A preset performance function based iterative method for furnace temperature control in copper smelting process

Abstract

The application discloses a copper smelting process furnace temperature control method based on an iteration preset performance function, and comprises the following steps: defining actual furnace temperature and its derivative as state variables to establish a copper smelting process furnace temperature system in a state space expression form; determining the iteration number of the preset performance function based on the iteration according to the required control precision; under the condition that the iteration number i is 1, constructing the preset performance function of the first iteration according to a traditional preset performance function and a first auxiliary function; under the condition that the iteration number i is greater than 1, constructing the preset performance function of the i-th iteration according to the preset performance function of the (i-1)-th iteration and a second auxiliary function; establishing a virtual controller according to the preset performance function based on the iteration; and establishing a controller based on the preset performance function based on the iteration as the input of the copper smelting process furnace temperature system according to the virtual controller, so that the copper smelting process furnace temperature system can track the expected furnace temperature. The application not only realizes the iteration improvement of the system control precision, but also accurately depicts the iteration process of the precision improvement.

Description

Technical Field

[0001] The invention relates to a copper smelting process furnace temperature control method based on an iterative preset performance function, belonging to the technical field of copper smelting process control. Background Art

[0002] In recent years, non-ferrous metals, as indispensable raw materials for the modern industrial system, have been widely used in many fields such as electronics, machinery manufacturing, and aerospace. As an important basic raw material in my country, the smelting process of non-ferrous metal copper has a huge impact on the development of the national economy. At present, the main methods of copper smelting in my country are electrolysis and pyrometallurgy. Compared with electrolysis, traditional pyrometallurgy equipment has low investment costs and high output, and therefore occupies a dominant position in metal smelting. However, pyrometallurgy smelting has problems such as high operating costs and serious environmental pollution, and the instability of the furnace temperature will lead to reduced product quality and production efficiency. Therefore, it has become a top priority for the non-ferrous metal industry to study the intelligent control method of furnace temperature in the copper smelting process to improve the production efficiency of pyrometallurgy and reduce energy consumption.

[0003] There are many types of intelligent furnace temperature control methods available, such as real-time control of the metal smelting process based on data-driven modeling, PID furnace temperature control, and adaptive furnace temperature control. However, the high process standards in the copper smelting process require accurate control of the smelting temperature to achieve the desired target when performing furnace temperature control. The superior performance of the adaptive control method in real-time adjustment of the control strategy based on furnace temperature feedback information has attracted many scholars to conduct related research. For adaptive furnace temperature control, how to design an adaptive law, develop an adaptive control strategy with a preset furnace temperature target, improve the accuracy and real-time performance of the control process, and ensure that the furnace temperature reaches the desired target is still an urgent task to be solved. The control accuracy of the furnace temperature has a direct impact on the smelting output. Low control accuracy will lead to reduced output and reduced production capacity. Therefore, how to improve the control accuracy of the furnace temperature and reduce the control error has attracted widespread attention in academia and industry.

[0004] To improve furnace temperature control accuracy, reducing control error and enhancing system transient performance are currently common approaches. Several traditional adaptive furnace temperature control strategies, such as adaptive PID control, reinforcement learning-based adaptive control, and neural network adaptive control, are designed to reduce control error. These strategies reduce error by compensating for errors caused by system disturbances or estimating unknown system dynamics. Another approach is to ensure that the control error converges within a desired range and enhance system transient performance by presetting system performance. Both approaches can effectively improve the control accuracy of furnace temperature control systems.

[0005] In furnace temperature systems, enhancing system transient performance can achieve accurate temperature control. A common approach to presetting system performance is to use a preset performance function. This function ensures that the system control error converges to a desired range. If the control error exceeds the preset limit, the furnace temperature control accuracy will decrease, resulting in a reduction in smelting output. Therefore, for furnace temperature systems, it is crucial to consider performance presetting during the smelting process. Furthermore, enhancing the transient performance of the furnace temperature system to achieve precise control of the smelting temperature is a key issue in improving system control accuracy. Summary of the Invention

[0006] The present invention provides a furnace temperature control method for a copper smelting process based on an iterative preset performance function. By introducing a virtual controller based on an iterative preset performance function, and then constructing a controller based on the iterative preset performance function, the furnace temperature system of the copper smelting process is enabled to track the desired furnace temperature.

