±0, equivalent to for all There is x T P -1 x>0, for all There is x T P -1 x≤0;

[0047] Definition: There exists a positive definite matrix P i ,H1,H2,symmetric matrix F,and any matrix Design Lyapunov double-sided loop functional to study the stability conditions of Markov jump systems:

[0048]

[0049] in,

[0050] V1(x,t)=x T (t)P i x(t),

[0051] V2(x,t)=2ζ1 T (t)[E1ζ2(t)+E2ζ3(t)],

[0052] V3(x,t)=2[x T (t)-x T (t k )]F[x(t)-x(t k+1 )],

[0053]

[0054]

[0055]

[0056] ζ1 T (t)=[(t k+1 -t)(x T (t)-x T (t k ))(tt k )(x T (t)-x T (t k+1 ))],

[0057]

[0058]

[0059]

[0060]

[0061] Taking the derivative of W(x,t) we get:

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068] in, Π9=ι1-ι2,Π 10 =ι3-ι1,Π 11 =ι1+ι2,Π 12 =ι1+ι3;

[0069] Applying Lemma 1, we can obtain:

[0070]

[0071] Given the free weight matrix Q i , we get the following equation:

[0072]

[0073] Combining the above inequalities and equations, we can get:

[0074]

[0075] in,

[0076]

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084] Using Schur's complement lemma and Lyapunov's theorem, we can get that when the following conditions are met,

[0085]

[0086]

[0087] Then the system reaches asymptotic stability;

[0088] (d) The following assumptions are made to study the model-based data-driven control problem: Assumption 1: The matrix A i and B i It’s all unknown;

[0089] (e) Considering the measured data and the noisy data:

[0090] Based on Assumption 1, the stability and stabilization of the system are studied by considering the measurement data and noise data. l ∈[0,t], assuming a system with perturbations Measurement is feasible, among which is a known full-rank matrix. Assume that the measured data is subject to unknown noise of the destruction, where ∈(t) captures the unknown noise.

[0091] Defining the Matrix X and U are feasible, E∈Γ is unknown and bounded, and the specific form is as follows:

[0092] E:=[(H1) (H2) … (H γ )],

[0093]

[0094] X: = [x(H1)x(H2)…x(H γ )],

[0095] U:=[u(H1)u(H2)…u(H γ )];

[0096] Then we can directly get:

[0097]

[0098] Noise data has the following specific constraints:

[0099]

[0100] in, is known. This noise data constraint is a bounded additive noise modeling form. Define a classic noise, Q d = -I, S d =0, R d =∈ 2 γI, where ∈>0, the above constraints are transformed into:

[0101]

[0102] (f) Definition of (A i B i ) collection:

[0103] According to the measured data and noise data, define i B i ) of the set Σ e :

[0104]

[0105] (g) Given an unknown matrix A based on data i and B i Indicates:

[0106] in,

[0107] (h) Make a statement about the set Σ e Assumptions:

[0108] Assumption 2: Matrix Ξ e is irreversible and has q positive eigenvalues;

[0109] (i) Based on the unknown matrix A i and B i , Formula (4) and Formula (5) are restated as:

[0110]

[0111]

[0112] in,

[0113]

[0114]

[0115] Ψ i =He{R i (-ι4)},

[0116] (j) Using the duality lemma and the full block S-process method:

[0117] Under the condition that Assumption 2 is satisfied, applying Lemma 4 (the duality principle) to Formula (9), we can prove that [A i B i ]∈Σ e If and only if

[0118]

[0119] in,

[0120] Using the full block S-process method, we find that there exists a scalar γ>0 such that

[0121]

[0122]

[0123] Where η1=col{0,ι1,K i ι2},η2=col{I,0,0};

[0124] Using Schur's complement lemma and Lyapunov's theorem, we can get that when the following linear matrix inequality is satisfied:

[0125]

[0126]

[0127] Then the system (2) reaches asymptotic stability, where

[0128] (k) Variable substitution, constructing a new system expression:

[0129] Define a non-singular matrix L, and substitute x(t) = Lν(t) into system (2) to obtain:

[0130]

[0131] in, Since the matrix L is non-singular, system (2) and system (12) have the same stable behavior;

[0132] (l) Replace the original free weight matrix equation (3):

[0133]

[0134] (m) We obtain a new inverted convex inequality:

[0135]

[0136] in,

[0137]

[0138]

[0139]

[0140] (n) Using matrix decomposition technology:

[0141]

[0142]

[0143] in,

[0144]

[0145]

