A data-driven event-triggered control method for a steam-water heat exchanger system with input saturation

Abstract

The present invention discloses a data-driven event-triggered control method for a steam-water heat exchanger system with input saturation. The method first obtains a compact data model of the steam-water heat exchanger system, and proposes a correction index that takes future costs into account based on the model to obtain an optimal controller; on the basis of the correction index, an improved dynamic penalty factor control law is constructed to ensure that the closed-loop error system is ultimately uniformly bounded; using instantaneous data and average data, a dynamic trigger mechanism that inserts a variable threshold is proposed. Compared with the traditional data-driven trigger mechanism, this method is a new triggering method. When applied to a network control system, this method reduces the frequency of communication transmission, 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, and in particular to a data-driven event-triggered control method for a steam-water heat exchanger system with input saturation. 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 a data-driven event-triggered control method for a steam-water heat exchanger system with input saturation, which can effectively solve the problem of limited bandwidth in a network environment for a steam-water heat exchanger system that cannot be modeled.

[0005] The specific technical scheme of the present invention is as follows: A data-driven event-triggered control method for a steam-water heat exchanger system with input saturation comprises the following steps:

[0006] A modified index considering future costs is proposed to obtain the optimal controller;

[0007] Based on the correction index, an improved dynamic penalty factor control law is constructed to ensure the final uniform boundedness of the closed-loop error system.

[0008] Using instantaneous data and average data, a dynamic trigger mechanism with variable thresholds inserted is proposed to reduce communication transmission when controlling the steam-water heat exchanger system.

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

[0010] y(k+1)=f(y(k),y(k-1),...,y(kc y ),u(k),u(k-1),...,u(kc u ))+d(k)

[0011] Where y(k)∈R m represents the output, u(k)∈R m represents the input, d(k)∈R m represents the disturbance, m represents the system dimension, which is a known integer, k∈{0, 1, ...T} represents the sampling time, f(·) represents the unknown nonlinear function, c y and c u Represents the unknown system order.

[0012] Furthermore, the specific steps of proposing a dynamic trigger mechanism for inserting a variable threshold using instantaneous data and average data include: obtaining a compact data model of the steam-water heat exchanger system, and proposing a correction index considering future costs based on this model to obtain the optimal controller; based on the correction index, constructing an improved dynamic penalty factor control law to ensure the ultimate consistent boundedness of the closed-loop error system; using instantaneous data and average data, proposing a dynamic trigger mechanism for inserting a variable threshold.

[0013] 5. Furthermore, a compact data model of the steam-water heat exchanger system is obtained. Based on this model, a correction index considering future costs is proposed to obtain the optimal controller. Based on the correction index, an improved dynamic penalty factor control law is constructed to ensure the final uniform boundedness of the closed-loop error system. Using instantaneous data and average data, a dynamic trigger mechanism with variable thresholds is proposed, which includes:

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

[0015] y(k+1)=y(k)+Φ(k)Δu(k)+Δd(k)

[0016] In the formula, is an unknown pseudo-partial derivative that satisfies Δy(k+1)=y(k+1)-y(k), Δu(k)=u(k)-u(k-1), Δd(k)=d(k)-d(k-1);

[0017] A saturation function is chosen to describe the system input saturation as follows:

[0018]

[0019] In the formula, ui (k) and u si (k) represent u(k) and u s (k) the i-th element, u s (k) represents saturated input, u min <0,u max >0,|u min |≠|u max |;

[0020] Define an event trigger sequence {k l}, l = 1, 2, ... N, the event trigger error is as follows:

[0021] e ET (k) = y(k) - y(k l )

[0022] In the formula, u i (k) and u si (k) represent u(k) and u s (k) the i-th element, u s (k) represents saturated input, u min <0,u max >0,|u min |≠|u max |;

[0023] An improved cost function is proposed to ensure that the controller designed under this cost function can guarantee the tracking performance under input saturation. The cost function is as follows:

[0024]

[0025] Solve the equation The optimal control rate u(k) in the event-triggered environment is obtained as follows:

[0026]

[0027] In the formula, 0<ρ<1, λ>0, τ>0, e(k+1)=r(k+1)-y(k+1), e l (k) = r(k) - y l (k) r(k+1) represents the expected output, u0(k) represents the initial admissible control, and γ(k) is the penalty factor to be designed;

[0028] Design the dynamic update rate of the penalty factor γ(k) as follows:

[0029]

[0030] For existing The estimation algorithm is modified to obtain the update algorithm in the event-triggered environment, as shown below:

[0031]

