Data-driven predictive control method for discrete networked control system

Abstract

The invention discloses a data-driven predictive control method for a discrete networked control system, and belongs to the field of network predictive control. The invention discusses a data-driven predictive control problem of a network control system with communication delay and unknown model parameters; a new data-driven predictive control algorithm is designed by constructing a Hankel matrix so as to ensure the stability of a closed-loop system under the influence of network time delay. On the basis, a linear matrix inequality method based on a database is provided to design a networked prediction controller; a numerical example shows that the method can achieve an effect similar to that of a traditional method while actively compensating network time delay.

Description

Technical Field

[0001] The present invention belongs to the field of network predictive control, and in particular relates to a data-driven predictive control method for a discrete networked control system. Background Art

[0002] With the trend of modern control systems becoming increasingly networked, digital, and information-based, NCS has become a research hotspot in the field of control. In NCS, network delay is inevitable, which may lead to system performance degradation or even instability. Therefore, how to tolerate the maximum delay as much as possible while ensuring stability is the focus of this type of research.

[0003] Early studies used the Lyapunov-Krasovskii (LK) method to study the mean square stability of time-delay systems. Later, by improving the LK method, time-delay-dependent stability conditions were given. However, these studies focused on continuous-time NCS rather than discrete-time NCS. Later, some improved time-delay-dependent stability criteria were established by introducing the free weight matrix. The improved free weight matrix method and the improved LK method were proposed, and the results were extended to discrete systems. However, the above results deal with time delays passively, resulting in limited applications.

[0004] At present, in the research of NCS, a network predictive control method with lower conservatism that can actively compensate for time delay has been proposed. The core idea of ​​this method is to calculate the future control strategy by predicting the future behavior of the system, and actively compensate the impact of delay on the system through the delay compensator. Sometimes, accurate models in industrial systems are difficult to obtain, and a large amount of process data that may contain potentially useful information is saved. Therefore, researchers combined the NPC method with the data-driven control method and proposed data-driven NPC strategies, such as PID-like predictive control, model-free adaptive NPC, etc. However, the above methods all have their scope of application, and completely abandon the research and analysis methods based on model control theory.

[0005] In order to utilize prior knowledge, researchers have explored the combination of data and models in their research. The combination of data-based and model-based methods can take advantage of their advantages. This type of method was originally called system identification, which refers to the process of inferring and modeling the dynamic behavior of an unknown system. The goal is to obtain the internal mechanism of the system by analyzing the relationship between the input and output of the system. The first method is parameterization, which first assumes that the dynamic behavior of the system can be described by a set of parameterized mathematical models, and then uses actual input and output data to estimate these parameters. By minimizing the error between the parameters and the actual data, an estimate of the dynamic behavior of the system can be obtained. The advantage of the parameterized method is that the model structure is clear, but the model structure and parameters need to be selected in advance. The second is the non-parametric method, which infers the dynamic behavior of the system by analyzing and processing data. The non-parametric method is more flexible and does not require the selection of a specific mathematical model in advance, but it may be more time-consuming than the parametric method when processing large amounts of data. The third is the subspace method, which extracts important features of the system from the subspace of the signal by decomposing or reducing the input and output data, thereby achieving modeling of the dynamic behavior of the system.

[0006] Later, by reorganizing these data and combining them with stability theory, a stability judgment method based on process data and a stable controller design method were proposed. However, this method becomes more complicated when dealing with network control systems with time delays. Summary of the invention

[0007] In view of the above-mentioned technical problems existing in the prior art, the present invention proposes a data-driven predictive control method for a discrete networked control system, which has a reasonable design, overcomes the shortcomings of the prior art, and has good effects.

[0008] In order to achieve the above object, the present invention adopts the following technical solution:

[0009] A data-driven predictive control method for a discrete networked control system, using sensors, controllers, and actuators; comprising the following steps:

[0010] S1: Collect normal system experimental data and make NCS with unknown model parameters and time delay;

[0011] S2: Pack the status data collected by the sensor and send it to the controller. Step length prediction;

[0012] S3: Send the prediction control signal to the actuator, and the network delay compensator on the actuator side selects the appropriate control law according to the delay size;

[0013] S4: Convert the model-based system to a data-based form, obtain further predictions and state feedback controller gains, and calculate future Step state prediction;

[0014] S5: Numerical example, analysis of simulation results.

