Aircraft system dynamic quantization anti-interference control method based on feedforward compensation

Abstract

The invention discloses an aircraft system dynamic quantization anti-interference control method based on feedforward compensation. According to the method, a Markov model of an aircraft system is established, a modal-dependent disturbance observer is constructed to estimate matching disturbance, a modal-dependent controller is designed to ensure random and bounded stability of the system, a dynamic uniform quantizer is introduced to effectively reduce network communication burden, a general transfer rate of a Markov jump system is processed in combination with a Young inequality and a Lyapunov stability theory, and the stability of the Markov jump system is improved. And obtaining a stable linear matrix inequality condition of the closed-loop system.

Description

Technical Field

[0001] The present invention relates to a dynamic quantized anti-interference control method for an aircraft system based on feedforward compensation, and in particular to a dynamic quantized anti-interference control method for an aircraft system based on Markov jump system theory. Background Art

[0002] Many real-world systems exhibit random jumps in their structures and parameters. These random mutations often arise from random failures and repairs of system components, changes in internal interconnected systems, sudden environmental fluctuations, and changes in the operating point range of nonlinear systems after linearization. Markov systems are subject to the influence of factors such as errors, environmental conditions, measurement costs, and external interference, making it difficult to accurately and completely determine the transition rate. Using the theory of Markov jump systems, a more accurate model of Markov systems can be established. Markov jump systems are crucial for Markov systems. A Markov jump system is an uncertain random process. Its physical meaning is a statistical distribution that describes the behavior of variables in the system under given conditions, and this statistical distribution exhibits Markov properties. Markov jump systems have three characteristics: first, the transition probabilities describing the system state are random processes; second, the random variables in a Markov jump system are state variables; and third, each random variable in a Markov jump system has a transition probability.

[0003] In addition, as a dynamic system, the energy source and consumption process of the aircraft system exist simultaneously in the Markov network. During the operation of the Markov system, factors such as changes in the network topology, repair of component failures, changes in operating parameters, and external interference will cause random jumps in aircraft parameters. The Markov jump system is particularly important. The power system is modeled using the Markov chain, and the random jump process of aircraft parameters is converted into a random process of the Markov chain using the state transition probability matrix. Then, the stability margin of the aircraft system is studied, and the aircraft system can be optimized and scheduled based on the calculation results.

[0004] However, the above research works mainly focus on estimating specific types of jumps, which leads to poor control effects for more general cases. In addition, the above research works mainly focus on the control of dynamic quantized outputs. Summary of the Invention

[0005] The purpose of the present invention is to propose a dynamic quantitative anti-interference control method for an aircraft system based on feedforward compensation, which can effectively improve the performance of the aircraft system and enable the output of the aircraft system to be accurately measured.

[0006] The specific technical solution of the present invention is as follows: A dynamic quantitative anti-interference control method for an aircraft system based on feedforward compensation comprises the following steps:

[0007] Based on the Markov jump system theory, the Markov model of the aircraft system is established to obtain the augmented form of the original system;

[0008] Based on the Markov jump system theory, the following aircraft model is established:

[0009] Among them, the value range of θ(t) is -4, -5, -6,

[0010] Where, represents the system state, α(t) represents the aircraft angle of attack, β(t) represents the aircraft pitch rate, represents the deflection angle of the aircraft elevator, u(t) represents the voltage input, d1(t) represents the external matching disturbance, and d2(t) represents the external mismatching disturbance. A(s(t)), B(s(t)), D(s(t)), F(s(t)) are known system matrices of appropriate dimensions. To simplify the representation, let A i =A(s(t)),B i =B(s(t)),D i =D(s(t)),F i =F(s(t)), S i =S(s(t)),M i =M(s(t)),G i = G(s(t)) Other matrices are abbreviated in the same way. s(t) is a right continuous Markov process and is from a finite set s(t) has the following properties:

[0011]

[0012] Where, dt>0, π ij is the transfer rate from mode i to mode j, and satisfies:

[0013] The general transfer rate matrix of the Markov jump system can be expressed as

[0014] where π ij is the known part of the transfer rate, ? represents the unknown transfer rate, Δ ij (Δ ij ∈[-δij , δ ij ]) represents the uncertain part, which has the same ij The same properties, where δ ij is known. Then, for the sake of simplicity, let and Contains all possible cases (known, unknown and uncertain) of the transition rate in row i. Therefore, the elements in the transition rate matrix are divided into the following three categories:

[0015] Known and uncertain metastasis rates were categorized as Completely unknown situation as follows:

[0016] The quantizer is shown below:

[0017]

[0018] and

[0019] Where μ(t) is the quantization function, v and k are known constants, is the known mean value of the quantization parameter, T * Switch intervals for known quantization parameters;

[0020] For a dynamic quantizer, the quantization error e q (t) can be expressed as |e q (t)|≤0.5μ(t),t∈[t0,+∞)

