Determination learning control method based on Rijke tube thermoacoustic instability data

Abstract

The invention relates to a deterministic learning control method based on Rijke tube thermoacoustic instability data, which comprises the following steps: step 1, on the basis of a Rijke tube control system experiment table, assuming the form of a Rijke tube thermoacoustic instability system; 2, approaching a nonlinear function in the Rijke tube thermo-acoustic instability system by adopting an RBF neural network, and replacing an unknown nonlinear function in the Rijke tube thermo-acoustic instability system; and 3, designing and determining a learning control method according to the Rijke tube thermo-acoustic instability system obtained in the step 2, and controlling a pressure signal and a speed signal. The control method can solve the problems that in the prior art, control over the complex pressure oscillation phenomenon is not accurate, and self-adaptive adjusting capacity is lacked.

Description

Technical Field

[0001] The invention belongs to the technical field of Rijke tube thermoacoustic instability control, and relates to a deterministic learning control method based on Rijke tube thermoacoustic instability data. Background Art

[0002] Rijke tubes are important experimental devices for studying thermoacoustic instabilities and are widely used in combustion systems and acoustics. Thermoacoustic instability refers to the phenomenon that when feedback occurs between the release of heat and sound waves, the pressure fluctuations in the thermoacoustic unstable system will gradually increase until saturation, resulting in unstable oscillations. This type of instability will have a negative impact on combustion equipment and its operating efficiency, so controlling and suppressing thermoacoustic instability is a key technical problem in related fields.

[0003] At present, the research on active control methods for the thermoacoustic unstable pressure oscillation of Rijke tubes is mainly based on mathematical model methods. For example, optimal control, by defining a cost function (or performance index) and using mathematical optimization methods under certain constraints to obtain the optimal control law of the system, is usually applied to dynamic systems, including linear systems and nonlinear systems. Due to the nonlinear characteristics and variable physical conditions of the thermoacoustic system, it is difficult for traditional mathematical models to accurately describe the dynamic behavior of the thermoacoustic instability phenomenon, and the modeling process is time-consuming and has limited accuracy. Optimal control depends on an accurate system model. If the model is inaccurate, optimal control may not achieve the desired effect.

[0004] Data-based control methods include BP neural networks, which use the back propagation algorithm to train and adjust weights by minimizing the loss function to approximate the desired output. The BP neural network control algorithm has limited adaptability to complex nonlinear problems. It takes a long time to train large data sets and high-dimensional data, and the selection of hidden layers usually requires experience. Summary of the invention

[0005] The purpose of the present invention is to propose a deterministic learning control method based on Rijke tube thermoacoustic instability data, aiming to solve the problems of inaccurate control of complex pressure oscillation phenomena and lack of adaptive regulation capability in the prior art.

[0006] The present invention provides a deterministic learning control method based on Rijke tube thermoacoustic instability data, comprising:

[0007] Step 1: Based on the Rijke tube control system test bench, assume the form of the Rijke tube thermoacoustic instability system;

[0008] Step 2: Use RBF neural network to approximate the nonlinear function in the Rijke tube thermoacoustic instability system and replace the unknown nonlinear function in the Rijke tube thermoacoustic instability system;

[0009] Step 3: Design and determine a learning control method for the Rijke tube thermoacoustic instability system obtained in step 2 to control the pressure signal and velocity signal.

[0010] The deterministic learning control method based on the Rijke tube thermoacoustic instability data of the present invention has the following beneficial effects:

[0011] 1. Compared with the control algorithm based on model design, the control algorithm based on data does not require an accurate mathematical model, but performs feedback control through experimental data. This is very beneficial for complex systems that are difficult to establish accurate physical models, such as nonlinear, time-varying systems or systems with uncertainty. Complex nonlinear relationships can be effectively handled.

[0012] 2. Compared with other data-based control algorithms, the deterministic learning control method based on the Rijke tube thermoacoustic instability data of the present invention has a simple structure and fast calculation speed. The Gaussian function of the hidden layer can locally and accurately approximate the unknown complex nonlinear terms. The RBF neural network has strong robustness to noise and data uncertainty. Due to the local sensitivity of the hidden layer nodes to the input data, it can effectively deal with local disturbances and uncertainties in the system.