[0032] In the formula, 0<η<2, μ>0, the algorithm can ensure The estimation error is bounded, and the proof process is as follows:

[0033] A001: 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;

[0034] A002: Order The above formula is transformed into the following formula:

[0035]

[0036] A003: Definition Subtract ψ from both sides of A002 j (k) The following formula is obtained:

[0037]

[0038] A004: Definition The following formula is obtained:

[0039]

[0040] A005: According to the selection range of η and μ, the following formula can be obtained:

[0041]

[0042] A006: Substitute A005 into A004 to obtain the following formula:

[0043]

[0044] Where, 0<d1<1;

[0045] A007: Because available Substituting it and A006 into A003, we get the following formula:

[0046]

[0047] A008: When the number of sampling moments increases to infinity, that is, k→∞, the above formula shows that the observation error Converge to this boundary So It also converges to this bound, and the proof ends;

[0048] Using neural network to approximate J[e(k)], the loss function Applying the gradient descent algorithm, we get the update rate of the neural network weights as follows:

[0049]

[0050] Where, 0<α<1, At this weight update rate, the approximate error of the indicator function is ultimately uniformly bounded. The proof process is as follows:

[0051] A009: During the trigger interval, the output at the last trigger time is used to update Therefore, it is only necessary to prove the approximate error of the neural network weights at the triggering moment;

[0052] A010: Order Substituting the weight update rate into it, we get the following formula:

[0053]

[0054] In the formula,

[0055] A011: By transforming the equation, we can get the following equation:

[0056]

[0057] A012: Substitute A011 into A010 to obtain the following formula:

[0058]

[0059] A013: Select the following Lyapunov function:

[0060]

[0061] A014: Perform a differential operation on A013 and obtain the following formula:

[0062]

[0063] A015: Substitute A012 into A014 to obtain the following formula:

[0064]

[0065] A016: Because the system output is continuously excited, the following formula can be obtained:

[0066]

[0067] A017: Substitute A016 into A015 to obtain the following formula:

[0068]

[0069] A018: Select 0<α<1, and get the following formula:

[0070]

[0071] A019: Substitute A016 into A018 to obtain the following formula:

[0072]

[0073] A020: A019 indicates Converge to this boundary Inside, the proof ends;

[0074] Using instantaneous data and average data, a dynamic trigger mechanism for inserting variable thresholds is proposed as follows:

[0075] k l+1 =inf{k|k>k l ,||e ET (k)||>ε(k)||e(k)||}

[0076] In the formula, Under this trigger mechanism, the designed controller can ensure that the tracking error is bounded. The proof process is as follows:

[0077] A021: 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.

[0078] A022: At the triggering moment, k = k l , we get the following formula:

[0079] e(k+1)=r(k+1)-y(k+1)

[0080] =r(k+1)-y(k)-Φ(k)Δu s (k)-Δd(k)

[0081] A023: Substitute the control rate at the triggering moment into A022 to obtain the following formula:

[0082]

[0083] A024: Transform the equation Substituting into A023, we get the following formula:

[0084]

[0085] A025: Perform a two-norm operation on A024 and obtain the following formula:

[0086]

[0087] A026: Since -1<tanh(·)<1, we get the following formula:

[0088]

[0089] A027: Substituting -1<tanh(·)<1 and A026 into A025, we get the following formula:

[0090]

[0091] A028: Since Y is a constant matrix, we have Also because and The following formula can be obtained:

[0092]

[0093] A029: Depending on the range of parameters ρ, λ and τ, there exist positive constants d2 and d3 such that the following holds:

[0094]

[0095]

[0096] A030: Substitute A029 into A028 to obtain the following formula:

[0097]

[0098] A031: Δr(k+1) represents the rate of change of input, assuming Then the following formula holds:

[0099]

[0100] A032: Because (d2+d3)<0.2<1, e(k) converges to this boundary at the triggering moment. Inside;

[0101] A033: In the trigger interval, that is, k l <k<k l+1 , we get the following formula:

[0102]

[0103] A034: According to the definition of trigger error, the following formula is obtained:

[0104] r(k+1)-y(k_1)=Δr(k+1)+r(k)-y(k l )

[0105] =Δr(k+1)+r(k)-y(k)+e ET (k)

[0106] =Δr(k+1)+e(k)+e ET (k)

[0107] A035: Combining A034 and A033, we get the following formula:

[0108]

[0109] A036: and Substituting into A035, we get the following formula:

[0110]

[0111] A037: Perform a two-norm operation on A036 to obtain the following formula:

[0112]