[0021] where the function |·| represents the absolute value;

[0022] Quantization error is also q (t) can be expressed as

[0023]

[0024] The disturbance d1(t) representing constant noise and harmonic noise can be expressed by the following expanded system

[0025] Among them, M i , S i and G i is a known matrix. d3(t) is the disturbance caused by the perturbations and uncertainties in the extended system; The disturbance observer is designed as

[0026] In addition, the controller u(t) is K i and L i are the controller gain and observer gain, respectively, where is the estimate of d1(t), the estimation error therefore,

[0027] The following closed-loop system is obtained

[0028] In addition, the regulated output z(t) is chosen to be: z(t)=C ri x(t)+D ri e ω (t)

[0029] This control scheme can ensure that the above closed-loop system is uniformly bounded and stable. The proof process is as follows:

[0030] C001: Select the Lyapunov function as:

[0031] Among them, P 1i and P 2i are all positive definite matrices, λ is a known constant, U is a known system matrix of appropriate dimension, and the function ||·||2 represents the 2-norm;

[0032] C002: Taking the derivative of V(t) we get

[0033] The function He(A) represents A+A T ;

[0034] C003: H ∞ performance Substituting into C002, we get C004: Select C003 can be written as ψ T (t)[∑] 5×5 ψ(t)≤0

[0035] in

[0036] C005: Next, consider the following congruence transformation: P 1i B i =B i Wi , Q i =W i K i ,

[0037] C006 It should be noted that P 1i B i =B i W i It is not an inequality and therefore cannot be solved directly by the MATLAB LMI toolbox. To solve this problem, the following constraint trajectory is used instead of the formula P 1i B i =B i W 1i :[(B i W i -P 1i B i ) T (B i W i -P 1i B i )]≤εI

[0038] C007: where ε is a scalar and satisfies ε>0. Then, by using Shur complement, C006 can be converted to

[0039] C006: Substitute C005 into C004: we can get

[0040] C007: Next, we can distinguish two cases based on the known and unknown values of the diagonal elements of the transfer rate:

[0041] C008: In the first case, the diagonal elements are known. In this case, in order to minimize the impact of unknown transfer rates, Substituting the known transfer rates, we get:

[0042] C009: It is worth noting that P l and There is a coupling relationship between them. In order to eliminate this coupling, the following transformation is given:

[0043] C010: can be obtained

[0044] Where T ij and T ii All are unknown matrices;

[0045] C011: The second case, due to You can get:

[0046] C012: Pass get:

[0047] C013: Substituting C010 and C012 into C004, we get Ξ≤0

[0048] in BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 is a flow chart of a controller according to an embodiment of the present invention;

[0050] Figure 2 Controller and controller quantitative response diagram of the method proposed by the present invention are used as an example;

[0051] Figure 3 This is a state response curve of the embodiment using the method proposed by the present invention;

[0052] Figure 4 1 is an interference estimation curve of the embodiment using the method proposed in the present invention; DETAILED DESCRIPTION

[0053] The present invention is further illustrated below with reference to specific examples. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, modifications of various equivalent forms of the present invention made by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0054] like Figure 1 As shown, a dynamic quantitative anti-interference control method for an aircraft system based on feedforward compensation includes the following steps:

[0055] Step 1: Set the initial values of various parameters;

[0056] Step 2: Calculate the derivative of the selected Lyapunov function.

[0057] Step 3: Design a dynamic quantizer to save communication resources;

[0058] Step 4: Design a disturbance observer to observe the matching interference; use H ∞ performance, suppressing mismatch interference;

[0059] Step 5: Use Young's inequality to deal with the unknown transfer rate in the Markov jump system.

[0060] Step 6: Solve the linear matrix inequality processed in the above steps to obtain the controller gain and observer gain that can maintain the stability of the system, and obtain the sufficient conditions for the system's random bounded stability;

[0061] Step 7: An embodiment of the present invention is described below:

[0062] Consider an aircraft system in reference [1], whose corresponding dynamic model is:

[0063]

[0064]

[0065] Among them, θ(t) is -4, -5, and -6, which represent modes 1, 2, and 3 respectively.

[0066]

[0067] Select x(0) = [1 -1 -2] T , f1(t, x(t)) = f2(t, x(t)) = x2(t)sin(t), and the value of d1(t) is

[0068] Figure 1 is a schematic diagram of the system of the present invention; applying the proposed method, the control signal and the quantized control signal are as follows Figure 2 As shown; the system status signal is as follows Figure 3 The estimated value of interference is shown as Figure 4 As shown in the figure, it can be seen that the proposed dynamic quantitative anti-interference control method based on Markov jump theory effectively maintains the stability of the system, and the designed controller and observer effectively offset the problems caused by matching interference.

