Double-hearth temperature synchronous control method and system based on pulse signals

Abstract

The invention discloses a double-hearth temperature synchronous control method and system based on a pulse signal, and the method comprises the steps: carrying out the nonlinear modeling of a hearth, including a temperature control model of a followed hearth and a temperature control model of a following hearth; a pulse differential equation model is used for describing a temperature error system of a following hearth and a followed hearth, on this basis, a set invariant condition of consistency of a temperature control system is obtained based on convex hull properties, and finally, by solving an optimal problem, the size of an attraction domain is estimated while a control gain is obtained, so that the control precision of the following hearth and the followed hearth is improved. And finally, a pulse control synchronization strategy of the double-hearth temperature system with input saturation is obtained. According to the method, the nonlinear characteristic of a hearth temperature system and the execution capability limitation of an execution mechanism are fully considered, and a control system is constructed into a system with input saturation nonlinearity; the system is controlled by using pulse signals, and low energy consumption and strong anti-interference performance in the regulation and control process of the system are realized.

Description

Technical Field

[0001] This invention relates to the field of synchronous control technology, and in particular to a method and system for synchronous temperature control of dual furnaces based on pulse signals. Background Technology

[0002] In industrial production, precise temperature control is crucial for ensuring production safety, improving product quality, and reducing energy consumption. Taking boilers as an example, furnace temperature directly affects combustion efficiency, emissions, and the boiler's safe operation. Excessive furnace temperature can easily lead to incomplete combustion and slagging, while excessively low temperatures result in unstable combustion and significantly reduced efficiency. Therefore, effective furnace temperature control is of great significance for improving energy efficiency, reducing environmental pollution, and meeting the heating needs of industrial production and residential life.

[0003] Existing furnace temperature control methods mostly focus on a single furnace and often simplify it into a linear model, employing the traditional PID method for temperature control. For example, CN114296489A discloses the use of an incremental PID controller for precise temperature control. However, actual furnace temperature systems exhibit significant nonlinear characteristics, making this simplification difficult to accurately reflect the true operating conditions of the furnace. Furthermore, in actual operation, the actuator's execution capability is limited, exhibiting input saturation. Traditional control methods often overlook this critical factor, causing the control system to fail to achieve the expected control effect in practical applications.

[0004] In industrial settings with multiple furnaces, achieving synchronous temperature control across all furnace chambers is extremely challenging. Existing temperature control systems, such as setpoint switch temperature control and classic PID temperature control, suffer from drawbacks such as excessive temperature differences and poor synchronization when handling dynamic temperature tracking control of multiple objects. Especially when dealing with multi-furnace systems with different heating and cooling characteristics, these traditional methods struggle to ensure synchronized heating across furnace chambers, leading to significant temperature differences between chambers and severely impacting the consistency and stability of product quality. Summary of the Invention

[0005] Purpose of the Invention: The purpose of this invention is to provide a method and system for synchronous temperature control of dual furnace chambers based on pulse signals, which solves the problems of poor temperature synchronization and excessive temperature difference between furnace chambers in the prior art, affecting the consistency of product quality; solves the problem that the simplified processing of the nonlinear characteristics of the furnace temperature system in traditional methods makes it difficult to accurately reflect the actual operating conditions; and solves the problem that ignoring the input saturation limit of the actuator leads to poor actual application effect of the control system.

[0006] Technical solution: The dual-furnace temperature synchronization control method based on pulse signals described in this invention includes:

[0007] A nonlinear control model for furnace temperature is established, including a temperature control model for the furnace being followed and a temperature control model for the furnace following it. In the temperature control model for the furnace following it, control inputs are used to... To achieve synchronous temperature control between the furnace and the controlled furnace, the control input... A pulse control strategy is adopted;

[0008] Based on the temperature control models of the followed furnace and the following furnace, an error model is established based on the pulse differential equation; based on the convex hull property, the set invariant conditions for the synchronous temperature control of the two furnaces are solved.

[0009] Establish a controller, and solve the control inputs that follow the furnace within the controller. .

