A data-based distributed periodic event-triggered cost-constrained control method for aero-engines

Abstract

The application provides a data-based distributed periodic event-triggered cost control method for an aero-engine. The method comprises the following steps: S1, establishing a distributed periodic event-triggered system model for the aero-engine; S2, based on a Lyapunov-Krasovskii functional method, solving an upper bound of a cost function and giving a controller gain design method dependent on unknown model parameters; and S3, continuously exciting the system offline and collecting data, and based on the data, jointly designing the controller gain and a trigger matrix. The application saves the system identification link, and saves the calculation resources to a certain extent; meanwhile, the method is suitable for the case that general data collection exists a bounded noise, and does not need to assume that the noise is subject to a probability distribution, and has a certain universality.

Description

Technical Field

[0001] This invention relates to a data-based distributed periodic event-triggered cost control method for aero-engines. Background Technology

[0002] With the rapid development of information technology, networked systems have made significant progress. By introducing bus networks and intelligent nodes to achieve information transmission and interaction, aero-engine control systems are transitioning from centralized control to distributed control. Compared with traditional point-to-point communication systems, distributed control systems offer advantages such as low cost and convenient maintenance due to the use of shared communication networks. However, the introduction of networks may lead to problems such as bandwidth limitations and network latency. To conserve network resources, some researchers have proposed various event-triggered control schemes to determine whether signals collected by sensors need to be transmitted to the controller. Continuous event-triggered control typically requires continuous checking of event triggering conditions, which is difficult to implement in hardware and also difficult to prove the non-existence of Zeno's phenomenon (an infinite number of triggers within a finite time). Unlike continuous event-triggered control, periodic event-triggered control only verifies triggering conditions at discrete moments. Therefore, periodic event-triggered control can guarantee an appropriate sampling period and is more suitable for practical implementation. In addition to bandwidth limitations, network-induced latency can also degrade system performance and even destabilize the closed-loop system. Currently, the main network latency modeling methods include discrete system modeling methods, hybrid system modeling methods, and time-delay system modeling methods. Discrete system modeling methods are generally less conservative but struggle to handle external disturbances. Hybrid system modeling methods are suitable for nonlinear systems but may introduce significant conservatism. Considering the advantages of time-delay system modeling methods—low conservatism and ease of handling various disturbances—many researchers employ time-delay methods for modeling and analyzing event-triggered control systems.

[0003] For a long time, research on distributed control systems for aero-engines has been based on explicit mathematical models derived from system identification. However, as systems become increasingly complex, establishing a satisfactory mathematical model from first principles becomes increasingly difficult.

[0004] Based on the above analysis, this invention proposes a data-based periodic event triggering mechanism and a cost-preservation controller collaborative design method for the distributed control problem of a certain type of twin-shaft turbofan engine. Summary of the Invention

[0005] To address the problem of distributed periodic event triggering control for aero-engines with unknown model parameters and transmission delays in the network, this invention provides a data-based method for cost-saving control of distributed periodic event triggering for aero-engines.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A data-driven method for controlling the cost of aero-engines through distributed periodic events includes the following steps:

[0008] S1. Establish a distributed periodic event triggering system model for aero-engines;

[0009] S2. Based on the Lyapunov-Krasovskii functional method, the upper bound of the cost function is solved and a controller gain design method that depends on unknown model parameters is given;

[0010] S3. Continuously stimulate the system offline and collect data, and design the controller gain and trigger matrix based on the data.

[0011] Further, step S1 includes:

[0012] S1.1 Establishing a distributed system model for aero-engines:

[0013] The small-deviation state-space model of the distributed system of an aero-engine is described as follows:

[0014]

[0015] in, For the system's state variables, For system control input. and These represent n-dimensional and m-dimensional vectors, respectively. l For the low-pressure rotor speed, n h W is the high-voltage rotor speed. f A is the main fuel flow rate, and A8 is the exhaust nozzle area. A and B are adaptive matrix.