[0007] The technical solution of the present invention is:

[0008] According to a first aspect of the present invention, a method for controlling furnace temperature in a copper smelting process based on an iterative preset performance function is provided, the method comprising the following steps:

[0009] The actual furnace temperature and its derivatives are defined as state variables to establish a furnace temperature system for the copper smelting process in the form of state space expression.

[0010] The number of iterations of the iterative preset performance function is determined based on the required control accuracy: when the number of iterations i=1, the preset performance function of the first iteration is constructed based on the traditional preset performance function and the first auxiliary function; when the number of iterations i is greater than 1, the preset performance function of the i-th iteration is constructed based on the preset performance function of the i-1th iteration and the second auxiliary function;

[0011] A virtual controller α is established based on an iterative preset performance function. Based on the virtual controller α, a controller based on an iterative preset performance function is established as an input to a furnace temperature system of a copper smelting process, thereby enabling the furnace temperature system of the copper smelting process to track a desired furnace temperature.

[0012] Furthermore, define the actual furnace temperature x1 and its derivative is a state variable, the furnace temperature mathematical model is expressed as the following state space expression, that is, the furnace temperature system of the copper smelting process is constructed:

[0013]

[0014] where x = [x1, x2] T , C = [1 0], K and T1 represent the mnemonics in the mathematical model of furnace temperature; x0 is the initial state of the state space expression, x1(0) and x2(0) represent the initial states of x1 and x2 respectively, and u is the controller based on the iterative preset performance function.

[0015] Furthermore, the preset performance function based on iteration is expressed as:

[0016]

[0017] Among them, ρ(t) is the traditional preset performance function, β(t) is the first auxiliary function; ρ0>ρ ∞ >0,λ>0 is an arbitrary positive design parameter, e represents an exponential constant; θ is an arbitrarily designed positive constant, κ is a positive constant and κ>1; is the preset performance function for the i-1th iteration; β i-1 (t) is the second auxiliary function; I represents the maximum number of iterations; and t represents time.

[0018] Furthermore, the virtual controller is expressed as:

[0019]

[0020] Where k1 is an arbitrary positive design parameter, is the preset performance function for the i-1th iteration The first derivative of is the preset performance function of the i-th iteration; e1 is the controlled furnace temperature error; is the desired furnace temperature T d The first derivative of is the first-order derivative of the traditional preset performance function ρ(t).

[0021] Furthermore, the controller based on the iterative preset performance function is expressed as follows:

[0022]

[0023] Where k2 is an arbitrary positive design parameter, x1 is the actual furnace temperature; e2 is the error between the state variable x2 and the virtual controller α; K and T1 are mnemonics in the furnace temperature mathematical model; τ is the constant lag time; The first derivative of the virtual controller α.

[0024] According to a second aspect of the present invention, a terminal device is provided, comprising a memory, a processor, and a program stored on the memory and executable by the processor, wherein when the processor executes the program, the method for controlling the furnace temperature of a copper smelting process based on an iterative preset performance function as described in any one of the above is implemented.

[0025] The beneficial effects of the present invention are as follows: for the furnace temperature system, its transient performance will directly affect the accuracy of the control system; and the present invention establishes an iterative preset performance function to design a controller according to the different control accuracies, thereby achieving the purpose of enhancing the transient performance of the system and improving the system control accuracy, and realizing that the change of control accuracy is accurately characterized by a design parameter in the iterative performance function, that is, given a preset performance function, the control accuracy of the system can be iteratively enhanced by a corresponding multiple, and the control error changes from converging to the accuracy range specified by the performance function before iteration to converging to the accuracy range specified by the performance function after iteration. From the above, it can be seen that the present invention not only achieves the iterative improvement of the system control accuracy, but also accurately characterizes the iterative process of accuracy improvement. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a flowchart of the present invention;

[0027] Figure 2 is the trajectory of β(t),1 / β(t) about time t;

[0028] Figure 3 is the function ρ(t), Trajectory comparison;

[0029] Figure 4 It is a schematic diagram of the traditional preset performance method;

[0030] Figure 5 Schematic diagram of the furnace temperature control effect of the copper smelting process for the preset performance function of the first iteration;

[0031] Figure 6 Schematic diagram of the furnace temperature control effect of the copper smelting process for the preset performance function of the second iteration. DETAILED DESCRIPTION

[0032] To make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. It should be noted that, in the absence of conflict, the embodiments in this application and the features in the embodiments can be combined with each other in any way.