[0015] Preferably, in S1, considering that both the feedforward and feedback channels have delays, the delay is uniformly defined as d = d sc +d ca , where d sc is the delay of the feedback channel, d ca is the delay of the forward path.

[0016] Preferably, in S2, the controller side calculates When predicting step length, is the assumed upper bound of the delay, and if a state feedback controller is adopted, it is further predicted as:

[0017]

[0018] The corresponding data-driven feedback controller is expressed as:

[0019] u(kd)=U 0,1,N Q(X 0,N Q) -1 x(kd)=Kx(kd);

[0020] In the formula, x(kd) is the data received by the actuator at time k, and K is obtained by the LMI method;

[0021] Λ=X 1,N Q(X 0,N Q) -1 ,K=U 0,1,N Q(X 0,N Q) -1 The eigenvalues ​​of and Λ are all inside the unit circle.

[0022] Preferably, the data-driven feedback controller is selected according to the size of the actual delay d, which is specifically expressed as u(k)=Λ d Kx(kd).

[0023] Preferably, S4 will be a model-based system Convert to data-based form: in, is the one-step prediction of the state vector; after obtaining the further prediction and the state feedback controller gain, the upper bound of the delay based on the assumption Computing the Future Step state prediction:

[0024] Among them, the delay meets the condition

[0025] Under the influence of time lag, the system is asymptotically stable if the following conditions are met:

[0026] in,

[0027] Preferably, a numerical example is performed in S5, firstly setting the values ​​of system parameters A and B, assuming that the network delay of the system is 10 steps and setting the initial state values ​​x(0) and u(0) of the system, obtaining the data-driven controller gain K, and finally performing simulation analysis on the system.

[0028] Beneficial technical effects brought by the present invention:

[0029] The method of the present invention studies the data-driven predictive control problem of the unknown parameter NCS with time delay. Based on the Hankel matrix, the data-dependent stability condition of the closed-loop unknown parameter NCS is given; then, a data-based LMI algorithm is proposed to design a suitable networked predictive controller; finally, simulation results are given to verify the effectiveness of the proposed strategy. The method of the present invention can effectively compensate for the influence of time delay. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 A flow chart of a data driven predictive control algorithm for a delayed discrete network control system;

[0031] Figure 2 This is a comparison diagram of the status with and without NPC under constant delay;

[0032] Figure 3 This is a comparison diagram of the status with and without NPC under random delay. DETAILED DESCRIPTION

[0033] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0034] First, define the following vector: x(k,N)=[x(k) T (k+1) T ···x(k+N-1) T ] T ,

[0035] Construct the Hankel matrix:

[0036] When M = 1, H k,N =[h(k)h(k+1)…h(k+N-1)].

[0037] Consider the following system: Where x(k)∈R n ,u(k)∈R mare the state vector and input vector respectively. p is the measured output. A, B, C, D are the unknown parameters of the system. The traditional method is to use data to identify them. Here, the identification process is omitted and the stability is analyzed directly using process data.

[0038] By adding N-1 step process data, the above classical state equation can be converted into input and output form: Among them, x0 is the initial state, then:

[0039]

[0040] If u(0,N-1) is continuously excited, the I / O trajectory of any m-length system can be expressed as: Where g∈R n-m+1 .

[0041] And the following equation holds:

[0042] Collect normal system experimental data and write it into the following table:

[0043]

[0044] It can be extended to H matrix form as follows:

[0045] The above describes the basic idea of ​​this data-driven control algorithm, but for NCS or time-delay system, the existence of time delay is inevitable. The main purpose of this paper is to design a reasonable data-driven controller to make such NCS with unknown model parameters and time delay based only on process data without system identification.

[0046] Embodiment 1

[0047] This embodiment provides a new operation process of a data-driven predictive control algorithm for a delayed discrete network control system under a constant delay condition.