[0016] For ease of system analysis and control design, it is assumed that the sensors in the above system are time-driven with a sampling period of h>0, and the controllers and actuators are event-driven; there is a time-varying bounded network-induced delay. Assume that data is transmitted in single packets without timing errors.

[0017] S1.2 Establish a closed-loop system model under periodic event-triggered control considering time delay:

[0018] To reduce the consumption of network resources, a periodic event triggering mechanism is adopted to control the system (1). The periodic event triggering mechanism in this invention includes two steps. The first step is that the sensor periodically samples the state of the system (1) with a fixed sampling period h. The sampling time can be expressed as: The value is a non-negative integer. The second step is to check whether the system state collected by the sensor meets the trigger condition. If the trigger condition is met, the sampled state is transmitted to the controller, and this sampling time is the trigger time. At this time, two adjacent trigger times t k and t k+1 The sampling times between can be expressed as The input is a positive integer; if the triggering condition is not met, the control input holds the state value of the most recently successfully transmitted state through a zero-order hold until the next triggering time. In summary, the design of the periodic event triggering mechanism is as follows:

[0019]

[0020] Where σ∈[0,1) is the triggering parameter, and Ω is a positive definite matrix, i.e., the triggering matrix jointly designed with the controller gain. When σ=0, this periodic event triggering mechanism is a periodic triggering mechanism. Considering the influence of time-varying network-induced delay, assume the system state is at time t. k If it is constantly collected by the sensor, then it will be in t k +τ k Real-time data is transmitted to the controller, where

[0021] Based on the above analysis, a state feedback controller is introduced:

[0022] u(t)=Kx(t k (3)

[0023] Where K is the state feedback gain.

[0024] Based on the analysis, the closed-loop expression of system (1) under the periodic event triggering mechanism is as follows:

[0025]

[0026] Where τ(t)∈[0,τ M ],

[0027] Further, step S2 includes:

[0028] S2.1 Establish the cost function:

[0029] For distributed systems of aero-engines, in order to balance the contradiction between network service quality and control performance, a cost function J is introduced as the objective function for the collaborative design of the periodic event triggering mechanism and the controller, so as to ensure that the system maintains good response performance under periodic event triggering control.

[0030] The cost function can be expressed as:

[0031]

[0032] Where N1 and N2 are symmetric positive definite matrices. The joint design objective of the controller gain and trigger matrix is ​​to maintain the asymptotic stability of the closed-loop system (9) while ensuring that the cost function (12) is less than an upper bound, and to calculate the upper bound of the cost function.

[0033] S2.2 Construct the Lyapunov-Krasovskii functional to obtain the stability criterion for the closed-loop system under periodic event-triggered control, and calculate the upper bound of the cost:

[0034] For the closed-loop system (4), a Lyapunov-Krasovskii functional of the following form is constructed:

[0035]

[0036] Where P, Q, and R are symmetric positive definite matrices, and s and θ are both integration variables.

[0037] By differentiating (6) and setting it to less than 0, using Park's lemma and the descriptive method, we can obtain a stability criterion based on the following linear matrix inequality:

[0038]

[0039] Φ<0 (8)

[0040] Where S is the appropriate dimension matrix. Matrix Φ is represented as follows:

[0041]

[0042] Where E is an invertible matrix. The matrix operator can be expressed as:

[0043] l i =[0 n×(i-1)n ,I n ,0 n×(5-i)n ],(i=1,2,3,4,5)

[0044] l0 = 0 n×5n

[0045] Among them I n For an n-dimensional unit vector, 0 a×b Let be the zero vector in row a and column b.

[0046] Matrix L can be represented as:

[0047] L = l1 + l2 + l3 + l4 + l5

[0048] sym{…} denotes the sum of a matrix and its transpose, i.e., sym{A} = A + A.T .