[0033] Please refer to Figures 1-6According to a first aspect of an embodiment of the present invention, a method for controlling furnace temperature in a copper smelting process based on an iterative preset performance function is provided, the method comprising the following steps: defining the actual furnace temperature and its derivatives as state variables to establish a copper smelting process furnace temperature system in a state space expression form; determining the number of iterations of the iterative preset performance function according to the required control accuracy: when the number of iterations i=1, constructing the preset performance function of the first iteration according to the traditional preset performance function and the first auxiliary function; when the number of iterations i is greater than 1, constructing the preset performance function of the i-th iteration according to the preset performance function of the i-1th iteration and the second auxiliary function; establishing a virtual controller α based on the iterative preset performance function; and establishing a controller based on the iterative preset performance function according to the virtual controller α as the input of the copper smelting process furnace temperature system to enable the copper smelting process furnace temperature system to track the desired furnace temperature.

[0034] Furthermore, define the actual furnace temperature x1 and its derivative is a state variable, the furnace temperature mathematical model is expressed as the following state space expression, that is, the furnace temperature system of the copper smelting process is constructed:

[0035]

[0036] where x = [x1, x2] T , C = [1 0], K and T1 represent the mnemonics in the mathematical model of furnace temperature; x0 is the initial state of the state space expression, x1(0) and x2(0) represent the initial states of x1 and x2 respectively, and u is the controller based on the iterative preset performance function.

[0037] Furthermore, the preset performance function based on iteration is expressed as:

[0038]

[0039] Among them, ρ(t) is the traditional preset performance function, β(t) is the first auxiliary function; ρ0>ρ ∞ >0,λ>0 is an arbitrary positive design parameter, e represents an exponential constant; θ is an arbitrarily designed positive constant, κ is a positive constant and κ>1; is the preset performance function for the i-1th iteration; β i-1 (t) is the second auxiliary function; I represents the maximum number of iterations; and t represents time.

[0040] Furthermore, the virtual controller is expressed as:

[0041]

[0042] Where k1 is an arbitrary positive design parameter, is the preset performance function for the i-1th iteration The first derivative of is the preset performance function of the i-th iteration; e1 is the controlled furnace temperature error; is the desired furnace temperature T d The first derivative of is the first-order derivative of the traditional preset performance function ρ(t).

[0043] Furthermore, the controller based on the iterative preset performance function is expressed as follows:

[0044]

[0045] Where k2 is an arbitrary positive design parameter, x1 is the actual furnace temperature, e2 is the error between the state variable x2 and the virtual controller α, K and T1 represent the mnemonics in the mathematical model of furnace temperature, and τ is the constant lag time.

[0046] According to a second aspect of an embodiment of the present invention, a terminal device is provided, comprising a memory, a processor, and a program stored on the memory and executable by the processor, wherein when the processor executes the program, the method for controlling the furnace temperature of a copper smelting process based on an iterative preset performance function as described in any one of the above is implemented.

[0047] The specific process of the present invention is further described below:

[0048] 1. Model Building and Problem Formulation

[0049] The smelting of nonferrous copper is primarily achieved by controlling the furnace temperature. First, a mathematical model of the furnace temperature during the copper smelting process must be established. This model must take into account not only the heating temperature of the furnace itself, but also the effects of factors such as the calorific value of the fuel, air density, and furnace material on the heating temperature. Based on this, the furnace used in the copper smelting process is equated to a dynamic thermodynamic system. Based on the furnace temperature heat balance equation, a mathematical model of the furnace temperature per unit time is established as follows:

[0050]