[0146] (o) Using the duality lemma and the full block S-process method:

[0147] Under the condition that Assumption 1 is satisfied, we apply Lemma 4 (the duality principle) to Formula (7) and prove that [A i B i ]∈Σ e If and only if

[0148]

[0149] Using the full block S-process method, we find that there exists a scalar γ>0 such that

[0150]

[0151]

[0152] in,

[0153] Using Schur's complement lemma and Lyapunov's theorem, we can get that when the following linear matrix inequality is satisfied:

[0154]

[0155]

[0156] The system (12) reaches asymptotic stability, where

[0157] This method combines some practical problems and designs a data-driven non-uniform sampling controller for an aircraft model with noise disturbance. Compared with the prior art, the technical solution provided by the present invention has the following beneficial effects:

[0158] (1) The modeled Markov system can simultaneously consider the different flight altitudes of the aircraft model, and the systems at different flight altitudes are modeled as subsystems of the Markov system, and the jumps between the subsystems obey the Markov connection; compared with the existing aircraft modeling as a general linear system controller, the present invention can simultaneously consider multiple flight states, so the control scheme proposed by the present invention can make the aircraft remain stable under different flight states;

[0159] (2) Since non-uniform sampling control can save bandwidth and communication resources, the existing control schemes usually design non-uniform sampling controllers to study the safety performance of the system. However, the existing Lyapunov single-side loop functional cannot fully consider the information within the sampling interval. Compared with the existing design schemes, the present invention constructs a Lyapunov double-side loop functional and considers the sampling interval [t k ,t] and [t,t k+1 ], and there is no strict positive definiteness requirement for the matrix in the ring functional, thereby reducing conservatism, obtaining a larger sampling interval, reducing the number of control signal generation, thereby avoiding the transmission of redundant data, reducing the communication burden, and reducing energy consumption;

[0160] (3) Since the parameter matrix of the system model is difficult to obtain, although the measurement data of the system is accessible, it is a thorny problem to obtain the target model from the first principles. To address this problem, the present invention considers a data-driven control method, in which the control rules are directly obtained from the data without relying on the explicit or implicit information of the mathematical model of the communication process. In addition, disturbance noise usually exists in the actual system, so the present invention considers the data-driven control problem based on noise data. BRIEF DESCRIPTION OF THE DRAWINGS

[0161] Figure 1 The present invention provides the aircraft longitudinal axis model.

[0162] Figure 2 The present invention provides the aircraft transverse axis model.

[0163] Figure 3 The present invention provides the state response and Markov jump mode of the longitudinal axis system.

[0164] Figure 4 The present invention provides the non-uniform sampling control and sampling period of the longitudinal axis system.

[0165] Figure 5The present invention provides the state response and Markov jump mode of the horizontal axis system.

[0166] Figure 6 The present invention provides the non-uniform sampling control and sampling period of the horizontal axis system. DETAILED DESCRIPTION

[0167] The specific implementation of the present invention is described below in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when the detailed description of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

[0168] As shown in the figure, the present invention provides a data-driven non-uniform sampling controller design method based on an aircraft model with bounded noise, comprising the following steps:

[0169] (a) Establish a state space model of the aircraft system; use Newton's second law of motion to establish a nonlinear model of the aircraft model, where the translational motion equation is:

[0170]

[0171]

[0172]

[0173] The rotational motion equation is:

[0174]

[0175]

[0176]

[0177] When the aircraft flies horizontally and straight, these six equations are decomposed into three longitudinal equations and three lateral equations. First, consider the longitudinal motion equation of the aircraft model. For this system, only the interference of X, Z and M is considered. Since V = P = R = Φ = 0, the remaining equations are simplified, and the longitudinal motion equation of the aircraft model is obtained as follows:

[0178]

[0179]

[0180]

[0181] Assuming the aircraft is in equilibrium, the total external forces and moments are written as the sum of their equilibrium values ​​and perturbation values: U = U0 + u, Z = Z0 + dZ, W = W0 + w, X = X0 + dX, Θ = Θ0 + θ, M = M0 + dM, Q = Q0 + q, where W0 = 0, Q0 = 0, M0 = 0, then we have:

[0182]

[0183]

[0184]

[0185] Therefore, the longitudinal linear equation of the aircraft model is simplified to:

[0186]

[0187] in, In addition, only disturbances Y, L and N are considered. Therefore, the three equations of the lateral motion equation are:

[0188]

[0189]

[0190]