[0049] Through calculation, the upper bound of the cost function J can be expressed as:

[0050] J≤x T (0)px(0)+τ M x T (0)Qx(0) (9)

[0051] S2.3, based on S2.2, presents a joint design method for controller gain and trigger matrix that depends on unknown model parameters:

[0052] To solve for the controller gain K using matrix inequalities, the inverse of the invertible matrix E is expressed as: By transforming the matrix in S2.2 We can obtain:

[0053]

[0054] in,

[0055] From matrix inequalities K can be calculated E , Therefore, the controller gain K = K E E and trigger matrix

[0056] Further, step S3 includes: S3.1 Offline data acquisition and quadratic data-driven system expression:

[0057] Since the joint design method in S2 is based on the premise that the model parameters A and B are known, it is necessary to use data to apply matrix inequalities. We will express the system (1) in a non-parametric manner. First, we will continuously stimulate the system (1) offline to collect input and state data. Considering the influence of external disturbances, sensor measurement noise and other factors on data acquisition, the system (1) can be expressed as:

[0058]

[0059] in Represents unknown disturbances and noise, t≥0, B w For a full-rank, well-dimensional matrix, B can typically be set. w =I. Assume the data acquisition time sequence is... That is, data was collected N times. The following data matrix is ​​defined:

[0060]

[0061] X = [x(T1), x(T2), ..., x(T)] N )]

[0062] U = [u(T1), u(T2), ..., u(T)] N )]

[0063] W = [w(T1), w(T2), ..., w(T)] N )]

[0064] The following equation is clearly true:

[0065]

[0066] This method only requires the assumption that the noise w(t) is bounded, without needing statistical information about the noise, which is more realistic. The set of noise data matrices that satisfy the boundedness condition is defined as... This can be expressed as:

[0067]

[0068] Q w It is a negative definite matrix, S w R w For a well-posed matrix, m d A ×N-dimensional real matrix. When Q is selected... w =-I,S w =0, When, the inequality in equation (23) can be simplified to:

[0069]

[0070] in, Let w(t) denote the upper bound of the 2-norm of the noise. When the noise satisfies the inequality in bounded condition (12), the set of system parameters (AB) dependent on the measurement data can be expressed as follows:

[0071]

[0072] in,

[0073] Next, the controller design results in S2.2 will be processed according to the above data-based model parameter expression.

[0074] S3.2, based on S3.1 and S2.3, utilizes mathematical tools such as the full-block S-procedure to jointly design the controller gain and triggering matrix based on data.

[0075] As shown in S2.3, by solving the linear matrix inequalities... The controller gain and triggering matrix that make the system asymptotically stable when the cost function is less than its upper bound can be calculated. (Rewrite the matrix.) as follows:

[0076]

[0077] in, The matrix Λ can be represented as:

[0078]

[0079] From the matrix inequalities in equation (12), combined with equation (15), and through the S-procedure, we can obtain:

[0080]

[0081] In summary, when the upper bound of the noise from offline data acquisition satisfies the inequality in equation (12), the controller gain K = K can be calculated by solving the linear matrix inequalities (7) and (16). E E and trigger matrix

[0082] This invention first establishes a time-delay system model under state feedback control based on the transmission characteristics of state variables and control variables under a periodic event triggering mechanism. Second, it solves for the upper bound of the cost function and provides a controller gain design method dependent on unknown model parameters. Finally, it continuously excites the system offline and collects data, jointly designing the controller gain and triggering matrix based on the data. Compared to the original method of obtaining model parameters through system identification and then designing a distributed cost-preservation controller for aero-engines, this invention innovatively utilizes a quadratic data-driven system expression, directly implementing the cost-preservation controller design using the collected data. This method eliminates the system identification step, saving computational resources to some extent; simultaneously, it is applicable to situations where bounded noise exists in general data acquisition, without assuming that the noise follows a probability distribution, thus possessing a certain degree of universality. Attached Figure Description

[0083] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0084] Figure 1 Flowchart of a data-based distributed periodic event-triggered cost control method for aero-engines;

[0085] Figure 2 This is a diagram of the architecture of a distributed control system for an aero-engine based on a bus network.

[0086] Figure 3 This is a schematic diagram of data-based periodic event triggering control;

[0087] Figure 4 This is a state trajectory diagram of a certain type of aero-engine under the action of a controller.