[0010] Furthermore, the temperature control model for the furnace being followed is as follows: The temperature control model following the furnace is ;

[0011] in, and These refer to the temperature states of the furnace being followed and the furnace following it, respectively. , , For time, and This represents a nonlinear, continuously differentiable function that satisfies the Lipschitz condition. As the first parameter, It is a real number.

[0012] Furthermore, the control input , ;

[0013] in, Represents a saturation function.

[0014] ;

[0015] , ;

[0016] Represents the Dirac function, time series. satisfy and , , For the second parameter, , To control the gain;

[0017] exist The jump at time is represented as ,in, , , For the jump moment, To approach from the left , To approach from the right .

[0018] Furthermore, the error model is as follows:

[0019] ;

[0020] To account for the state error between the following furnace and the furnace being followed, in the above formula, This is the derivative of the error at the pulseless moment. This represents the error difference at the moment of the pulse transition.

[0021] Furthermore, based on the aforementioned error model, the set invariant condition for synchronous temperature control of the dual furnaces is solved:

[0022] , ;

[0023] Among them, when for All have Lyapunov functions derivative hour, Called an attractive invariant set, the Lyapunov function , This is the third parameter.

[0024] Furthermore, the control gain is obtained simultaneously by estimating the size of the attraction region through the following optimal process:

[0025] ;

[0026] in and As constraints for the attraction domain, This indicates the region where saturation will not occur. ; yes The coverage area It is the fourth parameter, representing Multiples of, It is the fifth parameter. It is the sixth parameter, and L is the Lipschitz constant.

[0027] Furthermore, , Given a real number; the control gain is calculated simultaneously by solving the following optimal process:

[0028] ;

[0029] in, , , , , , Values ​​range from 1 to .

[0030] The pulse signal-based dual-furnace temperature synchronization control system of the present invention includes:

[0031] The model building module is used to establish a nonlinear control model for furnace temperature, including a temperature control model for the furnace being followed and a temperature control model for the furnace following it. In the temperature control model for the furnace following it, control inputs are used to... To achieve synchronous temperature control between the furnace and the controlled furnace, the control input... A pulse control strategy is adopted;

[0032] The error system construction module is used to establish an error model based on the pulse differential equation according to the temperature control models of the followed furnace and the following furnace; and to solve the set invariant conditions for the synchronous temperature control of the two furnaces based on the convex hull property.

[0033] The controller design module is used to build the controller and solve for the control inputs following the furnace. .

[0034] The electronic device of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, it implements the pulse signal-based dual-furnace temperature synchronization control method.

[0035] The computer program product of the present invention includes a computer program that, when executed by a processor, implements the dual-furnace temperature synchronization control method based on pulse signals.

[0036] Beneficial effects: Compared with the prior art, the advantages of the present invention are as follows:

[0037] (1) This invention fully considers the nonlinear characteristics of the furnace temperature system and models the furnace as a more general nonlinear model, which can more accurately reflect the actual operating conditions of the furnace and lay a good foundation for achieving precise temperature control.

[0038] (2) The present invention fully considers the execution capability limitations of the actuator and constructs the control system as a system with input saturation nonlinearity, making the control system more in line with the actual operation scenario, effectively avoiding the problem of poor control effect caused by ignoring input saturation, and improving the practicality of the system;

[0039] (3) The present invention uses pulse signals to control the system, thereby achieving low energy consumption and strong anti-interference performance in the system regulation process. While ensuring the control effect, it reduces energy consumption and enhances the stability of the system in complex interference environments.

[0040] (4) This invention can be directly extended to a multi-furnace temperature synchronous control method, which has strong scalability and can adapt to the needs of more industrial scenarios, providing an effective solution for multi-furnace temperature synchronous control. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the multi-furnace temperature synchronization control method according to an embodiment of the present invention.

