A data-driven event-triggered control method for steam-water heat exchangers

Abstract

The present invention discloses an event-triggered control method for a steam-water heat exchanger system based on data-driven. The method first constructs an output dynamic estimation method based on a compact data model, using the output at the trigger time or the estimated output at the trigger interval, and then updates the pseudo partial derivative and the control input through the estimated output. Then, an output trigger mechanism consisting of a true tracking error and an estimated error is proposed, and finally a controller is designed to make the output tracking error of the steam-water heat exchanger system ultimately uniformly bounded. Compared with the traditional data-driven trigger mechanism, this method is a new triggering method. When the method is applied to a network control system, it reduces the communication transmission frequency, effectively saves network resources, and has certain engineering application value.

Description

Technical Field

[0001] The present invention relates to a control method for a steam-water heat exchanger system, and in particular to an event-triggered control method for a steam-water heat exchanger system based on data drive. Background Art

[0002] Due to the complexity of the usage scenarios, steam-water heat exchangers usually use network control that is easy to install and has strong scalability. However, due to limited network bandwidth, data packets inevitably have problems such as delay, packet loss, and timing disorder during network transmission. How to reduce the frequency of communication transmission without sacrificing ideal stability and performance, event-triggered control is particularly important. In an event-triggered control environment, communication transmission will only take place when the preset conditions are violated. Based on this idea, researchers have conducted a lot of research on the design of trigger conditions and achieved a series of results.

[0003] However, the above research work mainly focuses on the situation where the mathematical model of the steam-water heat exchanger system can be established, and does not consider how to control the steam-water heat exchanger system without a model. For actual steam-water heat exchangers, it is difficult or even impossible to obtain an accurate model due to the inherent unmodeled dynamic characteristics. In order to break away from the constraints of the system model, it is necessary to study methods to design controllers using only input and output data. Summary of the invention

[0004] The purpose of the present invention is to propose an event-triggered control method for a steam-water heat exchanger system based on data-driven, which can effectively solve the problem of a steam-water heat exchanger system that cannot be modeled and has limited bandwidth in a network environment.

[0005] The specific technical solution of the present invention is as follows: An event-triggered control method for a steam-water heat exchanger system based on data drive comprises the following steps:

[0006] Using dynamic linearization technology, a compact data model of the steam-water heat exchanger system is established, and based on this data model, an output dynamic estimation method is constructed using the output at the triggering moment or the estimated output at the triggering interval, and then the pseudo partial derivatives and control inputs are updated through the estimated output;

[0007] Design an output trigger mechanism consisting of true tracking error and estimated error to reduce the communication transmission frequency;

[0008] Controlling a steam-water heat exchanger system using an event-based controller.

[0009] Further, the discrete mathematical expression of the steam-water heat exchanger system is as follows:

[0010] y k (t+1)=f(y k (t), ..., y k (tn y ),u k (t), ..., u k (tn u ))

[0011] In the formula, y k (t)∈R p Indicates system output, u k (t)∈R p represents the system input, p is related to the system dimension and is a known integer, t∈{0, 1, ...T} represents the sampling time, k∈{1, 2....} represents the iteration batch, f(·) represents the unknown nonlinear function, n y and n u Represents the unknown system order.

[0012] Furthermore, the specific steps of designing an output trigger mechanism composed of a true tracking error and an estimated error include: obtaining a compact data model of the steam-water heat exchanger system, constructing an output dynamic estimation method driven by the output at the trigger time or the estimated output at the trigger interval based on the model; using the optimal criterion function, using the input and output data to design pseudo partial derivatives respectively and control input u k (t); The difference of the Lyapunov function of the steam-water heat exchanger closed-loop control system is obtained and required to be negative definite, thereby obtaining an output trigger mechanism composed of a true tracking error and an estimation error.