[0013] 3. The existing technology mainly relies on the control algorithm with fixed parameters, which is difficult to deal with multi-frequency and nonlinear oscillation phenomena, and the ability of real-time feedback and control is limited. The present invention can adjust the control parameters in real time according to the dynamic changes of the system by introducing the fixed learning RBF neural network adaptive control algorithm and the real-time closed-loop feedback control mechanism, and effectively control the complex thermoacoustic oscillation phenomenon in the Rijke tube, especially in the case of high frequency and multi-modal oscillation. This method can improve the accuracy and flexibility of control, enhance the response speed and adaptability of the system, and thus achieve efficient control of thermoacoustic instability. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a flow chart of a determination learning control method based on Rijke tube thermoacoustic instability data of the present invention;

[0015] Figure 2 This is a schematic diagram of the Rijke tube control system test bench;

[0016] Figure 3 is a constant-valued neural network W T Schematic diagram of S(X(k));

[0017] Figure 4 It is the amplitude-frequency characteristic diagram of the pressure signal generated by the Rijke tube thermoacoustic instability system;

[0018] Figure 5It is the amplitude-frequency characteristic diagram of the pressure signal output by the trained RBF neural network model;

[0019] Figure 6 It is the velocity signal of the Rijke tube thermoacoustic instability system in the Rijke tube thermoacoustic instability closed-loop control system;

[0020] Figure 7 It is the pressure signal of the Rijke tube thermoacoustic instability system in the Rijke tube thermoacoustic instability closed-loop control system;

[0021] Figure 8 It is the update graph that determines the weights of the neural network within the learning RBF neural network controller. DETAILED DESCRIPTION

[0022] like Figure 1 As shown, a deterministic learning control method based on Rijke tube thermoacoustic instability data of the present invention comprises:

[0023] Step 1: Based on the Rijke tube control system test bench, assume the form of the Rijke tube thermoacoustic instability system, specifically:

[0024] Step 1.1: Build a Rijke tube control system experimental platform using a microphone, a speaker, a nickel-chromium metal heating wire, a quartz glass tube, a data acquisition device, a controller and a D / A conversion module.

[0025] like Figure 2 As shown, the microphone and the speaker are respectively arranged at the upper and lower ends of the quartz glass tube. The nickel-chromium metal heating wire is arranged in the quartz glass tube, 1 / 4 of the distance from the bottom. When a certain voltage is applied to the nickel-chromium metal heating wire, the hot air rises in the quartz glass tube, causing gas convection in the tube and stimulating thermoacoustic instability. The microphone at the upper end of the tube mouth is used to measure the voltage signal corresponding to the pressure fluctuation.

[0026] Step 1.2: According to the three conservation equations of mass, momentum and energy, the one-dimensional compressible gas dynamics is obtained to describe the acoustic field fluctuations in the Rijke tube; the ordinary differential equation description is obtained by the Galerkin method, and the Rijke tube thermoacoustic instability system can be obtained by combining the heat release model; the essence is to convert the three conservation equations into the changes of pressure field and velocity field over time, and the velocity field can be regarded as the integral of the pressure field; therefore, the Rijke tube thermoacoustic instability system is assumed to have the following form:

[0027]

[0028] Where X(k) = [v(k), p(k)] Tis the two-dimensional state vector of the thermoacoustically unstable system, v(k) represents the velocity signal at time k, p(k) represents the pressure signal at time k, and f(X(k)) is the unknown nonlinear function in the Rijke tube thermoacoustically unstable system.

[0029] Step 2: Use RBF neural network to approximate the nonlinear function in the Rijke tube thermoacoustic instability system and replace the unknown nonlinear function in the Rijke tube thermoacoustic instability system, specifically:

[0030] Step 2.1: When a certain voltage is applied to the nickel-chromium metal heating wire, the hot air rises in the Rijke tube, causing gas convection in the tube and stimulating thermoacoustic instability. A set of pressure signals measured by the microphone at different sampling times when equal-amplitude oscillations occur on the experimental platform are collected.

[0031] Step 2.2: According to the assumption of step 1, that is, in the Rijke tube thermoacoustic instability system, the velocity can be regarded as the integral of the pressure, the pressure signal p(k) is integrated to obtain the velocity signal. At this time, there are multiple pressure signals and velocity signals at different sampling times.

[0032] Step 2.3: Then, using the deterministic learning modeling theory, a set of RBF neural networks is used to approximate the unknown nonlinear function f(X(k)) in the Rijke tube thermoacoustic instability system in step 1, and a set of constant neural networks is obtained. like Figure 3 shown.