[0088] Figure 5 A schematic diagram illustrating the triggering time and interval under the periodic event triggering mechanism;

[0089] Figure 6 The image shows the low-pressure rotor speed trajectory of a certain type of aero-engine with different transmission delays. Detailed Implementation

[0090] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0091] like Figure 1 As shown in the figure, this invention discloses a data-based distributed periodic event-triggered cost control method for aero-engines, comprising the following steps:

[0092] S1. Establish a distributed periodic event triggering system model for aero-engines:

[0093] S1.1 Establishing a distributed system model for aero-engines:

[0094] The structure of a distributed control system for aero-engines based on a bus network is as follows: Figure 2 As shown, sensors, controllers, and actuators transmit and interact information via a bus. The small-deviation state-space model of the distributed system of an aero-engine is described as follows:

[0095]

[0096] in, For the system's state variables, For system control input. and These represent n-dimensional and m-dimensional vectors, respectively. l For the low-pressure rotor speed, n h W is the high-voltage rotor speed. fA is the main fuel flow rate, and A8 is the exhaust nozzle area. A and B are adaptive matrix.

[0097] For ease of system analysis and control design, it is assumed that the sensors in the above system are time-driven with a sampling period of h>0, and the controllers and actuators are event-driven; there is a time-varying bounded network-induced delay. Assume that data is transmitted in single packets without timing errors.

[0098] S1.2 Establish a closed-loop system model under periodic event-triggered control considering time delay:

[0099] To reduce the consumption of network resources, a periodic event triggering mechanism is used to control the system (1). The periodic event triggering mechanism in this invention includes two steps, such as... Figure 3 As shown. The first step is for the sensor to periodically sample the state of system (1) at a fixed sampling period h. The second step is to check whether the system state collected by the sensor meets the triggering conditions. If the triggering conditions are met, the sampled state is transmitted to the controller, and the sampling time is the triggering time; if the triggering conditions are not met, the control input holds the most recently successfully transmitted state value through a zero-order hold until the next triggering time. The controller and the triggering matrix are jointly designed using the pre-collected system input and state data, which will be described in detail later.

[0100] Considering the sampling period is h, the sampling time sequence is defined as follows: If the integer is non-negative, the trigger condition is checked at time ih. The controller data is only updated when the trigger condition is met. Since the minimum trigger interval is necessarily greater than the sampling period h, Zeno's phenomenon can be effectively avoided. Definition Where t k =s k h is the time of the kth successful trigger, therefore two adjacent trigger times t k and t k+1 The sampling times between can be expressed as It is a positive integer. Clearly, it has... The design of the periodic event triggering mechanism is as follows:

[0101]

[0102] Where σ∈[0,1) is the triggering parameter, and Ω is a positive definite matrix, i.e., the triggering matrix jointly designed with the controller gain. When σ=0, this periodic event triggering mechanism is a periodic triggering mechanism. Considering the influence of time-varying network-induced delay, assume the system state is at time t. k If it is constantly collected by the sensor, then it will be in t k +τk Real-time data is transmitted to the controller, where

[0103] Based on the above analysis, a state feedback controller is introduced:

[0104] u(t)=Kx(t k (3)

[0105] Where K is the state feedback gain, t∈[t k +τ k ,t k+1 +τ k+1 Next, consider two scenarios:

[0106] Scenario 1:

[0107] At this time, trigger time t k and t k+1 These are adjacent sampling times, i.e., t k+1 =t k +h. The following definition is given:

[0108] τ(t)=tt k ,t∈[t k +τ k ,t k+1 +τ k+1 (4)

[0109] e k (t)=0,t∈[t k +τ k ,t k+1 +τ k+1 (5)

[0110] Scenario 2:

[0111] At this point, there clearly exists a constant d. M This makes the following equation true:

[0112]

[0113] The following definition is given:

[0114]

[0115]

[0116] From equations (4) and (6), it can be seen that remember Let represent the maximum trigger interval, which is composed of the sampling period h and the maximum transmission delay. Composition. When When, then τM This indicates the maximum sampling period.

