A proportional control method for the thermoacoustic instability boundary of a Rijke tube

Abstract

The present invention designs a Rijke tube thermoacoustic instability boundary proportional control method; establishes a Rijke tube PDE model of a cascade of heat release model and gas dynamic equation; proposes boundary proportional control using the upper end pressure and lower end sound velocity of the Rijke tube as outputs to make the thermoacoustic unstable system exponentially stable; compared with the backstepping control method, it selects a feedback quantity that is easier to measure rather than full-state measurement, and chooses proportional control that is easy to implement, which brings convenience to practical application; theoretically, it strictly provides sufficient conditions to ensure the exponential stability of the system, and converts the conditions into sufficient and necessary conditions that are easier to solve; for the boundary feedback control parameter optimization problem when the system exponential stability decays fastest, the above conditions are converted into a nonlinear programming problem for solution, and the optimal design scheme of the control parameters is provided. The boundary proportional control method for the thermoacoustic instability phenomenon in the combustion chamber proposed by the present invention is feasible and effective, and can meet the requirements of suppressing the thermoacoustic instability phenomenon.

Description

Technical Field

[0001] The invention belongs to the field of automatic control, and in particular relates to a Rijke tube thermoacoustic instability boundary proportional control method. Background Art

[0002] Thermoacoustic instability has always been a thorny problem faced by gas turbines, aircraft engines, and rocket engines. Severe thermoacoustic instability can cause fatal damage to the combustion chamber structure. The Rijke tube, as a typical thermoacoustic instability experimental device, has promoted the study of thermoacoustic instability phenomena. So far, the control of thermoacoustic instability in the Rijke tube is mainly divided into passive control and active control. Passive control mainly suppresses thermoacoustic oscillations by changing the combustion chamber structure or adding acoustic dampers (such as Helmholtz resonators) to increase acoustic losses. Active control, on the other hand, suppresses thermoacoustic oscillations through the action of a controller without changing the combustion chamber structure.

[0003] Existing research on the control of thermoacoustic instabilities has employed partial differential equations (PDEs) based on practical conditions, often simplifying them into ordinary differential equations (ODEs). However, PDE models are a more effective approximation of the system in physical dynamics. However, research on active control of thermoacoustic unstable systems based on PDE models has primarily relied on backstepping control, which requires measuring all state information within the combustion chamber. This incurs high measurement costs and presents significant challenges in observing the state. Summary of the Invention

[0004] In view of the deficiencies of the prior art, the present invention designs a Rijke tube thermoacoustic instability boundary proportional control method.

[0005] A method for controlling the thermoacoustic instability boundary ratio of a Rijke tube comprises the following steps:

[0006] Step 1: For the Rijke tube, a typical device for revealing thermoacoustic instability, a mathematical model describing velocity and pressure fluctuations using partial differential equations is established based on the conservation of mass, momentum, and energy of the gas inside the tube.

[0007] Step 1.1: First, express the Rijke tube thermoacoustic instability system model as a cascade of partial differential equations and the Heckl heat release model, as shown below:

[0008]

[0009]

[0010]

[0011] Among them, L wis the length of the resistance wire of the heat source, d w is the diameter of the resistance wire of the heat source, T w is the temperature of the resistance wire of the heat source, T is the gas temperature, A is the cross-sectional area of the tube, k is the thermal conductivity of the air, c v is the constant pressure specific heat capacity, p(t,x) represents the dimensionless gas pressure, v(t,x) represents the dimensionless gas velocity, t∈[0,+∞) represents the dimensionless time, x∈[0,1] is any position in the dimensionless tube, x f is the position of the heat source in the tube, Indicates the nominal value of pressure, i.e. steady state; γ represents the adiabatic constant;

[0012] Step 1.2: After Riemann transformation of the Rijke tube system model, we can get:

[0013]

[0014]

[0015] The Riemann transformation decouples the velocity fluctuation v(t,x) and pressure fluctuation p(t,x) in the above cascade system;

[0016] Next, by processing the α function, the new state variables of the system are defined by the following formula:

[0017] α1(t,x)=R1(t,x),x∈[0,x f ]

[0018] α2(t,x)=R2(t,x),x∈[0,x f ]

[0019] α3(t,x)=R1(t,x),x∈[x f ,1]

[0020] α4(t,x)=R2(t,x),x∈[x f ,1]

[0021] And define:

[0022]

[0023] Therefore, the system of the above differential equations cascaded with the Heckl heat release model is converted into the following partial differential system:

[0024]

[0025]

[0026]

[0027]

[0028] And its boundary conditions are:

[0029] α1(t,0)=-α2(t,0)+2U(t)

[0030] α2(t,1)=c2α1(t,1)+(1-c2)α4(t,1)

[0031] α3(t,1)=(1+c2)α1(t,1)-c2α4(t,1)

[0032] α4(t,0)=wα3(t,0)

[0033] in, It is convenient to simplify the writing of the system. Z L >0 is constant acoustic impedance;

[0034] Step 2: Design a boundary proportional controller based on the partial differential mathematical model obtained in step 1;

[0035] The sound pressure at the upper end and the sound velocity at the lower end of the Rijke tube, which are easy to measure, are selected as feedback variables. The proportional control structure, which is the easiest to implement in practice, is adopted. A control method imposed on boundary conditions is given to stabilize the entire system.

[0036] The actual sound pressure at the end of the Rijke tube before dimensionless processing:

[0037]

[0038] in, is the steady-state speed of sound, is the Mach number, and the actual sound velocity at the lower end of the Rijke tube before dimensionless processing is:

[0039]

[0040] in, Indicates the nominal value of pressure, i.e. steady state;

[0041] The proportional control structure of the controller is:

[0042]

[0043] Where k1 and k2 are the controller parameters to be designed;

[0044] Step 3: Design and optimize the parameters of the boundary proportional controller designed in step 2;

[0045] Taking the convergence rate as the objective function and the stability of the partial differential system equation as the constraint function, the optimization problem is described as a nonlinear programming model; a design method for the controller is given through inequality conditions, and the optimal parameters of the controller are determined by solving the nonlinear programming problem.

[0046] Step 3.1: Design the optimal controller parameters for the boundary proportional controller.

[0047] Step 3.1.1: Taking the system stability as the constraint condition, where the stability condition of the system is:

[0048]

[0049] M1ζ(t, 0)+M2ζ(t, 1) = 0

[0050] where Λ is the coefficient of the partial differential equation of the velocity and pressure fluctuations in the Rijke tube; M1 and M2 are the boundary condition coefficients of the partial differential equation of the velocity and pressure fluctuations.

[0051] Step 3.1.2: Since the stability condition of the system is too complex, the stability condition is processed twice to make it more conducive to solving.

[0052] The stability condition is processed twice according to the existing Lemma 1; specifically, Lemma 1 is: If A is an n×n real symmetric matrix and B is an m×n (m < n) matrix, where the first m columns are linearly independent, if and only if all the sequential principal minors of order greater than 2m in are positive, then x T Ax > 0, x is non-zero and satisfies x ∈ S := {x ∈ R n |Bx = 0};

[0053] Therefore, according to Lemma 1 above, let the matrix and satisfy Bx = 0, B = (M1 M2); then, the stability condition of the system is converted to: If the first m columns of the matrix B = (M1 M2) are linearly independent, the condition for the matrix to be stable is that all the principal minors of the matrix of order greater than 2m are positive.

[0054] Step 3.2: Optimize the parameters of the boundary proportional controller and solve for the optimal parameters of the controller.

[0055] The boundary proportional feedback control parameters that make the system exponentially stable and have the fastest decay rate can be obtained by solving a nonlinear programming problem; the objective function is -μ, and the constraint function is the stability condition processed twice by Lemma 1, and the minimum solution of this programming problem is solved.

[0056] Advantageous technical effects of the present invention:

[0057] Compared with the existing technology, the present invention mainly studies the Rijke tube model of the cascade of the Heckl heat release model and the PDE type gas dynamic equation, which is closer to reality; it proposes a boundary proportional control using the upper end pressure and the lower end sound velocity of the Rijke tube as outputs, so that the thermoacoustic unstable system can achieve exponential stability. Compared with the backstepping control method, the feedback quantity that is easier to measure is selected instead of the full state measurement in the thermoacoustic tube, and the proportional control that is easy to implement is selected, which brings convenience to practical application; theoretically, sufficient conditions to ensure the exponential stability of the system are strictly given, and then according to the positive definite theorem under the quadratic equality constraint, the condition is converted into a sufficient and necessary condition that is easier to solve; at the same time, for the boundary feedback control parameter optimization problem when the system exponential stability decays fastest, the above conditions are converted into a nonlinear programming problem for solution, and the optimal design scheme of the control parameters is given. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 Schematic diagram of a Rijke tube according to an embodiment of the present invention;