[0051] Among them, K and T1 represent mnemonics; Q D is the calorific value of the fuel; C r ,C k ,C g ,C e ,C e ' are the average specific heat of fuel, the average specific heat of air, the average specific heat of the heated object, the average specific heat of the furnace gas, and the specific heat of the furnace gas outflow; Tr ,T k ,T e ' are the average fuel temperature, the average air temperature and the furnace gas outflow temperature; G g , G e are the output of heated objects and the output of gas in the furnace respectively; n is the air consumption coefficient, A is the gap area of ​​the furnace body; s1, s2, ... s N is the thickness of the furnace material, λ1,λ2,…λ N is the thermal conductivity of different materials, N is the total number of material types; τ is the constant lag time; T(s) and B(s) are the changes in furnace temperature and fuel, respectively, and s is the Laspeyres factor.

[0052] The traditional preset performance function ρ(t) is known to be expressed as:

[0053] ρ(t)=ρ0e -λt +ρ ∞ (2)

[0054] Where ρ0>ρ ∞ >0,λ>0 are arbitrary positive design parameters, and e represents an exponential constant. An auxiliary function β(t) is introduced, and the expression is:

[0055] β(t)=κtanh(tρ(t)+θ)(3)

[0056] Among them, θ is a positive constant that can be designed arbitrarily, κ is a positive constant and κ>1; the range of ρ(t) is (ρ ∞ ,ρ0+ρ ∞ ], the range of β(t) is (-κ,κ), and the range of 1 / β(t) is are all bounded functions; in the embodiment of the present invention, κ=1000,θ=0.002,ρ0=3,λ=0.5,ρ ∞ =0.1, the range of the functions β(t) and 1 / β(t) is (-1000,1000) and Specific images such as Figure 2 shown.

[0057] In order to further improve the transient performance of the furnace temperature control system, the present invention improves on the basis of the traditional performance function ρ(t) and constructs the first iteration performance function as follows:

[0058]

[0059] Accuracy of traditional preset performance function: As time t→∞, the traditional preset performance function ρ(t) approaches ρ ∞ ,Right now Therefore, the control precision of the traditional preset performance function is epsilon 1 = rho ∞ , the control error e1 converges to the boundary of |rho ∞ |, that is, (-rho ∞ < e1 < rho ∞ ).

[0060] The preset performance function precision of the first iteration: as time t approaches infinity, the preset performance function of the first iteration approaches , that is Therefore, the control precision of the preset performance function of the first iteration provided by the present application is The control error e1 converges to the boundary of , that is

[0061] The preset performance function of the first iteration is designed innovatively in the present application by constructing an auxiliary function beta (t) based on the traditional performance function rho (t). On the one hand, the control precision of the preset performance function of the first iteration is improved by kappa times compared with the traditional performance function rho (t). On the other hand, according to the preset performance function of the first iteration, a new auxiliary function can be further constructed, and a performance function of the second iteration with higher control precision can be obtained. In this way, the preset control precision is improved until the preset control precision is achieved. The specific expression of the performance function of the second iteration is as follows:

[0062]

[0063] The preset performance function of the second iteration is analyzed, and the control precision is Compared with the traditional preset performance function rho (t), the precision is improved by kappa 2 times; compared with the performance function of the first iteration, the precision is improved by kappa times. Therefore, by continuously updating the performance function and the auxiliary function, the iterative performance function with continuously improved precision compared with the traditional performance function can be obtained, so that the iterative improvement of the system control precision is realized.

[0064] The precision of the traditional preset performance function is determined by the size of the parameter rho ∞ , but in actual control problems, in the case of determined controller parameters, the requirement of high precision needs to be realized by adjusting the parameter rho ∞ , but the setting of too small rho ∞ will lead to the failure of the control method. The iterative preset performance function provided by the present application can avoid this problem, and it can not change the parameter rho ∞ ​​​Instead of changing the size of the vector, the required accuracy is achieved through iteration and adjustment of the parameter κ.