[0113] A038: Note that the designed event triggering rules satisfy the following formula:

[0114]

[0115] A039: Substitute A038 into A037 to obtain the following formula:

[0116]

[0117] A040: According to the selection range of parameters ρ and λ, the following formula is obtained:

[0118]

[0119]

[0120] A041: Choose the right and τ make the following equation true:

[0121]

[0122]

[0123] A042: Combine A039, A040 and A041 to get the following formula:

[0124]

[0125] A043: Combining A040 and A042, we get the following formula:

[0126]

[0127] A044: As k→∞, e(k) converges to

[0128] A045: Unifying the proofs of the above two cases, we can obtain that e(k) is eventually uniformly bounded, and the proof ends. BRIEF DESCRIPTION OF THE DRAWINGS

[0129] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0130] Figure 2 Output tracking diagram of the method proposed by the present invention is adopted in the embodiment;

[0131] Figure 3 This is a diagram of the trigger interval of relaxation using the method proposed by the present invention in an embodiment; DETAILED DESCRIPTION

[0132] 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.

[0133] 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:

[0134] Step 1: Set the initial value of the parameter;

[0135] Step 2: Update pseudo partial derivatives

[0136] Step 3: Update the indicator function

[0137] Step 4: Use the updated and Information, update control input

[0138] Step 5: Control Input The actual output y(k+1) is generated by the steam-water heat exchanger system and passed into the trigger mechanism;

[0139] Step 6: Determine whether the trigger condition is met. If so, the actual output y(k+1) of the system is transmitted to the control terminal through the network. Otherwise, it is not transmitted.

[0140] Step 7: Repeat step 2 to enter the next cycle.

[0141] An embodiment of the present invention is described below:

[0142] Consider the output tracking control problem of the steam-water heat exchanger system, which corresponds to the Hammerstein space model:

[0143]

[0144] The expected tracking trajectory is:

[0145]

[0146] Figure 1 is a flow chart of a method according to an embodiment of the present invention; applying the proposed method, the output tracking curve is as follows Figure 2 As shown, it can be seen that the output can track the expected trajectory; Figure 3 The trigger interval diagram showing the relaxation of the proposed event triggering method. From these three figures, it can be seen that the proposed method not only effectively reduces the communication frequency, but also obtains a satisfactory tracking performance.

[0147] References

[0148] [1] N. Lin, R. Chi, B. Huang. Event-triggered model-free adaptive control. IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol.51, pp.3358-3369, 2019.