[0117] From equations (4)-(7), the state feedback controller (3) becomes:

[0118] u(t)=Kx(t-τ(t))+Ke k (t) (8) Therefore, the closed-loop expression of system (1) under the periodic event triggering mechanism is:

[0119]

[0120] The triggering condition in the periodic event triggering mechanism (2) can also be rewritten as:

[0121] σx T (t-τ(t))Ωx(t-τ(t))≤e k T (t)Ωe k (t) (10)

[0122] where t∈[t k +τ k ,t k+1 +τ k+1 ),

[0123] Set the initial conditions of the system state as follows:

[0124] x(t)=φ(t), t∈[-τ M ,0] (11)

[0125] Where φ(t) is [-τ M A continuous function on [0, 0].

[0126] S2. Based on the Lyapunov-Krasovskii functional method, the upper bound of the cost function is solved, and a controller gain design method dependent on unknown model parameters is given:

[0127] S2.1 Establish the cost function:

[0128] For distributed systems of aero-engines, in order to balance the contradiction between network service quality and control performance, a cost function J is introduced as the objective function for the collaborative design of the periodic event triggering mechanism and the controller, so as to ensure that the system maintains good response performance under periodic event triggering control.

[0129] The cost function can be expressed as:

[0130]

[0131] Where N1 and N2 are symmetric positive definite matrices. The joint design objective of the controller gain and trigger matrix is ​​to maintain the asymptotic stability of the closed-loop system (9) while ensuring that the cost function (12) is less than an upper bound, and to calculate the upper bound of the cost function.

[0132] S2.2 Construct the Lyapunov-Krasovskii functional to obtain the stability criterion for the closed-loop system under periodic event-triggered control, and calculate the upper bound of the cost:

[0133] Construct a Lyapunov-Krasovskii functional of the following form:

[0134]

[0135] Where P, Q, and R are symmetric positive definite matrices, s and θ are both integration variables, and V(t) > 0. Taking the derivative of (13) yields:

[0136]

[0137] for By Park's lemma, we can obtain the following:

[0138]

[0139]

[0140] The condition for equation (15) to hold is:

[0141]

[0142] Where S is the appropriate dimension matrix.

[0143] From the descriptive method, we can obtain:

[0144]

[0145] Where E is an invertible matrix.

[0146] From (10), (12), (14)-(17), we can obtain:

[0147]

[0148] in, col{…} represents a column vector.

[0149] To facilitate the representation of complex matrices, matrix operators are defined:

[0150] l i =[0 n×(i-1)n ,I n ,0 n×(5-i)n],(i=1,2,3,4,5)

[0151] l0 = 0 n×5n

[0152] L = l1 + l2 + l3 + l4 + l5

[0153] Among them, I n For an n-dimensional unit vector, 0 a×b Let be the zero vector in row a and column b.

[0154] Then Φ can be represented as:

[0155]

[0156] Here, sym{…} denotes the sum of a matrix and its transpose, i.e., sym{A} = A + A. T .

[0157] Depend on When Φ < 0, we can obtain:

[0158]

[0159] Therefore, the closed-loop system (9) is asymptotically stable. That is, a sufficient condition for the asymptotic stability of the closed-loop system (9) is Φ < 0.

[0160] By integrating both sides of inequality (18), we can obtain:

[0161]

[0162] Right now

[0163] J≤V(0)-V(∞)≤V(0)

[0164] From the initial condition (11), we can obtain V(0) = x T (0)Px(0)+τ M x T If (0)Qx(0), then the upper bound of the cost function J can be expressed as:

[0165] J≤x T (0)Px(0)+τ M x T (0)Qx(0) (19)

[0166] S2.3, based on S2.2, presents a joint design method for controller gain and trigger matrix that depends on unknown model parameters:

[0167] When the controller gain K is unknown, the matrix inequality Φ<0 in S2.2 is non-convex. The inverse of the invertible matrix E is expressed as... By transforming the matrix in S2.2 We can obtain:

[0168]

[0169]

[0170] in,

[0171] By Schur's complement lemma, the matrix It can be rewritten as:

[0172]

[0173] in,

[0174]

[0175] From matrix inequalities K can be calculated E , Therefore, the controller gain K = K E E and trigger matrix

[0176] S3. Continuously stimulate the system offline and collect data, and jointly design the controller gain and triggering matrix based on the data:

[0177] S3.1 Offline Data Acquisition and Quadratic Data-Driven System Representation:

[0178] Since the joint design method in S2 is based on the premise that the model parameters A and B are known, it is necessary to use data to apply matrix inequalities. To express it in a non-parametric manner.