[0191] Assuming that the aircraft is in a straight horizontal equilibrium state, the total bus speed and angular velocity, Euler angle, total external force and torque are all expressed as the sum of their equilibrium point and perturbation value: P = P0 + p, R = R0 + r, V = V0 + v, Y = Y0 + dY, L = L0 + dL, N = N0 + dN, Φ = Φ0 + φ, Ψ = Ψ0 + ψ, and the lateral motion equation of the aircraft model is:

[0192]

[0193]

[0194]

[0195] Therefore, the lateral linear equation of the aircraft model is simplified to:

[0196]

[0197] in, Where g is gravity, I X is the inertia of the aircraft about the x-axis, I Y is the inertia of the aircraft about the y-axis, I Z is the inertia of the aircraft about the z-axis, I XZ is the inertia cross product, L is the rolling moment, Lβ is the derivative of the rolling moment with respect to the sideslip angle, L p is the derivative of the roll moment with respect to the roll angular velocity, L r is the derivative of the rolling moment with respect to the yaw rate, M is the pitching moment, and M α is the derivative of the pitching moment with respect to the angle of attack, M q is the derivative of the pitch moment with respect to the pitch rate, m is the mass, N is the yaw moment, N β is the derivative of the yaw moment with respect to the sideslip angle, N p is the derivative of the yaw moment with respect to the roll angular velocity, N r is the derivative of the yaw moment with respect to the yaw rate, P is the total roll rate, p is the perturbed total roll rate, Q is the total pitch rate, q is the perturbed pitch rate, R is the total yaw rate, r is the perturbed yaw rate, U is the total velocity along the x-axis, u is the perturbed velocity along the x-axis, V is the total velocity along the y-axis, v is the perturbed velocity along the y-axis, W is the total velocity along the z-axis, w is the perturbed velocity along the z-axis, X is the total force along the x-axis, Y is the total force along the y-axis, Y β is the derivative of the force along the y-axis with respect to the sideslip angle, Z is the total force along the z-axis, and Z α is the derivative of the force along the z-axis with respect to the angle of attack, Z q is the derivative of the force along the z-axis with respect to the pitch rate, α is the angle of attack, β is the bank angle, Φ is the roll Euler angle, φ is the perturbation roll Euler angle, Ψ is the yaw Euler angle, is the perturbed yaw Euler angle, θ is the perturbed pitch Euler angle, δ A is the aileron deflection, δ DT is the differential horizontal tail deflection, δ E is the differential horizontal tail deflection, δ PTV is the pitch thrust vector nozzle deflection, δ R is the rudder deflection, δ RTV is the differential pitch moment thrust vectoring nozzle deflection, δ YTV is the yaw thrust vector nozzle deflection T < 0;

[0198] Due to the different speeds and altitudes of the aircraft, the parameters of the system are also different. Based on the flight test data, the lateral model and longitudinal model of the aircraft are modeled as Markov jump systems, in which the jumps between different flight speeds and altitudes obey the Markov chain. The aircraft model is expressed as:

[0199]

[0200] in is the state vector, is the input vector, r(t) is a right-continuous Markov chain defined on a complete probability space, in a finite set The value in the transfer rate matrix With the following transition probabilities: Among them, σ>0, If i≠j, χ ij ≥0 is the transition rate from mode i at time t to mode j at time t+σ;

[0201] (b) Set sampling conditions:

[0202] t=t k is the system sampling time and satisfies Control input u(t) = K r(t) x(t k ), t∈[t k ,t k+1 ); sampling period t k+1 -t k =h k ∈[h min ,h max ], where h min represents the lower bound of the sampling data period, h max Indicates the upper bound of the sampling data period;

[0203] (c) Design feedback input to transform the system model into a closed-loop system:

[0204] Define the control input u(t) = K r(t) x(t k ), t∈[t k ,t k+1 ), where K r(t) is a mode-dependent state feedback controller. r(t) , B r(t) and C r(t) Abbreviated as A i , B i and C i Then we get a closed-loop system

[0205]

[0206] (d) The following assumptions are made to study the model-based data-driven control problem:

[0207] Assumption 1: Matrix A i and B i It’s all unknown;

[0208] (e) Considering the measured data and the noisy data:

[0209] Based on Assumption 1, the stability and stabilization of the system are studied by considering the measurement data and noise data. l ∈[0,t], assuming a system with perturbations Measurement is feasible, among which is a known full-rank matrix. Assume that the measured data is subject to unknown noise of the destruction, where ∈(t) captures the unknown noise.