[0059] Figure 2 Flowchart of design and optimization of boundary ratio controller according to an embodiment of the present invention;

[0060] Figure 3 The embodiment of the present invention does not control the downforce velocity fluctuation diagram;

[0061] Figure 4 Pressure and velocity fluctuation diagram of the Rijke tube under boundary proportional control according to an embodiment of the present invention;

[0062] Figure 5 The embodiment of the present invention controls the input U(t);

[0063] Figure 6 Pressure and velocity fluctuation diagram of the Rijke tube under boundary proportional control when the embodiment of the present invention contains time delay;

[0064] Figure 7 Pressure and velocity fluctuation diagram of the Rijke tube under boundary proportional control when the embodiment of the present invention contains nonlinearity;

[0065] Figure 8 Rijke tube under boundary proportional control of the embodiment of the present invention Pressure fluctuations at (i) without time lag and nonlinearity (ii) with time lag (iii) with nonlinearity;

[0066] Figure 9 Block diagram of the control structure for the thermoacoustic instability of a Rijke tube according to an embodiment of the present invention. DETAILED DESCRIPTION

[0067] The present invention will be further described below with reference to the accompanying drawings and embodiments;

[0068] This invention proposes a boundary proportional control method for thermoacoustic instability in a Rijke tube. It addresses the problem of pressure oscillation within an aeroengine combustion chamber. By designing a controller for the Rijke tube, a power device exhibiting thermoacoustic instability, the thermoacoustic oscillations within the Rijke tube are controlled. First, for a thermoacoustically unstable dynamic system described by combining the one-dimensional gas dynamic equations of the Rijke tube with the Heckl heat release model, the thermoacoustic coupling within the system domain is transformed to the boundary through small-device linearization and characteristic coordinate transformation. A mathematical model of the combustion chamber is established, expressed as a set of 4×4 linear transport partial differential equations coupled at the boundary. The easily measurable sound pressure and sound velocity at the upper and lower ends of the Rijke tube are selected as feedback quantities, reducing the difficulty of measuring state quantities. A readily implementable boundary proportional controller is designed to control the sound pressure and velocity within the tube to achieve exponential stability. Based on the boundary proportional control model, the controller parameters are optimized, and the boundary proportional control parameters that achieve the fastest system convergence are determined. This results in the fastest suppression of thermoacoustic oscillations within the aeroengine combustion chamber, stabilizing the aeroengine thermoacoustic instability through active control.

[0069] This invention innovatively employs a boundary proportional active control method based on a partial differential model. Using the easily measurable sound pressure and velocity at the upper and lower ends of the Rijke tube as feedback variables, it suppresses pressure and velocity oscillations within the aircraft engine combustion chamber, reducing measurement costs. By optimizing the control parameters, it achieves rapid convergence. This boundary proportional control method for thermoacoustic instabilities in aircraft engine combustion chambers is unique in the field of aircraft engine control.

[0070] A method for controlling the thermoacoustic instability boundary ratio of a Rijke tube comprises the following steps:

[0071] Step 1: For the typical device Rijke tube that reveals the phenomenon of thermoacoustic instability, according to the conservation of mass, momentum and energy of the gas in the tube, a mathematical model describing the velocity fluctuation and pressure fluctuation partial differential equations is established; the schematic diagram of the Rijke tube is shown in the attached figure. Figure 1 As shown;

[0072] It is a quartz tube with both ends open. A resistance wire is placed at the lower half of the tube as a heat source, a microphone is placed at the upper end of the tube as a sound pressure measurement sensor, and a sound velocity meter as a sound velocity measurement sensor and a speaker as an actuator are placed at the lower end of the tube.

[0073] Step 1.1: First, express the Rijke tube thermoacoustic instability system model as a cascade of partial differential equations and the Heckl heat release model, as shown below:

[0074]

[0075]

[0076]

[0077] Where L represents the length of the tube, L w is the length of the resistance wire of the heat source, d w is the diameter of the resistance wire of the heat source, T w is the temperature of the resistance wire of the heat source, T is the gas temperature, A is the cross-sectional area of the tube, k is the thermal conductivity of the air, c v is the constant pressure specific heat capacity, p(t,x) represents the dimensionless gas pressure, v(t,x) represents the dimensionless gas velocity, t∈[0,+∞) represents the dimensionless time, x∈[0,1] is any position in the dimensionless tube, x f is the position of the heat source in the tube, Indicates the nominal value of pressure, i.e. steady state; γ represents the adiabatic constant; in practice, workers can obtain the data in the model by measuring the parameters of the combustion chamber.