[0065] Select parameters κ = 1000, θ = 0.002, ρ0 = 3, λ = 0.5, ρ ∞ = 0.1, for the performance function of the present invention at different iteration times and the traditional preset performance function, the control accuracy of the traditional preset performance function is ε = 0.1, and the control accuracy of the preset performance function of the first iteration is ε = 1 × 10 -4 , the preset performance function control accuracy of the second iteration is ε=1×10 -7 Compared with the traditional preset performance function, the transient performance of the present invention is enhanced to 10 3 times and 10 6 times, function ρ(t), Images such as Figure 3 shown.

[0066] Define the controlled furnace temperature error as e1 = x1-T d , x1 and its derivative are is the state variable, x1 is the actual furnace temperature, T d is the desired furnace temperature, then the furnace temperature mathematical model (1) can be expressed as the following state space expression, that is, to construct the copper smelting process furnace temperature system:

[0067]

[0068] where x = [x1, x2] T , C = [1 0], x0 is the initial state of the state space expression, x1(0), x2(0) represent the initial states of x1 and x2 respectively, u is the controller, and T is the transpose.

[0069] The controller based on the above design is used as the input of the copper smelting process furnace temperature system to realize the actual furnace temperature x1 of the copper smelting process furnace temperature system to the desired furnace temperature T d The goal of this invention is to design a controller so that the actual furnace temperature x1 can track the desired furnace temperature T d At the same time, the closed-loop system satisfies the ultimate uniform boundedness and the convergence performance of the controlled furnace temperature error is higher than that of the traditional preset performance method, that is, e1 moves inward from the boundary of the traditional preset performance function ρ(t) to the boundary of the iterative performance function The boundaries move inward represents the preset performance function of the i-th iteration.

[0070] 2. The controller design is as follows:

[0071] First, the preset performance function based on iteration is as follows:

[0072]

[0073] The controlled furnace temperature error is e1=x1-T d , expected furnace temperature T d Is a smooth and bounded temperature curve function that satisfies T d and its derivatives Continuously bounded. Consider the following virtual controller α and controller u:

[0074]

[0075] Among them, k1, k2 are arbitrary positive design parameters, The error between the virtual controller α and the state variable x2 is e2=x2-α, is the derivative of the virtual controller α.

[0076] Selecting a barrier function satisfy e1(0) represents the initial value of the controlled furnace temperature error. Further, the stability of equation (6) is analyzed, and Theorem 1 is given as follows:

[0077] Theorem 1: Assume that there exists a given constant k0>0, for any There are |e0| <k0, Represents a set of real numbers. At the same time, Equation (6) is controlled by the virtual controller α and controller u of Equation (8) and Equation (9), and the closed-loop system is asymptotically stable and meets the preset system transient performance.

[0078] Consider a Lyapunov function V:

[0079]

[0080] When i=1, taking the derivative of V we get:

[0081]

[0082] When i=2,3,...I, taking the derivative of V we get:

[0083]

[0084] Substituting virtual controller (8) and controller (9) into the equation, we can get:

[0085]

[0086] Take c = min{2k1, 2k2}, and we get It can be concluded that the closed-loop system is asymptotically stable and the system control error converges to the preset iterative performance function Within the set boundaries, the control objectives of the present invention are achieved and the required controller is obtained.

[0087] In order to verify the feasibility of the method described in the present invention, the performance of the furnace temperature controller is preset using the traditional preset performance function and the iterative performance preset method proposed in the present invention. The tracking effect and transient performance curve are shown in Figure 2. Figure 4 、 5 As shown: Figure 4 The left half shows that the actual furnace temperature can track the expected furnace temperature T very well. d ; Figure 4 The right half shows that the controlled furnace temperature error e1 converges to the boundary of the traditional preset performance function ρ(t), and the preset accuracy error is ±5℃, that is, the preset accuracy is ρ ∞ =5℃. Figure 5 The left half shows that the actual furnace temperature can track the expected furnace temperature T very well. d ; Figure 5 The right half shows that the controlled furnace temperature error e1 converges to the preset performance function of the first iteration Within the boundaries of the preset accuracy error is ±1°C, that is, the preset accuracy is ρ ∞ =1℃, the transient performance is enhanced by κ=5 times compared with the accuracy set by the traditional performance function.