[0042] Figure 2 This diagram illustrates the control results of an embodiment of the present invention. Detailed Implementation

[0043] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0044] like Figure 1 As shown, the pulse signal-based dual-furnace temperature synchronization control method includes the following steps:

[0045] Step 1: Establish a nonlinear control model for the furnace temperature, including a temperature control model for the furnace being followed and a temperature control model for the furnace following the furnace. In the temperature control model for the furnace following the furnace, control inputs are used to... To achieve synchronous temperature control between the furnace and the controlled furnace, the control input... A pulse control strategy is adopted.

[0046] Specifically, in this embodiment, the furnace system is nonlinearly modeled, and one furnace is selected as the followed furnace and the other furnace as the following furnace to achieve synchronous temperature control of the two furnaces.

[0047] The temperature dynamics model following the furnace is as follows:

[0048] (1)

[0049] The temperature dynamics model following the furnace is as follows:

[0050] (2)

[0051] The state of furnace temperature , , This indicates that the control input follows the furnace. A pulse control strategy is adopted; As the first parameter, It is a real number , Representing a nonlinear, continuously differentiable function, in this embodiment, we assume that the nonlinear function... Satisfying the Lipschitz condition:

[0052] Assumption 1: The Lipschitz constant exists. Make , .

[0053] In some optional embodiments, the present invention can be directly extended to a multi-furnace temperature synchronous control method. In the case of multiple furnaces, one furnace needs to be identified as the furnace to be followed, and the other furnaces are all used as following furnaces. The control strategy of the present invention is applied to each following furnace.

[0054] Step 2: Based on the temperature control models of the followed furnace and the following furnace, establish an error model based on the pulse differential equation; based on the convex hull property, solve the set invariant conditions for the synchronous temperature control of the two furnaces.

[0055] Specifically, the error dynamics model is expressed as follows:

[0056] (3)

[0057] in, To address the state error between the furnace and the furnace being followed, this invention employs pulse control, thus dividing time into transition moments and non-transition moments. Non-transition moments are those when no pulse is applied. This is the derivative of the error at the pulseless moment. The error difference is the time of pulse transition. exist The jump at time is represented as ,in, , , For the jump moment, To approach from the left , To approach from the right .

[0058] in, Saturation function:

[0059] (4)

[0060] , , To control the gain.

[0061] Define the region where saturation will not occur. It is in the following form:

[0062] (5)

[0063] Constructing Lyapunov functions It is in the following form:

[0064] (6)

[0065] ellipsoid ,in, As the third parameter, If for Both have the derivative of the Lyapunov function. ,but It is called the attraction-invariant set.

[0066] Step 3: Establish a controller and solve for the control inputs following the furnace within the controller. .

[0067] Specifically, Pulse control strategy adopted:

[0068] (7)

[0069] in Represents the Dirac function, time series. satisfy and , , For the second parameter, , To control the gain

[0070] The following will prove that the state of the following furnace exponentially approximates the state of the furnace being followed. The proof requires the following lemma:

[0071] Lemma 1: Given Let represent the saturation function, and let , Suppose that for any All Then we have:

[0072] (10)

[0073] in Indicates the convex hull. .

[0074] The following theorem must be satisfied for a nonlinear dual-furnace temperature system (Equations (1) and (2)) to implement a distributed pulse control strategy (Equation (7)):

[0075] Theorem 1: Based on Assumption 1, if there exists a constant... Satisfying formulas (11) and (12):

[0076] (11)

[0077] (12)

[0078] and ,in To attract invariant sets, the nonlinear dual-furnace temperature system can achieve exponential uniformity, and the uniformity convergence rate is... , It is the fifth parameter. It is the sixth parameter, and L is the Lipschitz constant.

[0079] The proof is as follows:

[0080] when At that time, along the dynamic trajectory (4) Differentiation yields:

[0081] (13)

[0082] when hour:

[0083] (14)

[0084] use and Replace each of the following in Lemma 1 get:

[0085] (15)

[0086] in .