[0078] Step 1.2: After Riemann transformation of the Rijke tube system model, we can get:

[0079]

[0080]

[0081] The Riemann transform decouples the velocity fluctuation v(t, x) and pressure fluctuation p(t, x) in the above cascade system. Then, the α function is processed to define the new state variables of the system through the following formula:

[0082]

[0083] And define:

[0084]

[0085] Therefore, the system of the above differential equations cascaded with the Heckl heat release model is converted into the following partial differential system:

[0086]

[0087]

[0088]

[0089]

[0090] And its boundary conditions are:

[0091]

[0092] in, To simplify the expression of the equation, Z L >0 is constant acoustic impedance;

[0093] The thermoacoustic unstable dynamic system is described by combining the Rijke tube one-dimensional gas dynamic equation with the Heckl heat release model. By decoupling the variables and transforming the state using Riemann transformation, the thermoacoustic coupling in the system domain is transformed to the boundary, thus transforming it into a dynamic system described by a set of 4×4 linear transport partial differential equations coupled at the boundary.

[0094] At this point, the complex mathematical model with coupled boundaries is converted into a partial differential mathematical model that couples only at the boundaries. Based on this, a boundary feedback controller is designed to stabilize the system and achieve active control of thermoacoustic instabilities.

[0095] Step 2: Design a boundary proportional controller based on the partial differential mathematical model obtained in step 1; the boundary proportional controller design and optimization flow chart is shown in the attached figure. Figure 2 As shown;

[0096] The sound pressure at the upper end and the sound velocity at the lower end of the Rijke tube, which are easy to measure, are selected as feedback variables. The proportional control structure, which is the easiest to implement in practice, is adopted. A control method imposed on boundary conditions is given to stabilize the entire system.

[0097] A proportional control method, easily implemented in practice, was chosen. A proportional output feedback boundary controller, which has the fastest convergence rate and is physically easy to implement, eliminated thermoacoustic instabilities and exponentially converged the system's pressure and velocity fluctuations toward zero. The easily measurable sound pressure at the top and velocity at the bottom of the Rijke tube were selected as feedback variables, simplifying the measurement of state variables.

[0098] According to the selected variable transformation, proportional feedback is achieved by measuring the pressure fluctuation at the upper end of the pipe and the velocity fluctuation at the lower end of the pipe, which not only saves measurement resources but also facilitates engineering implementation.

[0099] Based on the measured values of the pressure fluctuation at the upper end of the pipe and the velocity fluctuation at the lower end, the proportional control structure, which is the easiest to implement in practice, is used to give the control law imposed on the boundary conditions:

[0100] The actual sound pressure at the end of the Rijke tube before dimensionless processing:

[0101]

[0102] in, is the steady-state speed of sound, is the Mach number, and is the actual lower end sound speed of the Rijke tube before dimensionless processing:

[0103]

[0104] where represents the nominal value of the pressure, that is, the steady state;

[0105] Then the proportional control structure of the controller is:

[0106]

[0107] where k1 and k2 are the controller parameters to be designed;

[0108] This step designs the structure of the output feedback boundary proportional controller according to the characteristics of the tube.

[0109] Step 3: Design and optimize the parameters of the boundary proportional controller designed in Step 2;

[0110] The optimization goal is to achieve the stabilization of the gas pressure and velocity at the fastest speed, that is, the fastest exponential convergence. Therefore, with the convergence speed as the objective function and the stability of the partial differential system equation as the constraint function, the optimization problem is described as a nonlinear programming model; the design method of the controller is given through inequality conditions, and the optimal parameters of the controller are determined by solving the nonlinear programming problem;

[0111] Step 3.1: Design the optimal controller parameters for the boundary proportional controller;

[0112] Step 3.1.1: With the system stability as the constraint condition, where the system stability condition is:

[0113]

[0114]

[0115] where Λ is the coefficient of the partial differential equation of the velocity and pressure fluctuations in the Rijke tube; M1 and M2 are the boundary condition coefficients of the partial differential equation of the velocity and pressure fluctuations;

[0116] Step 3.1.2: Since the system stability condition is too complex, the stability condition is processed quadratically to make it more conducive to solving;

[0117] The stability condition is processed quadratically according to the existing Lemma 1; where Lemma 1 is specifically: If A is an n×n real symmetric matrix and B is an m×n (m < n) matrix, where the first m columns are linearly independent, if and only if all the sequential principal minors of order greater than 2m are positive, then x TAx>0, x is non-zero and satisfies x∈S:={x∈R n |Bx=0};