[0013] Furthermore, a compact data model of the steam-water heat exchanger system is obtained, and based on this model, an output dynamic estimation method driven by the output at the trigger time or the estimated output at the trigger interval is constructed; using the optimal criterion function, the pseudo partial derivatives are designed using the input and output data respectively. and control input u k (t); obtain the difference of the Lyapunov function of the steam-water heat exchanger closed-loop control system and require it to be negative definite, and derive the output trigger mechanism composed of the true tracking error and the estimated error, which specifically includes:

[0014] Using dynamic linearization technology, a compact data model of the steam-water heat exchanger system is obtained as follows:

[0015] Δy k (t+1)=Φ k (t)Δu k (t)

[0016] In the formula, ||Φ k (t)||≤b(b>0) is called pseudo partial derivative, Δy k (t+1)=y k (t+1)-y k-1 (t+1), Δu k (t) = u k (t)-u k-1 (t);

[0017] Define a discrete sequence of events {k l}, l = 1, ..., in an event-triggered environment, based on the compact data model of the steam-water heat exchanger system, an output estimation method is constructed using the output at the triggering moment or the estimated output at the triggering interval, as shown below:

[0018]

[0019] and Respectively represent y k (t+1) and Φ k (t) is an estimated value;

[0020] Using the optimal criterion function, design pseudo partial derivatives using input and output data Update algorithm; select the following cost function:

[0021]

[0022] Solve the equation Under the triggering environment, the pseudo partial derivative is obtained The update algorithm is as follows:

[0023]

[0024] Where 0<η<1, μ>0 are selected parameters. The algorithm can ensure the pseudo partial derivative Φ k (t) The estimation error is bounded. The proof process is as follows:

[0025] C001: Due to The updated value at the trigger interval is equal to the updated value at the last trigger time, so we only need to prove that at the trigger time It is bounded;

[0026] C002: Define Φ k The estimated error of (t) Subtract both sides of the above equation The following formula is obtained:

[0027]

[0028] C003: From the compact format model, we can get Therefore, the above formula can be further derived into:

[0029]

[0030] C004: Because 0<η<1, μ>0, there exists d1 that makes the following equation true:

[0031]

[0032] C005: Substituting the above formula into the formula in C003, we can get:

[0033]

[0034] C006: The above formula can be further recursively derived into:

[0035]

[0036] C007: As the iteration proceeds, i.e., l→∞, the above formula shows that the observation error Converge to this boundary End of proof;

[0037] Using the optimal criterion function, use the input and output data to design the control input u k (t) update algorithm; select the following cost function:

[0038] J(u k (t))=|y * (t+1)-y k (t+1)| 2 +|u k (t)-u k-1 (t)| 2

[0039] Solve the equation Get event-based control input u k (t) Update the algorithm as follows:

[0040]

[0041] In the formula, y * (t+1) represents the desired trajectory to be tracked, ρ>0, λ>0 are the selected parameters;

[0042] Get the Lyapunov function of the closed-loop control system of the steam-water heat exchanger in the following form:

[0043] V k =e k (t+1) 2

[0044] In the formula, e k (t+1)=y * (t+1)-y k (t+1) represents the tracking error. At the non-triggering moment, the difference of the Lyapunov function of the steam-water heat exchanger closed-loop control system is obtained and required to be negative definite, and the following output trigger condition is obtained:

[0045]

[0046] In the formula, χ(e ETk (t+1), e k (t+1))=D(e ETk (t+1))-Λe k (t+1)e ETk (t+1), Λ=(2(1-ν)) / ν, D(e ETk (t+1)) is a dead zone function if |e k (t+1)|>B e , Otherwise, D(e ETk (t+1))=0, B e is a selected constant. Under the designed output trigger condition, the event-based controller can ensure that the output tracking error of the steam-water heat exchanger closed-loop control system is bounded. The proof process is as follows:

[0047] C008: The proof is divided into two steps. First, it is proved that the output tracking error of the steam-water heat exchanger closed-loop control system is bounded at the triggering moment, and then it is proved that the output tracking error of the system is also bounded during the triggering interval.

[0048] C009: At the triggering moment, k = k l , select the following Lyapunov function:

[0049] V k =e k (t+1) 2

[0050] C010: Difference of Lyapunov functions

[0051] C011: Combining the compact data model and the control rate update algorithm, the tracking error of the closed-loop control system is derived as follows:

[0052]

[0053] C012: Because |Φ k (t)|<b, where 0<ρ<1 and λ>λmin So that the following is true:

[0054]

[0055] C013: Substitute the above formula into the formula in C011 to obtain the following formula:

[0056]

[0057] C014: Therefore, at the triggering moment, the output tracking error of the closed-loop control system is bounded;

[0058] C015: In the trigger interval, that is, k l <k<k l+1 , define the trigger error The tracking error e k+1 (t+1) has the following form:

[0059]