[0087] Then we have:

[0088] (16)

[0089] Based on the above analysis, we can obtain from equation (11):

[0090] (17)

[0091] when Combining the comparison lemma, we obtain from equation (13):

[0092] (18)

[0093] when Then, by further calculation from equation (17):

[0094] (19)

[0095] when We can obtain:

[0096] (20)

[0097] when hour:

[0098] (twenty one)

[0099] Similarly, we can obtain:

[0100] (twenty two)

[0101] Using equation (12), and according to We can obtain that for all The following equation holds true:

[0102] (twenty three)

[0103] because ,therefore:

[0104] (twenty four)

[0105] Therefore, the state of the furnace being followed approximates the state of the furnace being followed exponentially. Proof complete!

[0106] In order to obtain the maximum range of invariant sets that satisfy Theorem 1, the attraction domain will be estimated through an optimization process.

[0107] First, define a bounded convex set. As a set of covering units, it is shown in the following formula:

[0108] (25)

[0109] in It is a real number given in advance.

[0110] Next, we will consider all cases that satisfy the conditions in Theorem 1. Find the largest coverage area in the region. , The fourth parameter indicates Multiples of. This process can be described by the following optimal process:

[0111] (26)

[0112] To facilitate solving this optimization process using MATLAB's built-in functions, the constraints of the optimization process will be expressed in the form of linear matrix inequalities:

[0113] (1) Constraints Equivalent to:

[0114] (27)

[0115] By Schur's complement lemma, we can obtain a sufficient condition to ensure that the above equation holds:

[0116] (28)

[0117] in .

[0118] (2) Constraint (b) is equivalent to

[0119] (29)

[0120] and

[0121] (30)

[0122] in .

[0123] (3) Constraint (c) is equivalent to:

[0124] (31)

[0125] By Schur's complement lemma, we can obtain a sufficient condition to ensure that the above equation holds:

[0126] (32)

[0127] Therefore, the optimal process (26) can be described as the optimal process under the following linear matrix inequality constraint:

[0128] (33)

[0129] By solving the optimal process based on linear matrix inequality constraints, the control input that satisfies the constraints can be obtained, thus enabling the estimation of the attraction domain size and the determination of the control gain simultaneously. This further enables temperature control that exponentially approximates the state of the furnace being followed, following the furnace state.

[0130] The method described in this invention will be verified through specific experiments below.

[0131] In this experiment, we set nonlinear functions for , The temperature dynamics model following the furnace is as follows:

[0132]

[0133] The temperature dynamics model of the furnace being followed is as follows:

[0134]

[0135] When assuming an upper bound for the maximum pulse interval The following parameters are obtained by solving equation (33) using the LMI toolbox provided in Matlab:

[0136] , , , , , .

[0137] When the initial condition of furnace temperature is selected as The beneficial effects can be visualized at any time. Figure 2 In the graph, the horizontal axis represents time in seconds, and the vertical axis represents temperature. h1 is the temperature of the furnace being followed, and h2 is the temperature of the furnace being followed. The moments in the graph where a jump occurs are the moments when a pulse is applied. After multiple pulse control applications, h1 and h2 converge.

[0138] Therefore, this invention fully considers the nonlinear characteristics of the furnace temperature system and the input saturation limit of the actuator to achieve efficient and accurate temperature synchronization control, thereby improving the overall efficiency and product quality of industrial production; at the same time, it has the advantages of low energy consumption and strong anti-interference, adapting to the needs of industrial production for efficient and energy-saving control strategies, and providing a scalable solution for multi-furnace temperature synchronization control.

[0139] The pulse signal-based dual-furnace temperature synchronization control system of the present invention includes:

[0140] The model building module is used to establish a nonlinear control model for furnace temperature, including a temperature control model for the furnace being followed and a temperature control model for the furnace following it. In the temperature control model for the furnace following it, control inputs are used to... To achieve synchronous temperature control between the furnace and the controlled furnace, the control input... A pulse control strategy is adopted;

[0141] The error system construction module is used to establish an error model based on the pulse differential equation according to the temperature control models of the followed furnace and the following furnace; and to solve the set invariant conditions for the synchronous temperature control of the two furnaces based on the convex hull property.