[0210] Defining the Matrix X and U are feasible, E∈Γ is unknown and bounded, and the specific form is as follows:

[0211] E:=[(H1) (H2) … (H γ )],

[0212]

[0213] X: = [x(H1)x(H2)…x(H γ )],

[0214] U:=[u(H1)u(H2)…u(H γ )],

[0215] Then we can directly get:

[0216]

[0217] Noise data has the following specific constraints:

[0218]

[0219] in, is known. This noise data constraint is a bounded additive noise modeling form. Define a classic noise, Q d = -I, S d =0, R d =∈ 2 γI, where ∈>0, the above constraints are transformed into:

[0220]

[0221] (f) Definition of (A i B i ) collection:

[0222] According to the measured data and noise data, define i B i ) of the set Σ e :

[0223]

[0224] (g) Given an unknown matrix A based on data i and B i Indicates:

[0225]

[0226] in,

[0227] (h) Make a statement about the set Σ e Assumptions:

[0228] Assumption 2: Matrix Ξ e is irreversible and has q positive eigenvalues;

[0229] The above description is only a preferred feasible embodiment of the present invention, and does not limit the scope of rights of the present invention. All equivalent structural changes made using the contents of the present invention description and drawings are included in the scope of rights of the present invention.

[0230] In this embodiment, the system parameters shown in Table 1 and the design parameters given during simulation are set:

[0231] Table 1: System parameters and design parameters

[0232]

[0233]

[0234]

[0235] The minimum sampling period of the system is defined as h min =0.00001, in the designed aircraft longitudinal axis model, aircraft transverse axis model, the state response and Markov jump mode of the longitudinal axis system, the non-uniform sampling control and sampling period of the longitudinal axis system, the state response and Markov jump mode of the transverse axis system, the non-uniform sampling control and sampling period of the transverse axis system are respectively as follows: Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 and Figure 6 As shown. Figure 3 , Figure 4 , Figure 5 and Figure 6 It can be seen that the designed controller can stabilize the longitudinal axis aircraft system and the lateral axis aircraft system, and realize non-uniform sampling control, which shows that the proposed control design scheme can save communication resources and reduce the communication burden.

[0236] The technical means disclosed in the scheme of the present invention are not limited to the technical means disclosed in the above-mentioned implementation mode, but also include technical schemes composed of any combination of the above-mentioned technical features. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications are also regarded as the protection scope of the present invention.

