A priority negotiation-based multi-agent model predictive control method for microwave metallurgy process

Abstract

The present application relates to a kind of priority negotiation-based microwave metallurgical process multi-agent model predictive control method.Face to microwave metallurgical process, its control input, controlled variable, temperature measuring point distribution are analyzed, and microwave metallurgical process is multi-agent and forms multi-agent system.The input response model of the present application to microwave metallurgical process is identified, establishes the priority negotiation mechanism of the agent based on interactive game and the model predictive control mechanism of multi-agent system under sequential game framework, establishes each function required by the above mechanism, selects each constraint, and based on the above mechanism, the temperature of metallurgical material in microwave metallurgical process is predicted and controlled, and the optimal control input increment that each microwave source should adopt is obtained and used to actually control microwave metallurgical process.The present application can improve temperature control precision, reduce energy consumption and ensure economic benefits.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of priority negotiation-based microwave metallurgical process multi-agent model predictive control method, application to interactive game mechanism determines the priority of agent, in the sequential game framework, using multi-agent model predictive control method to realize the temperature optimization control of microwave metallurgical process, belong to multi-agent system model predictive control and microwave metallurgical technical field. BACKGROUND

[0002] As a clean energy, microwave energy has been widely used in metallurgy, pharmaceutical, chemical and material fields. Microwave is used in metallurgical industry because it has the advantages of convenient control, fast heating speed, selective heating and volume heating compared with traditional heating methods. However, due to the principle of microwave generation, microwave metallurgical industrial process needs to consume a large amount of electric power resources. Given the vigorous development of microwave metallurgical technology and the deep application of microwave energy in multiple fields, it is crucial to optimize the energy utilization efficiency of microwave metallurgical process, reduce energy consumption and improve economic benefits. SUMMARY

[0003] The present application provides a priority negotiation-based microwave metallurgical process multi-agent model predictive control method, which can track the set value of the metallurgical material temperature through temperature control in the microwave metallurgical process, and the temperature control is more accurate, while effectively reducing the system energy consumption.

[0004] To achieve the above functions, the present application provides the following technical solutions: the present application provides a priority negotiation-based microwave metallurgical process multi-agent model predictive control method, the specific steps of the method include:

[0005] Step 1, a process mathematical model with prediction function is established according to the actual dynamic characteristics of microwave metallurgical process. The microwave metallurgical process is to change the output microwave power of magnetron by adjusting the input electric power of magnetron, the microwave generated by magnetron is fed into the metallurgical furnace resonant cavity and forms resonance in it, thereby heating the metallurgical material and extracting metal or metal compound from the metallurgical material at a predetermined temperature; the metallurgical furnace used in the microwave metallurgical process is installed with N a magnetrons, the control input of each magnetron is its input electric power, the input electric power is continuously adjustable in the range of 0.075-1.5kW, and the metallurgical furnace can withstand the metallurgical temperature range of room temperature-1200℃.

[0006] Further, the process mathematical model with prediction function is shown in formula (3), which is obtained by formula (1) and (2), in addition, let the control time domain be N C , the prediction time domain be N P , and N C ≤NP .

[0007] y P,i (k) = y Pol (k) + A i Δu P,i (k) (1)

[0008]

[0009]

[0010] The variables in Equations (1) - (3) are as follows:

[0011]

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] where a i,mn,t is the sampled value of the nth system output at time t subjected to the mth input unit step excitation of the ith magnetron, i.e., the step response; m = N I,i = 1 and t = 1,..., N P , yP,i (k) is the predicted value of the output of the system related to the ith magnetron, y n,P,i (k+t|k) is the value of the nth system output related to the ith magnetron at time step k+t predicted at time step k and t = 1, 2, …, N P , n = 1, 2, …, N O , y Pol (k) is the open loop predicted value of the system output, y n,Pol (k+t|k) is the open loop value of the nth system output at time step k+t predicted at time step k and t = 1, 2, …, N P , n = 1, 2, …, N O , A i is the dynamic matrix of the system with respect to the control input excitation of the ith magnetron, Δu P,i (k) is the predicted value of the control input increment of the ith magnetron, Δu P,i,m (k+t|k) is the value of the mth control input increment of the ith magnetron at time step k+t predicted at time step k and t = 0, 1, …, N C -1, M S is a shift matrix, is a matrix composed of unit step responses, Δu(k-1) is the actual control input increment of each agent at time step k-1 and Δu i,m (k-1) = Δu P,i,m (k-1|k-1), h is a prediction error correction matrix, e(k) is the prediction error at time step k, N a is the number of magnetrons installed in the device used in the microwave metallurgical process. y n (k) is the actual measured value of the nth system output at time step k, y n,P (k|k-1) is the value of the nth system output at time step k predicted at time step k-1.