[0142] The controller design module is used to build the controller and solve for the control inputs following the furnace. .

[0143] The electronic device of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded onto the processor, it implements the pulse signal-based dual-furnace temperature synchronization control method. The processor executes the computer program stored in the memory to implement the various steps of the methods described in the above embodiments.

[0144] The computer program product of the present invention includes a computer program that, when executed by a processor, implements the dual-furnace temperature synchronization control method based on pulse signals.

Claims

1. A method for synchronous temperature control of a dual-furnace chamber based on pulse signals, characterized in that, include: A nonlinear control model for furnace temperature is established, including a temperature control model for the furnace being followed and a temperature control model for the furnace following it. In the temperature control model for the furnace following it, control inputs are used to... To achieve synchronous temperature control between the furnace and the controlled furnace, the control input... A pulse control strategy is adopted; Based on the temperature control models of the followed furnace and the following furnace, an error model is established based on the pulse differential equation; based on the convex hull property, the set invariant conditions for the synchronous temperature control of the two furnaces are solved. Establish a controller, and solve the control inputs that follow the furnace within the controller. .

2. The method for synchronous temperature control of a dual furnace chamber based on pulse signals according to claim 1, characterized in that, The temperature control model for the furnace being followed is: The temperature control model following the furnace is ; in, and These refer to the temperature states of the furnace being followed and the furnace following it, respectively. , , For time, and This represents a nonlinear, continuously differentiable function that satisfies the Lipschitz condition. This is the first parameter.

3. The method for synchronous temperature control of a dual furnace chamber based on pulse signals according to claim 1, characterized in that, The control input , ; in, Represents a saturation function. ； ， ； Represents the Dirac function, time series. satisfy and , , For the second parameter, , To control the gain; exist The jump at time is represented as ,in, , , For the jump moment, To approach from the left , To approach from the right .

4. The method for synchronous temperature control of a dual furnace chamber based on pulse signals according to claim 3, characterized in that, The error model is as follows: ； To account for the state error between the following furnace and the furnace being followed, in the above formula, This is the derivative of the error at the pulseless moment. This represents the error difference at the moment of the pulse transition.

5. The method for synchronous temperature control of a dual furnace chamber based on a pulse signal according to claim 4, characterized in that, Based on the aforementioned error model, solve for the set invariant condition of the dual-furnace temperature synchronization control: ， ； Among them, when for All have Lyapunov functions derivative hour, Called an attractive invariant set, the Lyapunov function , This is the third parameter.

6. The method for synchronous temperature control of a dual furnace chamber based on a pulse signal according to claim 5, characterized in that, The control gain is calculated simultaneously by solving the following optimal process: ； in and As constraints for the attraction domain, This indicates the region where saturation will not occur. ; yes The coverage area It is the fourth parameter, representing Multiples of, It is the fifth parameter. It is the sixth parameter, and L is the Lipschitz constant.

7. The method for synchronous temperature control of a dual furnace chamber based on pulse signals according to claim 6, characterized in that, , Given a real number; the control gain is calculated simultaneously by solving the following optimal process: ； in, , , , , , .

8. A dual-furnace temperature synchronization control system based on pulse signals, characterized in that, include: The model building module is used to establish a nonlinear control model for furnace temperature, including a temperature control model for the furnace being followed and a temperature control model for the furnace following it. In the temperature control model for the furnace following it, control inputs are used to... To achieve synchronous temperature control between the furnace and the controlled furnace, the control input... A pulse control strategy is adopted; The error system construction module is used to establish an error model based on the pulse differential equation according to the temperature control models of the followed furnace and the following furnace; and to solve the set invariant conditions for the synchronous temperature control of the two furnaces based on the convex hull property. The controller design module is used to build the controller and solve for the control inputs following the furnace. .

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is loaded into the processor, it implements the pulse signal-based dual-furnace temperature synchronization control method according to any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the pulse signal-based dual-furnace temperature synchronization control method according to any one of claims 1-7.

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