[0149] [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. A data driven event triggered control method for a steam-water heat exchange system with input saturation, characterized in that: The following steps are involved: A modified index considering future costs is proposed to obtain the optimal controller; Based on the correction index, an improved dynamic penalty factor control law is constructed to ensure the final uniform boundedness of the closed-loop error system. By using instantaneous data and average data, a dynamic trigger mechanism with variable threshold inserted is proposed to reduce the communication transmission when controlling the steam-water heat exchange system, specifically including: the discrete mathematical expression of the steam-water heat exchange system is as follows: y(k+1)=f(y(k),y(k-1),...,y(k-c y ),u(k),u(k-1),...,u(k-c u ))+d(k) In the formula, Indicates the output, Indicates input, represents the disturbance, m represents the system dimension, which is a known integer, k∈{0,1,...N} represents the sampling time, f(·) represents the unknown nonlinear function, c y and c u Represents the unknown system order. (1) Using dynamic linearization technology, a compact data model of the steam-water heat exchange system is obtained as follows: y(k+1)=y(k)+Φ(k)Δu(k)+Δd(k) In the formula, is an unknown pseudo-partial derivative satisfying Δy(k+1)=y(k+1)-y(k), Δu(k)=u(k)-u(k-1), Δd(k)=d(k)-d(k-1); (2) Select a saturation function Sat(·) to describe the system input saturation, as shown below: In the formula, u i (k) and u si (k) represent u(k) and u s (k) the i-th element, u s (k) represents saturated input, u min <0,u max >0,|u min |≠|u max |; (3) Define an event trigger sequence {k l }, l = 1, 2, ... N, event trigger error e ET (k) is as follows: and ET (k)=y(k)-y(k l ) (4) An improved cost function J[e(k)] is proposed to ensure that the controller designed under this cost function can guarantee the tracking performance under input saturation. The cost function is as follows: In the formula, e(k+1)=r(k+1)-y(k+1), r(k+1) represents the expected output, γ(k) is the penalty factor to be designed, λ>0; Solve the equation The optimal control law u(k) under event-triggered environment is obtained as follows: In the formula, 0<ρ<1, e l (k) = r(k) - y l (k) u0(k) represents the initial admissible control; (5) Design the dynamic update law of the penalty factor γ(k) as follows: Where τ>0, (6) Existing The estimation algorithm is modified to obtain the update algorithm in the event-triggered environment, as shown below: In the formula, 0<η<2, μ>0, the algorithm can ensure The estimation error is bounded, and the proof process is as follows: A001: 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; A002: Order The above formula is transformed into the following formula: A003: Definition Subtract ψ from both sides of A002 j (k) The following formula is obtained: A004: Definition The following formula is obtained: A005: According to the selection range of η and μ, the following formula can be obtained: A006: Substitute A005 into A004 to obtain the following formula: Where, 0<d1<1; A007: Because available Substituting it and A006 into A003, we get the following formula: A008: When the number of sampling moments increases to infinity, that is, k→∞, the above formula shows that the observation error Converge to this boundary So It also converges to this bound, and the proof ends; (7) Using neural network to approximate J[e(k)], the loss function Apply the gradient descent algorithm to get the neural network weights The update law is as follows: Where, 0<α<1, Under this weight update law, the approximate error of the indicator function is ultimately uniformly bounded. The proof process is as follows: A009: During the trigger interval, the output at the last trigger time is used to update Therefore, it is only necessary to prove the approximate error of the neural network weights at the triggering moment; A010: Order Substituting the weight update law into it, we get the following formula: In the formula, A011: By transforming the equation, we can get the following equation: A012: Substitute A011 into A010 to obtain the following formula: A013: Select the Lyapunov function V[h] as follows: A014: Perform differential operation V[h+1]-V[h] on A013 to obtain the following formula: A015: Substitute A012 into A014 to obtain the following formula: A016: Because the system output is continuously excited, the following formula can be obtained: A017: Substitute A016 into A015 to obtain the following formula: A018: Select 0<α<1, and get the following formula: A019: Substitute A016 into A018 to obtain the following formula: A020:A019 indicates Converge to this boundary Inside, the proof ends; (8) Using instantaneous data and average data, a dynamic trigger mechanism with variable thresholds is proposed as follows: k l+1 =inf{k|k>k l ,‖e ET (k)‖>ε(k)‖e(k)‖} In the formula, ι(0≤ι≤1), α1>0, α2>0. Under this trigger mechanism, the designed controller can ensure that the tracking error is bounded. The proof process is as follows: A021: The proof is divided into two steps. First, it is proved that the output tracking error of the steam-water heat exchange 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. A022: At the triggering moment, k = k l , we get the following formula: e(k+1)=r(k+1)-y(k+1) =r(k+1)-y(k)-Φ(k)Δu s (k)-Δd(k) A023: Substitute the control law at the triggering moment into A022 to obtain the following formula: A024: Convert the equation Substituting into A023, we get the following formula: A025: Perform a two-norm operation on A024 and obtain the following formula: A026: Because -1<tanh(·)<1, we get the following formula: A027: Substituting -1<tanh(·)<1 and A026 into A025, we get the following formula: A028: Because Y is a constant matrix, we have Also because and The following formula can be obtained: A029: According to the range of parameters ρ, λ and τ, there exist positive constants d2 and d3 such that the following equation holds: A030: Substitute A029 into A028 to obtain the following formula: A031:Δr(k+1) represents the rate of change of input, assuming Then the following formula holds: A032: Because (d2+d3)<0.2<1, e(k) converges to this boundary at the triggering moment. Inside; A033: In the trigger interval, i.e. k l <k<k l+1 , we get the following formula: A034: According to the definition of trigger error, the following formula is obtained: r(k+1)-y(k l )=Δr(k+1)+r(k)-y(k l ) =Δr(k+1)+r(k)-y(k)+e ET (to) =Δr(k+1)+e(k)+e ET (to) A035: Combining A034 and A033, we get the following formula: A036: and Substituting into A035, we get the following formula: A037: Perform a two-norm operation on A036 and obtain the following formula: A038: Note that the designed event triggering rules satisfy the following formula: A039: Substitute A038 into A037 to obtain the following formula: A040: According to the selection range of parameters ρ and λ, the following formula is obtained: A041: Choose the right and τ make the following equation true: A042: Combine A039, A040 and A041 to obtain the following formula: A043: Combine A040 and A042 to get the following formula: A044: As k→∞, e(k) converges to A045: Unifying the proofs of the above two cases, we can obtain that e(k) is eventually uniformly bounded, and the proof ends.

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