[0118] Therefore, according to Lemma 1 above, let the matrix And satisfy Bx=0,B=(M1 M2); then, the stability condition of the system is converted to: If the matrix B=(M1 M2) the first m columns are linearly independent, the matrix stability condition is the matrix All principal minors of order greater than 2m are positive;

[0119] Step 3.2: Optimize the boundary proportional controller parameters and solve for the optimal controller parameters;

[0120] The boundary proportional feedback control parameters that make the system exponentially stable and have the fastest decay rate can be obtained by solving a nonlinear programming problem; the objective function is -μ, and the constraint function is the stability condition after the quadratic processing of Lemma 1. The minimum solution of this programming problem is solved.

[0121] The contribution of this step is that the optimal solution procedure for the output feedback boundary controller parameters is given.

[0122] Step 4: Verify the effectiveness and robustness of the output feedback boundary controller; the control system structure is shown in the attached Figure 9 As shown;

[0123] Matlab is used to write a simulation program for the verification system, thereby verifying the convergence effect of the designed boundary proportional controller under the optimized parameters, and further verifying the effect of the controller of the present invention in the case of heat release inertia and heat release nonlinearity.

[0124] First, without a controller, the Rijke tube used to simulate the thermoacoustic instability of the aircraft engine combustion chamber is simulated. The gas pressure and velocity fluctuations are as follows: Figure 3 As shown in the figure, before boundary feedback control is applied, the pressure and velocity at 0 to 1 meter in the Rijke tube show large oscillations. At this time, the system is unstable and a controller needs to be designed.

[0125] By adopting the method of the present invention, after designing the boundary ratio controller, the gas pressure and velocity fluctuations of the Rijke tube simulating the thermoacoustic instability phenomenon of the aircraft engine combustion chamber are as follows: Figure 4 As shown in the figure, when boundary feedback control is applied, the pressure and velocity fluctuations of the Rijke tube converge to 0 within 0.25 seconds, that is, the combustion instability phenomenon is quickly suppressed. The simulation shows the effectiveness of the designed boundary feedback controller. Figure 5 The changing trend of the boundary feedback control U(t) is shown. It can be seen that the rapid exponential convergence of the system can be achieved by adopting the boundary proportional control with a limited small control gain.

[0126] The controller design of the present invention is based on the mathematical model of heat release described by the linearized Heckl model. Next, the robustness of the designed boundary proportional control in the presence of time lag and nonlinear characteristics in the heat release Heckl model will be verified. The heat release model considered in the present invention ignores time lag. In fact, time lag is an important factor affecting the thermoacoustic instability in the Rijke tube. Therefore, in the presence of time lag, the pressure and velocity fluctuations of the Rijke tube under the action of boundary proportional control are simulated and analyzed, such as Figure 6 In the case of a small time lag, the controller designed by the present invention can still quickly stabilize the system exponentially.

[0127] Secondly, the robustness of the boundary proportional control with respect to the nonlinear characteristics in the heat release model is analyzed. Figure 7 As shown in , the controller designed in this paper can also make the system exponentially stable in the presence of nonlinearity. Figure 8 Shows the existence of the above time delay or nonlinearity In the case of pressure fluctuations at the pressure point, when there is a time lag or nonlinear link in the heat release, the fluctuation amplitude of the system becomes larger and the convergence speed becomes slower, but the present invention can still make it converge, verifying the robustness of boundary proportional control to nonlinear terms and time lag.

[0128] In summary, the boundary ratio control method for thermoacoustic instability in an aero-engine combustion chamber proposed in the present invention is feasible and effective, and can meet the requirements of suppressing thermoacoustic instability.