[0179] First, the system (1) is continuously stimulated offline to collect input and status data. Considering the influence of external disturbances, sensor measurement noise, and other factors on data acquisition, the system (1) can be expressed as:

[0180]

[0181] in Represents unknown disturbances and noise, t≥0, B w For a full-rank, well-dimensional matrix, B can typically be set. w =I.

[0182] Assume the data acquisition time sequence is That is, data was collected N times. The following data matrix is ​​defined:

[0183]

[0184] X = [x(T1), x(T2), ..., x(T)] N )]

[0185] U = [u(T1), u(T2), ..., u(T)] N )]

[0186] W = [w(T1), w(T2), ..., w(T)] N )]

[0187] X and U can usually be measured directly. It can be estimated using methods such as finite difference finite differences. Note that when continuously exciting the system, the data matrix is ​​required. Since X and U are measurable, the condition for full rank can be directly obtained. Clearly, the following equation holds:

[0188]

[0189] This method only requires the assumption that the noise w(t) is bounded, without needing statistical information about the noise, which is more realistic. The set of noise data matrices satisfying the boundedness condition is defined as W, which can be expressed as:

[0190]

[0191] Q w It is a negative definite matrix, S w R w For a well-posed matrix, m d ×N-dimensional real matrix.

[0192] The inequality in equation (23) is a general expression. When Q is selected... w =-I,S w =0, When, the inequality in equation (23) can be simplified to:

[0193]

[0194] in, Let w(t) denote the upper bound of the 2-norm of the noise. When the noise satisfies the inequality in the bounded condition (23), the set of system parameters (AB) dependent on the measurement data is defined as follows:

[0195]

[0196] From the inequalities in equations (22) and (23), we can obtain the following through mathematical transformation:

[0197]

[0198] in, Therefore, when the noise satisfies the inequality in the bounded condition (23), the set (25) of system parameters (AB) dependent on the measurement data can also be equivalently expressed as:

[0199]

[0200] in,

[0201] Next, the controller design results in S2.2 will be further processed based on the data-based model parameter expression described above.

[0202] S3.2, based on S3.1 and S2.3, utilizes mathematical tools such as the full-block S-procedure to jointly design the controller gain and triggering matrix based on data.

[0203] As shown in S2.3, by solving the linear matrix inequalities... The controller gain and triggering matrix that make the system asymptotically stable when the cost function is less than its upper bound can be calculated. (Rewrite the matrix.) as follows:

[0204]

[0205] in,

[0206]

[0207] Furthermore, regarding matrices The linear matrix inequality can be expressed as:

[0208]

[0209] in,

[0210] From the matrix inequalities in equation (26), combined with equation (28), and through the S-procedure, we can obtain:

[0211]

[0212] Where λ is a constant. That is, if there exists a constant λ such that equation (29) holds, then the inequality in equation (26) is a sufficient condition for equation (28).

[0213] In summary, when the upper bound of the noise from offline data acquisition satisfies the inequality in equation (23), the controller gain K = K can be calculated by solving the linear matrix inequalities (16) and (29). W E and trigger matrix

[0214] Next, we will conduct experimental simulation verification.

[0215] A small deviation state-space model is selected for a certain type of aero-engine operating at its maximum idle state on the ground, with a flight altitude H = 0 km and a Mach number Ma = 0.