[0060] C016: In the formula,

[0061] C017: According to the formula in C015, the Lyapunov function at the trigger interval can be derived as:

[0062]

[0063] C018: The above formula can be further expanded into:

[0064]

[0065] C019: Because Φ k+1 (t) can be Instead, therefore It can be seen from the designed output trigger conditions that during the trigger interval, the output tracking error of the closed-loop control system is bounded. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0067] Figure 2 This is a diagram showing the number of data transmissions when the method proposed in the present invention is iterated 60 times in an embodiment;

[0068] Figure 3 Output tracking graph of the 10th iteration using the method and non-event triggering method of the present invention in the embodiment;

[0069] Figure 4Output tracking graph of the embodiment using the method proposed by the present invention and the non-event triggering method at the 20th iteration;

[0070] Figure 5 Output tracking graph of the embodiment using the method proposed by the present invention and the non-event triggering method at the 60th iteration; DETAILED DESCRIPTION

[0071] The present invention is further explained below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0072] like Figure 1 As shown, an event-triggered control method for a steam-water heat exchanger system based on data drive comprises the following steps:

[0073] Step 1: Set the initial value of the parameter;

[0074] Step 2: Update pseudo partial derivatives

[0075] Step 3: Use the updated Information, update control input u k (t);

[0076] Step 4: (1) Using known and u k (t), calculate the estimated output and passed into the trigger mechanism; (2) control input u k (t) is fed into the steam-water heat exchanger system to produce the actual output y k (t+1) and passed into the trigger mechanism;

[0077] Step 5: Determine whether the trigger condition is met. If so, the system actually outputs y k (t+1) is transmitted to the control end through the network, otherwise, the estimated output Enter the control terminal;

[0078] Step 6: Repeat step 2 to enter the next cycle.

[0079] An embodiment of the present invention is described below:

[0080] Consider the output tracking control problem of the steam-water heat exchanger system, which corresponds to the Hammerstein space model:

[0081]

[0082] The expected tracking trajectory is:

[0083]

[0084] Figure 1 is a flow chart of the method of an embodiment of the present invention; applying the proposed method, the sum of the triggering moments of 60 iterations is as follows Figure 2 As shown, it can be seen that only 14% (3373 / 24000) are triggered during the iteration; Figure 3 , 4 ,5 show the output trajectories of the proposed event triggered method and the non-event triggered method at the 10th, 20th and 60th iterations.,From these three figures, it can be seen that the proposed method not only,effectively reduces the communication frequency, but also,can obtain a satisfactory tracking performance after the 60th,iteration.

[0085] References

[0086] [1] S.Wang,

[0087] [2]Z.Hou, S.Jin.Data-driven model-free adaptive control for a class ofMIMO nonlinear discrete-time systems.IEEE Transactions on Neural Networks, vol.22, pp.2173-2188, 2011.