[0028] Step 2, the microwave metallurgical process is multi-agent, the control input, the controlled variable and the soft and hard constraints of the microwave metallurgical process are determined, the relationship between the control input, the controlled variable and the input and output of the multi-agent system of the microwave metallurgical process is clarified, and the multi-agent system is formed;

[0029] Further, the microwave metallurgical process is multi-agent, which means that each magnetron and its corresponding control component are regarded as an agent, called microwave source agent, that is, the ith magnetron and its corresponding control component are the ith microwave source agent;

[0030] Further, the control input of the microwave metallurgical process is determined as the input electric power of each magnetron of the microwave source, the controlled variable of the system is determined as the temperature of the metallurgical material (specifically the temperature of the temperature measuring point); the upper and lower limits of the input electric power of the magnetron are determined as 1.5 kW and 0.075 kW respectively, and the upper and lower limits of the temperature of the metallurgical material are determined as 1200℃ and room temperature respectively; therefore, the control input of the corresponding multi-agent system is the input electric power of each microwave source agent, that is, the control input of the microwave metallurgical process, and therefore, the upper and lower limits of the control input of the multi-agent system are 1.5 kW and 0.075 kW respectively; the output of the system is the temperature of the metallurgical material, that is, the controlled variable, and the number of temperature measuring points is consistent with the number of system outputs; in summary, the multi-agent system formed has N a microwave source agents.

[0031] Step 3, an intelligent agent priority negotiation mechanism based on interactive game is established, and the interaction between the microwave source agents is modeled as an interactive game between multiple agents, denoted as The definition is as follows:

[0032] Time step: a game is performed once every time step k.

[0033] Agent: the set of all microwave source agents is denoted as The i-th microwave source agent

[0034] is denoted as

[0035] Strategy: each microwave source agent selects its own strategy in the strategy set Ω i ={0,1}. At time step k, the microwave source agent selects its strategy by interacting with its neighbors to minimize its cost function

[0036]

[0037] The cost function of the microwave source agent is

[0038]

[0039] The value of the cost function formula (4) is the priority of the microwave source agent at time step k, and the smaller the value is, the higher the priority is. Wherein, denotes the neighbors of the microwave source agent ; in the cost function formula (4), is the cost function when the agent and the agent perform the interactive game, which is specifically shown in formula (5),

[0040]

[0041] where s ij ∈Ω i is the intelligent agent The strategy chosen by the intelligent agent when playing the interactive game with the intelligent agent is denoted as follows:

[0042]

[0043] where y t (k) is the temperature target of each temperature measurement point, is the output prediction of the multi-agent system about the intelligent agent in the priority negotiation stage, is the vector for tensor operation on y t (k), is the Kronecker product for tensor calculation, is the "winner takes all" control scheme (see step 5 for specific calculation method), and Q PN1 is the weight matrix about the deviation between the system output and the target, which is specifically:

[0044]

[0045] where y Pol (k) is the open-loop prediction value of the system output, and the subscript N O indicates that there are N O system outputs in total, and N P is the prediction time domain, is the weight matrix of the n-th system output corresponding to the deviation between the sum and the target when priority negotiation is performed, and n = 1, 2, …, N O , from to are the weight values of the n-th system output corresponding to the deviation between the sum and the target at each time step within the prediction time domain N P .

[0046] Step 4, establish a multi-agent system model predictive control mechanism under the sequential game framework;

[0047] At time step k, each microwave source intelligent agent obtains its optimal control input increment prediction value Δu P,i (k) from high to low by solving the optimization problem (6) according to the priority obtained based on the intelligent agent priority negotiation mechanism based on the interactive game.