[0088] Then the iterative performance function proposed by the present invention is used to perform the second iteration, and the tracking effect and transient performance curve are as follows: Figure 6 As shown:

[0089] Figure 6 The left half shows that the actual furnace temperature can track the expected furnace temperature T very well. d ; Figure 6 The right half shows that the controlled furnace temperature error e1 converges to the preset performance function of the second iteration Within the boundaries, the preset accuracy error is ±0.2℃, that is, the preset accuracy is ρ ∞ =0.2℃, compared with the accuracy of the traditional performance function setting, the transient performance is enhanced by κ=25 times; compared with the accuracy of the iterative preset performance function setting of the first iteration, the transient performance is enhanced by κ=5 times.

[0090] The above analysis demonstrates that, within the constraints of the iteratively pre-set performance function, the actual furnace temperature during the copper smelting process converges to the desired temperature range, with the control error remaining within the specified bounds. Furthermore, comparative analysis of different iteration times demonstrates that the iterative performance function designed in this invention achieves iterative enhancement of system control accuracy, with changes in control accuracy accurately captured by a single design parameter during each iteration.

[0091] The specific embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in this field without departing from the scope of the present invention.

Claims

1. A method for controlling furnace temperature in a copper smelting process based on an iterative preset performance function, characterized in that: The method comprises the following steps: The actual furnace temperature and its derivatives are defined as state variables to establish a furnace temperature system for the copper smelting process in the form of state space expression. The number of iterations of the iterative preset performance function is determined based on the required control accuracy: when the number of iterations i=1, the preset performance function of the first iteration is constructed based on the traditional preset performance function and the first auxiliary function; when the number of iterations i is greater than 1, the preset performance function of the i-th iteration is constructed based on the preset performance function of the i-1th iteration and the second auxiliary function; Establishing a virtual controller α based on the iterative preset performance function; establishing a controller based on the iterative preset performance function based on the virtual controller α as an input to a furnace temperature system of a copper smelting process, so as to enable the furnace temperature system of the copper smelting process to track a desired furnace temperature; The preset performance function based on iteration is expressed as: Among them, ρ(t) is the traditional preset performance function, β(t) is the first auxiliary function; ρ0>ρ ∞ >0,λ>0 is an arbitrary positive design parameter, e represents an exponential constant; θ is an arbitrarily designed positive constant, κ is a positive constant and κ>1; is the preset performance function for the i-1th iteration; β i-1 (t) is the second auxiliary function; I represents the maximum number of iterations; and t represents time.

2. The method for controlling furnace temperature in a copper smelting process based on an iterative preset performance function according to claim 1, characterized in that: Define the actual furnace temperature x1 and its derivative is a state variable, the furnace temperature mathematical model is expressed as the following state space expression, that is, the furnace temperature system of the copper smelting process is constructed: where x = [x1, x2] T , C = [1 0], K and T1 represent the mnemonics in the mathematical model of furnace temperature; x0 is the initial state of the state space expression, x1(0) and x2(0) represent the initial states of x1 and x2 respectively, and u is the controller based on the iterative preset performance function.

3. The method for controlling furnace temperature in a copper smelting process based on an iterative preset performance function according to claim 1, characterized in that: The virtual controller is expressed as: Where k1 is an arbitrary positive design parameter, is the preset performance function for the i-1th iteration The first derivative of is the preset performance function of the i-th iteration; e1 is the controlled furnace temperature error; is the desired furnace temperature T d The first derivative of is the first-order derivative of the traditional preset performance function ρ(t).

4. The method for controlling furnace temperature in a copper smelting process based on an iterative preset performance function according to claim 1, wherein: The controller based on the iterative preset performance function is expressed as: Where k2 is an arbitrary positive design parameter, x1 is the actual furnace temperature; e2 is the error between the state variable x2 and the virtual controller α; K and T1 are mnemonics in the furnace temperature mathematical model; τ is the constant lag time; The first derivative of the virtual controller α.

5. A terminal device, characterized in that: The method comprises a memory, a processor, and a program stored in the memory and executable by the processor, wherein when the processor executes the program, the method for controlling the furnace temperature of a copper smelting process based on an iterative preset performance function according to any one of claims 1 to 4 is implemented.

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