[0048] Considering NCS with time delay in both feedforward and feedback channels, the delay is uniformly defined as d = d sc +d ca , where d sc is the delay of the feedback channel, d ca is the delay of the forward channel. The status data collected by the sensor is packaged and sent to the controller.

[0049] Calculated on the controller side Step length prediction, It is the assumed upper bound of delay. These predictive control signals are sent to the actuator side, and the network delay compensator on the actuator side selects the appropriate control law according to the size of the delay.

[0050] If a state feedback controller is used, the further prediction is: Where x(kd) is the data received by the actuator at time k.

[0051] Here we have: Where G is an N×n dimensional matrix. If the above equation is regarded as a non-homogeneous linear equation, then G is the only solution to the equation.

[0052] Then the matrix A+BK can be converted into the following form:

[0053]

[0054] Among them, X 1,N =[x(1)x(2)…x(N)].

[0055] Model-based systems Convert to data-based form: in, is the one-step prediction of the state vector.

[0056] The data-driven feedback controller can be expressed as: u(kd)=Kx(kd)=U 0,1,N Gx(kd).

[0057] Rewrite the above formula as:

[0058] u(kd)=U 0,1,N Q(X 0,N Q) -1 x(kd)=Kx(kd),

[0059] Where Λ=X 1,N Q(X 0,N Q) -1 ,K=U 0,1,N Q(X 0,N Q) -1 The eigenvalues ​​of and Λ are all inside the unit circle.

[0060] After further prediction and state feedback controller gain, the upper bound of the delay based on the assumption Computing the Future Step state prediction:

[0061] Among them, the delay meets the condition

[0062] Data-driven predictive control is:

[0063] in,

[0064] BK can be expressed as:

[0065] When the delay is d, that is, i = d, the controller is introduced into the system, and we get:

[0066] Among them, W=GL.

[0067] The augmented function of the closed-loop system and x(kd) forming a one-step prediction is:

[0068] in,

[0069] Under the influence of time lag d, the following conditions are satisfied so the system is asymptotically stable:

[0070] in,

[0071] make Q=GP,H=LP, then the sufficient condition for the system to be stable is: as long as the matrices Q, H and The following conditions are met: Then the system is asymptotically stable.

[0072] In addition, there are:

[0073] in, K=U 0,1,N Q(X 0,N Q) -1 .

[0074] Numerical example:

[0075] Set the system parameters to:

[0076] The system is only a collection of input variables and state variables, not a design of control law. Assume that the network delay of the system is 10 steps, and set the initial state value of the system to x(0) = [1-234] T , the initial input is 0. The data-driven controller gain is:

[0077] According to the simulation results, the control effect of the data-driven method proposed in this paper is similar to that of the pole configuration method. Figure 2 (b)) and the method without predictive control ( Figure 2(a)) are compared and the results show that the system will gradually diverge with the influence of delay, and the proposed method can effectively compensate for the influence of delay.

[0078] Embodiment 2

[0079] This embodiment provides a new operation process of a data-driven predictive control algorithm for a delayed discrete network control system under random delay conditions.

[0080] For random delay, we also regard it as the sum of the forward channel delay and the feedback channel delay, and its upper bound is A, the difference is that d(k) is random and satisfies the condition d(k).

[0081] One-step state prediction expression:

[0082] Among them, x(kd(k)) is the data received by the actuator at time k.

[0083] In this case, the one-step state prediction based on the data can be expressed as:

[0084]

[0085] The corresponding controller can be expressed as: u(kd(k))=Kx(kd(k))=U 0,1,N Gx(kd(k)).

[0086] On this basis, the status and control signals can be obtained. Step length prediction:

[0087]

[0088] Then the k-step predictive control signal is:

[0089] Bring the obtained control signal into the system to obtain:

[0090]

[0091] From this we can deduce: X(k+1)=ΩX(k),

[0092] in,

[0093]

[0094] When the random delay value is Within the range, the coefficient D of the closed-loop system X(k+1)=DX(k) is an upper triangular matrix, and when the eigenvalues ​​of the matrix are within the unit circle, the closed-loop system is ultimately uniformly asymptotically stable.