[0033] in, Represents the weight vector connecting the hidden layer and the output layer. Each component in the weight vector is a constant value determined during the modeling process. is the RBF function vector, and the RBF function is taken as a Gaussian function, which is in the following form: S1(X(k))

[0034]

[0035] Where j = 1…N, ξ j represents the center of the jth neuron node, η j represents the width between adjacent neuron nodes, and N is the number of hidden layer neuron nodes; the step 2.3 is specifically as follows:

[0036] Step 2.3.1: Take the pressure signals and velocity signals at different sampling times as Figure 3 The input of the RBF neural network shown.

[0037] Step 2.3.2: The RBF neural network adjusts the weights through the weight adjustment law until the weights stabilize to Fix the weights to get a constant neural network

[0038] Step 2.4: Constant value neural network Substitute it into the Rijke tube thermoacoustic instability system assumed in step 1 to replace the unknown nonlinear function f(X(k)), and we get the following constant neural network: The Rijke tube thermoacoustic instability system consists of:

[0039]

[0040] In the specific implementation, when no control action is applied, the pressure signal p(k) generated by the Rijke tube thermoacoustic instability system is used to train the RBF neural network. The amplitude-frequency characteristic diagram is obtained by fast Fourier transforming the time domain signal of the pressure signal p(k), as shown in Figure 4 shown. Figure 5 The amplitude-frequency characteristic diagram of the pressure signal output by the trained RBF neural network model is shown in Figure 2. The main frequency of the output pressure oscillation is around 400Hz, and there is a harmonic frequency with a slightly larger amplitude at around 750Hz, which is consistent with the pressure data used to train the neural network. We learned the knowledge and rules of pressure data changes when the Rijke tube exhibits thermoacoustic instability, and were able to reproduce the rules of pressure oscillation.

[0041] Step 3: Design and determine the learning control method for the Rijke tube thermoacoustic instability system obtained in step 2, and control the pressure signal and velocity signal, specifically:

[0042] Step 3.1: Design and determine the learning RBF neural network controller for the Rijke tube thermoacoustic instability system obtained in step 2. The control signal is in the form of:

[0043]

[0044] Among them, p d (k) represents the reference value of the pressure signal p(k); W(k) represents the neural network weight vector in the RBF neural network controller; A is the control constant to be designed; r(k) represents the control tracking error, λ1 is a constant; e p (k) is the pressure tracking error, which represents the difference between the pressure amplitude of the thermoacoustically unstable system and the expected value; e v (k) is the velocity tracking error, which represents the difference between the velocity amplitude of the thermoacoustically unstable system and the expected value. Let A = 0.1, λ1 = 0.1.

[0045] r(k)=ep (k)+λ1e v (k)

[0046] e p (k) = p(k) - p d (k)

[0047] e v (k) = v(k) - v d (k)

[0048] The weight vector adjustment formula is as follows:

[0049] W(k+1)=W(k)+αS(X(k))·r T (k+1)

[0050] Among them, α represents the learning rate.

[0051] Step 3.2: The constant value neural network The Rijke tube thermoacoustic instability system is combined with the deterministic learning RBF neural network controller to form a Rijke tube thermoacoustic instability closed-loop control system:

[0052]

[0053] Step 3.3: Control the pressure signal and velocity signal through the Rijke tube thermoacoustic instability closed-loop control system.

[0054] Figure 6 is the velocity signal of the Rijke tube thermoacoustic instability system in the Rijke tube thermoacoustic instability closed-loop control system. Figure 7 It is the pressure signal of the Rijke tube thermoacoustic instability system in the Rijke tube thermoacoustic instability closed-loop control system. Figure 6 and 7 It can be seen that the control action of the determined learning RBF neural network controller intervenes at the time step k=500, and the pressure fluctuation amplitude and velocity fluctuation amplitude of the thermoacoustic unstable system converge to the expected value in a very short time. The simulation results show the effectiveness of the determined learning control algorithm for the Rijke tube thermoacoustic unstable system.

[0055] Figure 8 It is the update diagram of the neural network weights in the determined learning RBF neural network controller. It can be seen that the neural network weights in the determined learning RBF neural network controller have also converged to a stable optimal value.

[0056] The above description is only a preferred embodiment of the present invention and is not intended to limit the concept of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A deterministic learning control method based on Rijke tube thermoacoustic instability data, characterized in that: include: Step 1: Based on the Rijke tube control system test bench, assume the form of the Rijke tube thermoacoustic instability system; Step 2: Use RBF neural network to approximate the nonlinear function in the Rijke tube thermoacoustic instability system and replace the unknown nonlinear function in the Rijke tube thermoacoustic instability system; Step 3: Design and determine a learning control method for the Rijke tube thermoacoustic instability system obtained in step 2 to control the pressure signal and velocity signal.