Claims

1. A data-driven non-uniform sampling controller design method based on an aircraft model, characterized in that: The following steps are involved: (a) Establish a state space model of the aircraft system; use Newton's second law of motion to establish a nonlinear model of the aircraft model, where the translational motion equation is: The rotational motion equation is: When the aircraft flies in a straight and horizontal direction, the six equations are decomposed into three longitudinal equations and three lateral equations. First, the longitudinal motion equation of the aircraft model is considered. For this system, only the interference of X, Z and M is considered. Since V = P = R = Φ = 0, the remaining equations are simplified, and the longitudinal motion equation of the aircraft model is obtained as follows: Assuming the aircraft is in equilibrium, the total external forces and moments are written as the sum of their equilibrium values ​​and perturbation values: U=U0+u,Z=Z0+dZ,W=W0+w,X=X0+dX,Θ=Θ0+θ,M=M0+dM,Q=Q0+q,assuming W0=0,Q0=0,M0=0,then we get: Therefore, the longitudinal linear equation of the aircraft model is simplified to: in, In addition, only disturbances Y, L and N are considered; therefore, the three equations of the lateral motion equation are: Assuming that the aircraft is in a straight horizontal equilibrium state, the total bus speed and angular velocity, Euler angle, total external force and torque are all expressed as the sum of their equilibrium point and perturbation value: P = P0 + p, R = R0 + r, V = V0 + v, Y = Y0 + dY, L = L0 + dL, N = N0 + dN, Φ = Φ0 + φ, Ψ = Ψ0 + ψ, and the lateral motion equation of the aircraft model is: Therefore, the lateral linear equation of the aircraft model is simplified to: in, Where g is gravity, I X is the inertia of the aircraft about the x-axis, I Y is the inertia of the aircraft about the y-axis, I Z is the inertia of the aircraft about the z-axis, I XZ is the inertia cross product, L is the rolling moment, L β is the derivative of the rolling moment with respect to the sideslip angle, L p is the derivative of the roll moment with respect to the roll angular velocity, L r is the derivative of the rolling moment with respect to the yaw rate, M is the pitching moment, and M α is the derivative of the pitching moment with respect to the angle of attack, M q is the derivative of the pitch moment with respect to the pitch rate, m is the mass, N is the yaw moment, N β is the derivative of the yaw moment with respect to the sideslip angle, N p is the derivative of the yaw moment with respect to the roll angular velocity, N r is the derivative of the yaw moment with respect to the yaw rate, P is the total roll rate, p is the perturbed total roll rate, Q is the total pitch rate, q is the perturbed pitch rate, R is the total yaw rate, r is the perturbed yaw rate, U is the total velocity along the x-axis, u is the perturbed velocity along the x-axis, V is the total velocity along the y-axis, v is the perturbed velocity along the y-axis, W is the total velocity along the z-axis, w is the perturbed velocity along the z-axis, X is the total force along the x-axis, Y is the total force along the y-axis, Y β is the derivative of the force along the y-axis with respect to the sideslip angle, Z is the total force along the z-axis, and Z α is the derivative of the force along the z-axis with respect to the angle of attack, Z q is the derivative of the force along the z-axis with respect to the pitch rate, α is the angle of attack, β is the bank angle, Φ is the roll Euler angle, φ is the perturbation roll Euler angle, Ψ is the yaw Euler angle, is the perturbed yaw Euler angle, θ is the perturbed pitch Euler angle, δ A is the aileron deflection, δ DT is the differential horizontal tail deflection, δ E is the differential horizontal tail deflection, δ PTV is the pitch thrust vector nozzle deflection, δ R is the rudder deflection, δ RTV is the differential pitch moment thrust vectoring nozzle deflection, δ YTV is the yaw thrust vector nozzle deflection T < 0; Due to the different speeds and altitudes of the aircraft, the parameters of the system are also different; based on the flight test data, the lateral model and longitudinal model of the aircraft are modeled as Markov jump systems, where the jumps between different flight speeds and altitudes obey the Markov chain, and the aircraft model is expressed as: in is the state vector, is the input vector, r(t) is a right-continuous Markov chain defined on a complete probability space, in a finite set The value in the transfer rate matrix With the following transition probabilities: Among them, σ>0, If i≠j, χ ij ≥0 is the transition rate from mode i at time t to mode j at time t+σ; (b) Set sampling conditions: t=t k is the system sampling time and satisfies Control input u(t) = K r(t) x(t k ), t∈[t k ,t k+1 ); sampling period t k+1 -t k =h k ∈[h min ,h max ], where h min represents the lower bound of the sampling data period, h max Indicates the upper bound of the sampling data period; (c) Design feedback input to transform the system model into a closed-loop system: Define the control input u(t) = K r(t) x(t k ), t∈[t k ,t k+1 ), where K r(t) is a mode-dependent state feedback controller; A r(t) , B r(t) and C r(t) Abbreviated as A i , B i and C i Then we get a closed-loop system (d) The following assumptions are made to study the model-based data-driven control problem: Assumption 1: Matrix A i and B i It’s all unknown; (e) Considering the measured data and the noisy data: Based on Assumption 1, the stability and stabilization of the system are studied by considering the measurement data and noise data; at the discrete time H l ∈[0,t], assuming a system with perturbations Measurement is feasible, among which is a known column-full rank matrix; assuming that the measured data is subject to unknown noise The destruction of , where ∈(t) captures the unknown noise; Defining the Matrix X and U are feasible, E∈Γ is unknown and bounded, and the specific form is as follows: E:=[∈(H1)∈(H2)…∈(H γ )], X:=[x(H1)x(H2)…x(H γ )], U:=[u(H1)u(H2)…u(H γ )], Then we can get directly: Noise data has the following specific constraints: in, is known; the noise data constraint is a bounded additive noise modeling form; define a classic noise, Q d = -I, S d =0, R d =∈ 2 γI, where ∈>0, the above constraints are transformed into: (f) Definition of (A i B i ) collection: According to the measured data and noise data, define i B i ) of the set Σ e : (g) Given an unknown matrix A based on data i and B i Indicates: in, (h) Make a statement about the set Σ e Assumptions: Assumption 2: Matrix Ξ e is irreversible and has q positive eigenvalues; (i) Define the sampling controller expression condition for the aircraft system to achieve asymptotic stability: there exists a positive definite matrix P i ,H1,H2,symmetric matrix F,and arbitrary matrices E1,E2,G,Y 1i , Y 2i , Z 1i ,Z 2i ,Q i ,h k ∈{h min ,h max }, And the following linear matrix inequality is satisfied: in, Through the above steps, a sampling controller is obtained which enables the aircraft system to achieve asymptotic stability.

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