[0216]

[0217] Since the controller design method in this invention is data-based, the system parameter matrices A and B are not directly used when designing the controller. Instead, the input and state data collected after continuous excitation of the system are used. First, 100 sets of input data are obtained by random sampling from [-1,1]. By setting the parameter Q in the inequality in equation (23)... w =-I,S w =0, When this condition is met, the 2-norm bounded condition for noise, as shown in equation (24), is obtained for noise w(t) in... 100 sets of noise data were obtained through random sampling. Based on the data matrix relationship shown in equation (22), set B w =I, using the input data to continuously excite the open-loop system (1), thereby obtaining 100 sets of state data. The sampling interval during data acquisition is as follows:

[0218] T k -T k-1 =1.5, k∈[2,50]

[0219] T k -T k-1 =3, k∈[51,100]

[0220] Based on the obtained data, the trigger condition parameter σ = 0.5 and the maximum trigger interval τ are set. M =0.02, simulation time is 4s. Solving linear matrix inequalities (16) and (29), the controller gain and trigger matrix are obtained as follows:

[0221]

[0222]

[0223] Under the aforementioned controller and triggering conditions, the system's state trajectory is as follows: Figure 4 As shown in the figure, under the action of the data-based controller and triggering matrix, the system state converges well, indicating that the data-based periodic event-triggered cost-preservation controller can effectively stabilize the distributed control system of aero-engines. The triggering time and triggering interval are as follows: Figure 5As shown in the figure, within the set simulation time, the sensor sampled a total of 200 state data packets. Under the periodic event triggering mechanism (2), only 25 state data packets were transmitted to the controller, accounting for 12.5% ​​of the total sampled data. This indicates that the periodic event triggering mechanism (2) greatly reduces the number of transmissions and controller updates while maintaining stable system performance, effectively saving network and computing resources. The low-pressure rotor speed trajectory of the system under different transmission delays is shown in the figure. Figure 6 As shown. Where τ M They were set to 0.02, 0.03, and 0.04 respectively. Because... Therefore, when the sensor sampling period h = 0.02 during system operation, it means the maximum transmission delay. The values ​​are 0, 0.01, and 0.02, respectively. As shown in the figure, the system state converges well under different transmission delays. When the delay is large, the convergence speed of the system state decreases, indicating that the delay will reduce the system performance to some extent.