2. The deterministic learning control method based on Rijke tube thermoacoustic instability data according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1.1: Use microphone, speaker, nickel-chromium metal heating wire, quartz glass tube, data acquisition device, controller and D / A conversion module to build a Rijke tube control system experimental platform; Step 1.2: According to the three conservation equations of mass, momentum and energy, the one-dimensional compressible gas dynamics is obtained to describe the acoustic field fluctuations in the Rijke tube; the ordinary differential equation description is obtained by the Galerkin method, and the Rijke tube thermoacoustic instability system can be obtained by combining the heat release model; the essence is to convert the three conservation equations into the changes of pressure field and velocity field over time, and the velocity field can be regarded as the integral of the pressure field; therefore, the Rijke tube thermoacoustic instability system is assumed to have the following form: Where X(k) = [v(k), p(k)] T is the two-dimensional state vector of the thermoacoustically unstable system, v(k) represents the velocity signal at time k, p(k) represents the pressure signal at time k, and f(X(k)) is the unknown nonlinear function in the Rijke tube thermoacoustically unstable system.

3. The deterministic learning control method based on Rijke tube thermoacoustic instability data according to claim 2, characterized in that: The step 2 is specifically as follows: Step 2.1: When a certain voltage is applied to the nickel-chromium metal heating wire, the hot air rises in the Rijke tube, causing gas convection in the tube and stimulating thermoacoustic instability. The pressure signals measured by the microphone at multiple different sampling times when a set of equal-amplitude oscillations occur on the experimental platform are collected; Step 2.2: Integrate the pressure signal to obtain the velocity signal. At this time, there are multiple pressure signals and velocity signals at different sampling times. Step 2.3: Then, using the deterministic learning modeling theory, a set of RBF neural networks is used to approximate the unknown nonlinear function f(X(k)) in the Rijke tube thermoacoustic instability system in step 1, and a set of constant neural networks is obtained. in, Represents the weight vector connecting the hidden layer and the output layer. Each component in the weight vector is a constant value determined during the modeling process. is the RBF function vector, and the RBF function is taken as a Gaussian function, which is in the following form: Where j = 1…N, ξ j represents the center of the jth neuron node, η j Represents the width between adjacent neuron nodes, and N is the number of hidden layer neuron nodes; Step 2.4: Constant value neural network Substitute it into the Rijke tube thermoacoustic instability system assumed in step 1 to replace the unknown nonlinear function f(X(k)), and we get the following constant neural network: The Rijke tube thermoacoustic instability system consists of:

4. The deterministic learning control method based on Rijke tube thermoacoustic instability data according to claim 3, characterized in that: The step 2.3 is specifically as follows: Step 2.3.1: Use the pressure signals and velocity signals at multiple different sampling times as the input of the RBF neural network; Step 2.3.2: The RBF neural network adjusts the weights through the weight adjustment law until the weights stabilize to Fix the weights to get a constant neural network 5. The deterministic learning control method based on Rijke tube thermoacoustic instability data according to claim 3, characterized in that: The step 3 is specifically as follows: Step 3.1: Design and determine the learning RBF neural network controller for the Rijke tube thermoacoustic instability system obtained in step 2. The control signal is in the form of: Among them, p d (k) represents the reference value of the pressure signal p(k), W(k) represents the neural network weight vector in the RBF neural network controller; A is the control constant to be designed, r(k) represents the control tracking error, λ1 is a constant, e p (k) is the pressure tracking error, which represents the difference between the pressure amplitude of the thermoacoustically unstable system and the expected value; e v (k) is the velocity tracking error, which represents the difference between the velocity amplitude of the thermoacoustically unstable system and the expected value; r(k)=e p (k)+λ1e v (k) e p (k)=p(k)-p d (k) e v (k)=v(k)-v d (to) The weight vector adjustment formula is as follows: W(k+1)=W(k)+αS(X(k))·r T (k+1) Among them, α is the learning rate; Step 3.2: The constant value neural network The Rijke tube thermoacoustic instability system is combined with the deterministic learning RBF neural network controller to form a Rijke tube thermoacoustic instability closed-loop control system: Step 3.3: Control the pressure signal and velocity signal through the Rijke tube thermoacoustic instability closed-loop control system.

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