Claims

1. A Rijke tube thermoacoustic instability boundary proportional control method, characterized in that: The specific steps include: Step 1: For the Rijke tube, a typical device for revealing thermoacoustic instability, a mathematical model describing velocity and pressure fluctuations using partial differential equations is established based on the conservation of mass, momentum, and energy of the gas inside the tube. Step 1.1: First, express the Rijke tube thermoacoustic instability system model as a cascade of partial differential equations and the Heckl heat release model, as shown below: Among them, L w is the length of the resistance wire of the heat source, d w is the diameter of the resistance wire of the heat source, T w is the temperature of the resistance wire of the heat source, T is the gas temperature, A is the cross-sectional area of the tube, k is the thermal conductivity of the air, c v is the constant pressure specific heat capacity, p(t,x) represents the dimensionless gas pressure, v(t,x) represents the dimensionless gas velocity, t∈[0,+∞) represents the dimensionless time, x∈[0,1] is any position in the dimensionless tube, x f is the position of the heat source in the tube, Indicates the nominal value of pressure, i.e. steady state; γ represents the adiabatic constant; Step 1.2: After Riemann transformation of the Rijke tube system model, we can get: The Riemann transformation decouples the velocity fluctuation v(t,x) and pressure fluctuation p(t,x) in the above cascade system; Next, by processing the α function, the new state variables of the system are defined by the following formula: α1(t,x)=R1(t,x),x∈[0,x f ] α2(t,x)=R2(t,x),x∈[0,x f ] α3(t,x)=R1(t,x),x∈[x f ,1] α4(t,x)=R2(t,x),x∈[x f ,1] And define: Therefore, the system of the above differential equations cascaded with the Heckl heat release model is converted into the following partial differential system: And its boundary conditions are: α1(t,0)=-α2(t,0)+2U(t) α2(t,1)=c2α1(t,1)+(1-c2)α4(t,1) α3(t,1)=(1+c2)α1(t,1)-c2α4(t,1) α4(t,0)=wα3(t,0) in, To simplify writing, Z L >0 is constant acoustic impedance; Step 2: Design a boundary proportional controller based on the partial differential mathematical model obtained in step 1; Step 3: Design and optimize the parameters of the boundary proportional controller designed in step 2.

2. A Rijke tube thermoacoustic instability boundary proportional control method according to claim 1, characterized in that: Step 2 is as follows: The sound pressure at the upper end and the sound velocity at the lower end of the Rijke tube, which are easy to measure, are selected as feedback variables. A proportional control structure is adopted, and a control method imposed on boundary conditions is given to stabilize the entire system. The actual sound pressure at the end of the Rijke tube before dimensionless processing: in, is the steady-state speed of sound, is the Mach number, and the actual sound velocity at the lower end of the Rijke tube before dimensionless processing is: in, Indicates the nominal value of the speed, i.e. the steady state; The proportional control structure of the controller is: Where k1 and k2 are the controller parameters to be designed.

3. The method for controlling the thermoacoustic instability boundary ratio of a Rijke tube according to claim 1, characterized in that: Step 3 is as follows: Taking the convergence rate as the objective function and the stability of the partial differential system equation as the constraint function, the optimization problem is described as a nonlinear programming model. The controller design method is given through inequality conditions, and the optimal parameters of the controller are determined by solving the nonlinear programming problem. Step 3.1: Design the optimal controller parameters for the boundary proportional controller; Step 3.2: Optimize the boundary proportional controller parameters and solve for the optimal controller parameters.

4. A Rijke tube thermoacoustic instability boundary proportional control method according to claim 3, characterized in that: Step 3.1 is as follows: Step 3.1.1: Take system stability as the constraint condition, where the system stability condition is: M1ζ(t,0)+M2ζ(t,1)=0 Where Λ is the coefficient of the partial differential equation for velocity and pressure fluctuations in the Rijke tube; M1 and M2 are the boundary condition coefficients of the partial differential equation for velocity and pressure fluctuations; Step 3.1.2: Since the stability conditions of the system are too complex, the stability conditions are processed twice to make them easier to solve; According to the existing Lemma 1, the stability condition is treated twice; So according to Lemma 1, let the matrix And satisfy Bx=0,B=(M1M2); then, the stability condition of the system is converted to: If the matrix B=(M1 M2) the first m columns are linearly independent, the matrix stability condition is the matrix All principal minors of order greater than 2m are positive.

5. The method for controlling the thermoacoustic instability boundary ratio of a Rijke tube according to claim 4, characterized in that: Step 3.1.2 Lemma 1 specifically states that: If A is an n×n real symmetric matrix and B is an m×n (m < n) matrix, where the first m columns are linearly independent, then and only then when all sequential principal minors of order greater than 2m in T are positive, x n Ax > 0, x is non-zero and satisfies x ∈ S := {x ∈ R n | Bx = 0}.

6. The method for controlling the thermoacoustic instability boundary ratio of a Rijke tube according to claim 3, characterized in that: Step 3.2 is as follows: The boundary proportional feedback control parameters that make the system exponentially stable and have the fastest decay rate can be obtained by solving a nonlinear programming problem; the objective function is -μ, and the constraint function is the stability condition after the quadratic processing of Lemma 1. The minimum solution of this programming problem is solved.

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