[0224] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A data-based distributed periodic event-triggered cost-constrained control method for aeroengines, characterized in that, The method comprises the following steps: S1. establishing an aero-engine distributed periodic event-triggered system model; S2. based on the Lyapunov-Krasovskii functional method, solving the upper bound of the cost function and giving a controller gain design method dependent on unknown model parameters; S3. off-line continuous excitation of the system and data collection, joint design of the controller gain and the trigger matrix based on the data; The step S1 comprises: S1.1 establishing an aero-engine distributed system model: The small deviation state space model of the aero-engine distributed system is described as follows: (1) wherein, is a state variable of the system, is a system control input, and represent a vector of the system, a vector of the system, is a low pressure rotor speed, is a high pressure rotor speed, is a main fuel flow, is a nozzle area, B is a suitable dimensional matrix; For the convenience of system analysis and control design, it is assumed that the sensors in the above system are time-driven with a sampling period , the controller and the actuators are event-driven; there exists a time-varying bounded network-induced delay ; it is assumed that the data are transmitted in single packets without timing disorder; S1.2 establishing a closed-loop system model under periodic event-triggered control considering time delay: In order to reduce the consumption of network resources, a periodic event-triggered mechanism is adopted to control the system (1); The periodic event-triggered mechanism includes two steps, the first step is that the sensor samples periodically with a fixed sampling period The system (1) is sampled, and the sampling time is represented as , is a non-negative integer, and the second step is to check whether the system state collected by the sensor satisfies the trigger condition. If the trigger condition is satisfied, the sampling state is transmitted to the controller, and the sampling time is the trigger time At this time, the sampling time between two adjacent trigger times and is represented as , is a positive integer; if the trigger condition is not satisfied, the control input is kept by the zero-order holder The state value of the last successful transmission until the next trigger time, in summary, the design of the periodic event-triggered mechanism is as follows: (2) wherein is a triggering parameter, is a positive definite matrix, i.e. a triggering matrix jointly designed with the controller gain, when the periodic event-triggered mechanism is a periodic triggered mechanism, considering the time-varying network-induced delay, it is assumed that the system state is collected by the sensor at time, then it will be transmitted to the controller at time, wherein ; According to the above analysis, a state feedback controller is introduced: (3) wherein is the state feedback gain; According to the analysis, the closed loop expression of the system (1) under the periodic event-triggered mechanism is as follows: (4) wherein ; The step S2 comprises: S2.1 establishing a cost function: For aero-engine distributed system, in order to balance the contradiction between network service quality and control performance, the cost function is introduced As the target function of the periodic event trigger mechanism and the controller, it ensures that the system maintains good response performance under periodic event trigger control. The cost function is expressed as: (5) wherein and are symmetric positive definite matrices, the controller gain and the triggering matrix are jointly designed to guarantee that the closed-loop system (9) is asymptotically stable and to compute an upper bound of the cost function (12) under the premise that the cost function (12) is less than an upper bound. S2.2 constructing a Lyapunov-Krasovskii functional to obtain a stability criterion of the closed-loop system under periodic event-triggered control and calculating the cost upper bound: For the closed-loop system (4), a Lyapunov-Krasovskii functional of the following form is constructed: (6) wherein , and are symmetric positive definite matrices, and are integration variables; By deriving (6) and making it less than 0, a stability criterion based on the following linear matrix inequality is obtained by using the Park lemma and the description method: (7) (8) wherein is a suitable matrix, and matrix is represented as follows: wherein is a reversible matrix, the matrix operator is represented as: wherein is a unit vector in the direction of is a zero vector of dimension a by b, matrix is represented as: denotes the sum of a matrix and its transpose, i.e. , By calculation, the cost function The upper bound is expressed as: (9) S2.3 based on S2.2, a joint design method of the controller gain and the trigger matrix dependent on unknown model parameters is given: To solve the controller gain by matrix inequality The inverse matrix of the invertible matrix is expressed as By transforming the matrix in S2.2 , we get: wherein , From matrix inequalities , Calculate , , Thus, the controller gain is obtained. With trigger matrix ; The step S3 comprises: S3.1 off-line data collection and quadratic data-driven system expression: Considering the joint design method in S2 is based on model parameters and known, therefore need to use data on the matrix inequality non-parametric expression, first in the case of off-line system (1) for continuous excitation, input and state data collection, considering the external disturbance, sensor measurement noise factors on data collection, system (1) is expressed as: (10) wherein represents unknown disturbances and noise, , is a full rank dimensional matrix, usually set as , assuming the data acquisition time sequence as , that is, the data is collected times, define the following data matrix: Apparently, the following equation is established: (11) The method only needs to assume that the noise is bounded, without the statistical information of the noise, which is more practical. The set of noise data matrices that satisfy the bounded condition is defined as , is expressed as: (12) where is a negative definite matrix, , is a positive definite matrix, denotes a real matrix of dimension n x n, when , , the inequality in (23) simplifies to (13) where represents an upper bound on the 2-norm of the noise when the noise satisfies the inequality in the boundedness condition (12), in terms of the system parameters The set of system parameters (14) wherein , Next, the controller design result in S2.2 will be processed according to the above data-based model parameter expression; S3.2 based on S3.1 and S2.3, the controller gain and the trigger matrix are jointly designed based on data by using the full-block S-procedure mathematical tool: From S2.3, the controller gain and the triggering matrix that make the cost function smaller than its upper bound and make the system asymptotically stable are calculated by solving the linear matrix inequality , , and rewriting the matrix as follows: (15) wherein , , center matrix is represented as: From the matrix inequality in equation (12), combined with equation (15), by S-procedure, we get: (16) In summary, when the noise upper bound of the offline data collection satisfies the inequality in equation (12), the controller gain is calculated by solving the linear matrix inequalities (7) and (16) with the trigger matrix .

Images