Claims

1. An event-triggered control method for a steam-water heat exchanger system based on data drive, characterized in that: The following steps are involved: Using dynamic linearization technology, a compact data model of the steam-water heat exchanger system is established. Based on this data model, an output dynamic estimation method is constructed using the output at the trigger time or the estimated output at the trigger interval. Then, the pseudo partial derivatives and control inputs are updated through the estimated output. An output trigger mechanism consisting of the true tracking error and the estimated error is designed to reduce the communication transmission frequency. The steam-water heat exchanger system is controlled using an event-based controller, as follows: The discrete mathematical expression of the steam-water heat exchanger system is as follows: y k (t+1)=f(y k (t),...,y k (t-n y ),u k (t),...,u k (t-n u )) In the formula, y k (t)∈R p Indicates system output, u k (t)∈R p represents the system input, p is related to the system dimension and is a known integer, t∈{0,1,...T} represents the sampling time, k∈{1,2....} represents the iteration batch, f(·) represents the unknown nonlinear function, n y and n u Represent the unknown system order, obtain the compact data model of the steam-water heat exchanger system, construct an output dynamic estimation method driven by the output at the trigger time or the estimated output at the trigger interval based on this model, use the optimal criterion function, and use the input and output data to design the pseudo partial derivatives respectively and control input u k (t) is updated by obtaining the difference of the Lyapunov function of the steam-water heat exchanger closed-loop control system and requiring it to be negative definite, thereby obtaining an output trigger mechanism consisting of the true tracking error and the estimation error, which specifically includes: (1) Using dynamic linearization technology, a compact data model of the steam-water heat exchanger system is obtained as follows: Δy k (t+1)=Φ k (t)D k (t) In the formula, ‖Φ k (t)‖≤b(b>0) is called pseudo partial derivative, Δy k (t+1)=y k (t+1)-y k-1 (t+1), Δu k (t) = u k (t)-u k-1 (t), y k (t)∈R p Indicates system output, u k (t)∈R p represents the system input, p is related to the system dimension and is a known integer, t∈{0,1,...T} represents the sampling time, and k∈{1,2....} represents the iteration batch; (2) Define a discrete sequence of events {k l }, l=1,..., in the event-triggered environment, based on the compact data model of the steam-water heat exchanger system, an output estimation method is constructed using the output at the triggering moment or the estimated output at the triggering interval, as shown below: In the formula, and Respectively represent y k (t+1) and Φ k (t) is an estimated value; (3) Using the optimal criterion function, use the input and output data to design pseudo partial derivatives Update algorithm; select the following cost function: Solve the equation Under the triggering environment, the pseudo partial derivative is obtained The update algorithm is as follows: Where 0<η<1,μ>0 are the selected parameters. The algorithm can ensure the pseudo partial derivative Φ k (t) The estimation error is bounded. The proof process is as follows: B001: Due to The updated value at the trigger interval is equal to the updated value at the last trigger time, so we only need to prove that at the trigger time It is bounded; B002:Define Φ k The estimated error of (t) Subtract both sides of the above equation The following formula is obtained: B003: From the compact format model, we can get Therefore, the above formula can be further derived into: B004: Because 0<η<1,μ>0, there exists d1 that makes the following equation true: B005: Substituting the above formula into the formula in B003, we can get: B006: The above formula can be further recursively derived into: B007: As the iteration proceeds, i.e., l→∞, the above formula shows that the observation error Converge to this boundary End of proof; (4) Using the optimal criterion function, use the input and output data to design the control input u k (t) update algorithm; select the following cost function: J(u k (t))=|y * (t+1)-y k (t+1)| 2 +|u k (t)-u k-1 (t)| 2 Solve the equation Get event-based control input u k (t) Update the algorithm as follows: In the formula, y * (t+1) represents the desired trajectory to be tracked, ρ>0, λ>0 are the selected parameters; (5) Obtain the Lyapunov function of the closed-loop control system of the steam-water heat exchanger in the following form: V k =e k (t+1) 2 In the formula, e k (t+1)=y * (t+1)-y k (t+1) represents the tracking error. At the non-triggering moment, the difference of the Lyapunov function of the steam-water heat exchanger closed-loop control system is obtained and required to be negative definite, and the following output trigger condition is obtained: In the formula, χ(e ETk (t+1),e k (t+1))=D(e ETk (t+1))-Λe k (t+1)e ETk (t+1), Λ=(2(1-ν)) / ν, D(e ETk (t+1)) is a dead zone function if |e k (t+1)|>B e , Otherwise, D(e ETk (t+1))=0, B e is a chosen constant, Under the designed output triggering conditions, the event-based controller can ensure that the output tracking error of the steam-water heat exchanger closed-loop control system is bounded. The proof process is as follows: B008: The proof is divided into two steps. First, it is proved that the output tracking error of the steam-water heat exchanger closed-loop control system is bounded at the triggering moment, and then it is proved that the output tracking error of the system is also bounded during the triggering interval. B009: At the triggering moment, k = k l , select the following Lyapunov function: V k =e k (t+1) 2 B010: Finding the difference of Lyapunov function B011: Combining the compact data model and the control rate update algorithm, the tracking error of the closed-loop control system is derived as follows: B012: Because |Φ k (t)|<b, where 0<ρ<1 and λ>λ min So that the following is true: B013: Substitute the above formula into the formula in B011 to obtain the following formula: B014: Therefore, at the triggering moment, the output tracking error of the closed-loop control system is bounded; B015: In the trigger interval, i.e. k l <k<k l+1 , define the trigger error The tracking error e k+1 (t+1) has the following form: B016: In the formula, B017: According to the formula in B015, the Lyapunov function at the trigger interval can be derived as: B018: The above formula can be further expanded into: B019: Because Φ k+1 (t) can be Instead, therefore It can be seen from the designed output trigger conditions that during the trigger interval, the output tracking error of the closed-loop control system is bounded.

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