[0095] The closed-loop system X(k+1)=ΩX(k) is always asymptotically stable if and only if the matrix X 1,N The eigenvalues ​​of W and Λ are inside the unit circle.

[0096] Furthermore, according to the following conditions, the controller K can be obtained:

[0097]

[0098] Numerical example:

[0099] Set the system parameters to:

[0100] The system is only a set of input variables and state variables, not a design of control law. Assume that the network delay of the system is 10 steps, and set the initial state value of the system to x(0) = [1 -2 3 4] T , the initial input is 0. The data-driven controller gain can be obtained as:

[0101] Under the influence of random delay, the state responses using the NPC algorithm and not using the NPC algorithm are as follows Figure 3 As shown, Figure 3 (a) is the state response without active delay compensation method. The state response diverges significantly under the influence of delay. Figure 3 (b)) Compared with the simulation results, the simulation results finally converge. In addition, simulation is a data-driven control method, which can achieve similar results to those in known situations when the system coefficients are unknown.

[0102] This indicates that the method of the present invention is also applicable to the case where the upper bound of the random delay is known.

[0103] In summary, the data-driven predictive control problem of NCS with unknown parameters and time lag is studied in this paper. Based on the Hankel matrix, the data-dependent stability condition of the closed-loop unknown parameter NCS is given. Then, a data-based LMI algorithm is proposed to design a suitable networked predictive controller. Finally, simulation results are given to verify the effectiveness of the proposed strategy.

[0104] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A data-driven predictive control method for a discrete networked control system, characterized in that: Using sensors, controllers, and actuators; including the following steps: S1: Collect normal system experimental data and make NCS with unknown model parameters and time delay; S2: Pack the status data collected by the sensor and send it to the controller. Step length prediction; S3: Send the prediction control signal to the actuator, and the network delay compensator on the actuator side selects the appropriate control law according to the delay size; S4: Convert the model-based system to a data-based form, obtain further predictions and state feedback controller gains, and calculate future Step state prediction; S5: Numerical example, analysis of simulation results.

2. The discrete networked control system data-driven predictive control method according to claim 1, characterized in that: In S1, considering that both the feedforward and feedback channels have delays, the delay is uniformly defined as d = d sc +d ca , where d sc is the delay of the feedback channel, d ca is the delay of the forward path.

3. The discrete networked control system data-driven predictive control method according to claim 1, characterized in that: In S2, the controller side calculates When predicting step length, is the assumed upper bound of the delay, and if a state feedback controller is adopted, it is further predicted as: The corresponding data-driven feedback controller is expressed as: u(k-d)=U 0,1,N Q(X 0,N Q) -1 x(k-d)=Kx(k-d); In the formula, x(kd) is the data received by the actuator at time k, and K is obtained by the LMI method; Λ=X 1,N Q(X 0,N Q) -1 ,K=U 0,1,N Q(X 0,N Q) -1 The eigenvalues ​​of and Λ are all inside the unit circle.

4. The discrete networked control system data-driven predictive control method according to claim 3, characterized in that: The data-driven feedback controller is selected according to the actual delay d, which is specifically expressed as u(k)=Λ d Kx(kd).

5. The discrete networked control system data-driven predictive control method according to claim 1, characterized in that: S4 will be a model-based system Convert to data-based form: in, is the one-step prediction of the state vector; after obtaining the further prediction and the state feedback controller gain, the upper bound of the delay based on the assumption Computing the Future Step state prediction: Among them, the delay meets the condition Under the influence of time lag, the system is asymptotically stable if the following conditions are met: in, 6. The discrete networked control system data-driven predictive control method according to claim 1, characterized in that: In S5, a numerical example is performed. First, the values ​​of system parameters A and B are set. It is assumed that the network delay of the system is 10 steps and the initial state values ​​of the system are set to x(0) and u(0). The gain K of the data-driven controller is obtained, and finally the system is simulated and analyzed.

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