[0069] References

[0070] [1]Wang Z, Liu Y, Liu

[0071] [2]Yong K,Chen M,Wu Q.Anti-disturbance control for nonlinear systemsbased on interval observer[J].IEEE Transactions on Industrial Electronics,2019,67(2):1261-1269。

Claims

1. A dynamic quantitative anti-interference control method for an aircraft system based on feedforward compensation, characterized in that: The following steps are involved: Establish a Markov model of the aircraft system as follows: Among them, θ(t) is the uncertain modal parameter, and its value range is -4, -5, and -6. Where, represents the system state, ɑ(t) represents the aircraft angle of attack, β(t) represents the aircraft pitch rate, represents the deflection angle of the aircraft elevator, u(t) represents the voltage input, d1(t) represents the external matching disturbance, and d2(t) represents the external mismatching disturbance. A(s(t)), B(s(t)), D(s(t)), F(s(t)) are known system matrices of appropriate dimensions; to simplify the representation, let A i =A(s(t)),B i =B(s(t)),D i =D(s(t)),F i =F(s(t)), S i =S(s(t)),M i =M(s(t)),G i = G(s(t)), the other matrices are abbreviated in the same way; s(t) is a right continuous Markov process and is from a finite set The value is taken from the middle; it has the following properties: Where, dt>0, π ij is the transfer rate from mode i to mode j, and satisfies: The general transfer rate matrix of the Markov jump system can be expressed as where π ij is the known part of the transfer rate, ? represents the unknown transfer rate, Δ ij (Δ ij ∈[-δ ij , δ ij ]) represents the uncertain part, which has the same ij The same properties, where δ ij It is known that, then, for the sake of simplicity, let and Contains all possible cases (known, unknown, and uncertain) of the transition rate in row i; therefore, the elements in the transition rate matrix are divided into the following three categories: Known and uncertain metastasis rates were categorized as Completely unknown situation as follows: Using a dynamic quantizer, the quantization parameters can be adjusted online and discretely to ensure appropriate quantization error while ensuring system stability, thereby reducing system load. The specific steps are as follows: The mathematical function round(·) is used to map the input to the nearest integer, also known as the quantization function. The quantizer is shown below and Where μ(t) is the quantization function, v and k are known constants, is the known mean value of the quantization parameter, T * Switch intervals for known quantization parameters; For dynamic quantizers, the quantization error e q (t) can be expressed as |e q (t)|≤0.5μ(t), t∈[t0,+∞), where the function |·| represents the absolute value; Quantization error is also q (t) is expressed as Design a controller based on feedforward compensation to offset the impact of unknown disturbances. The specific steps are as follows: The disturbance d1(t) representing constant noise and harmonic noise can be expressed by the following expanded system Among them, M i , S i and G i is a known matrix. d3(t) is the disturbance caused by the perturbations and uncertainties in the extended system; The disturbance reconstruction unit is designed as Therefore, a controller u(t) based on feedforward compensation is designed as K i and L i are the controller gain and observer gain, respectively, where is the estimate of d1(t), the estimation error therefore, The following closed-loop system is obtained In addition, the regulated output z(t) is chosen to be: z(t)=C ri x(t)+D ri e ω (t) This control scheme can ensure that the above closed-loop system is uniformly bounded and stable. The proof process is as follows: B001: Select the Lyapunov function as: Among them, P 1i and P 2i are all positive definite matrices, λ is a known constant, U is a known system matrix of appropriate dimension, and the function ||·||2 represents the 2-norm; B002: Taking the derivative of V(t) we get Where He(A) represents A+A T abbreviation of ; B003: H ∞ performance Substituting into B002, we get B004: Selection B003 can be written as ψ T (t)[∑] 5×5 ψ(t)≤0 in B005: Next, consider the following congruence transformation: P 1i B i =B i W i ,Q i =W i K i , B006 It should be noted that P 1i B i =B i W i It is not an inequality and therefore cannot be solved directly by the MATLAB LMI toolbox. To solve this problem, the following constraint trajectory is used instead of the formula P 1i B i =B i W 1i ; [(B i W i -P 1i B i ) T (B i W i -P 1i B i )]≤εI B007: where ε is a scalar and satisfies ε>0. Then, by using Shur complement, B006 can be converted to B006: Substitute B005 into B004: we can get B007: Next, we can distinguish two cases based on the known and unknown values of the diagonal elements of the transfer rate: B008: In the first case, the diagonal elements are known. In this case, in order to minimize the impact of unknown transfer rates, Substituting the known transfer rates, we get: B009: It is worth noting that P l and There is a coupling relationship between them. In order to eliminate this coupling, the following transformation is given: B010: can be obtained Where T ij and T ii All are unknown matrices; B011: The second case, due to You can get: B012: Pass get: B013: Substituting B010 and B012 into B004, we get Ξ≤0 in X 23 =P 2i L i F i ,X 24 =P 2i L i D i ,X 25 =P 2i S i ,X 26 =0,

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