[0048]

[0049] where y t (k) is the temperature target of each temperature measurement point, is the vector of tensor operation on y t (k), N P is the prediction horizon, y P,i (k) is the predicted value of system output related to the ith magnetron, denotes the neighbors of the microwave source agent , and the “SG” in the upper index of some symbols is the abbreviation of Sequential Game, Δu P,i (k) is the predicted value of control input increment of the ith magnetron, u i (k-1) is the actual control input of the microwave source agent at time step k-1, A j' and Δu P,j' (k) are the dynamic matrix and the optimal control input increment sequence of the agents with higher priority than the microwave source agent at time step k, respectively, A j and are the dynamic matrix of the agents with lower priority than the microwave source agent at time step k and the optimal control input increment sequence of the agents with lower priority than the microwave source agent at time step k-1 after shifting, respectively, M u,i is a matrix with diagonal elements being unit lower triangular matrix (other elements are 0), is the vector of tensor operation on control input and its increment; u min,i and u max,i are the lower and upper limits of the control input of the microwave source agent , respectively, Δu min,i and Δu max,i are the lower and upper limits of the control input increment of the microwave source agent , respectively, y min and y max are the lower and upper limits of the system output, respectively; Specifically,

[0050]

[0051] Q SG1 , and are the weight matrices of the deviation between system output and target, the control input increment of the agent and the total amount of control input when performing sequential game, and they are specifically:

[0052]

[0053]

[0054]

[0055] Where, N I,i Represents a microwave source intelligent agent There are a total of N I,i One control input, N C For predicting the time domain and N C ≤N P , The weight matrix corresponding to the output of the nth system in a sequential game, where n = 1, 2, ..., N O N O This indicates that there are a total of N. O System output, Microwave source intelligent agent for sequential game The weight matrix corresponding to the increment of the m-th control input, from arrive Microwave source intelligent agent The increment of the m-th control input in the control time domain N C The weight value corresponding to each time step within the time frame. Microwave source intelligent agent for sequential game The weight matrix corresponding to the total amount of the m-th control input, from arrive Microwave source intelligent agent The total amount of the m-th control input in the control time domain N C The weight value corresponding to each time step within the time frame.

[0056] Step 5: Under the established agent priority negotiation mechanism based on interactive game theory, at each time step k, each agent obtains its own computational priority through the agent priority negotiation mechanism based on interactive game theory. The specific scheme for determining its own computational priority is as follows:

[0057] First, each agent obtains its own "winner-takes-all" control scheme at time step k, i.e., the optimal control input increment sequence, by solving the optimization problem (7). (Not used for actual metallurgical furnace control, but only for calculating agent priorities):

[0058]

[0059]

[0060] in, microwave source agent total cost function in the priority negotiation phase, not used as actual metallurgical furnace control, only for calculating the agent priority, y t (k) is the temperature target of each temperature measurement point, refers to the output prediction of the multi-agent system about the agent in the priority negotiation phase, N P is the prediction horizon; is the Kronecker product, which is used for tensor calculation, u i (k-1) is the actual control input of the microwave source agent at time step k-1, M u,i is a matrix with unit diagonal elements and lower triangular elements; u min,i and u max,i are the lower limit and the upper limit of the control input of the i-th microwave source agent, respectively; Δu min,i and Δu max,i are the lower limit and the upper limit of the increment of the control input of the i-th microwave source agent, respectively, y min and y max are the lower limit and the upper limit of the system output, respectively; Q PN1 is the weight matrix about the deviation between the system output and the target, and are the weight matrices of the control input increment and the total control input of the agent , which are specifically:

[0061]

[0062]

[0063] wherein is the weight matrix corresponding to the increment of the m-th control input of the microwave source agent when the priority negotiation is performed, from to are the weight values corresponding to the increment of the m-th control input of the microwave source agent at each time step within the control horizon N C , is the weight matrix corresponding to the total amount of the m-th control input of the microwave source agent when the priority negotiation is performed, from to are the weight values corresponding to the total amount of the m-th control input of the microwave source agent within the control horizon N CThe weight value corresponding to each time step.

[0064] Then, each microwave source agent calculates its own optimal control input increment sequence Δu The revenue brought by the "winner takes all" scheme is obtained by solving formula (8):

[0065]

[0066] Finally, at each time step k, each agent The calculation priority of each agent is obtained by calculating the value of formula (4).

[0067] Step 6, at each time step k, each agent calculates its own optimal control input increment sequence Δu P,i (k) according to the calculation priority in step 5, and takes the first element in the sequence as its actual optimal control input increment.

[0068] Step 7, each microwave source agent repeats steps 5 and 6 at each time step k to obtain its actual optimal control input increment at each time step k, and accordingly performs real-time dynamic optimization control on the microwave metallurgical process.

[0069] The main equipment and module components of the microwave metallurgical furnace to which the application is applied include: 6*1.5KW magnetrons and related control components, a microwave metallurgical furnace resonant cavity coated with thermal insulation material made of stainless steel and steel plate, a cooling water circulation system, a thermocouple, an infrared thermometer, etc. The energy conversion efficiency of each magnetron is different, which is the main source of energy consumption.

[0070] From the perspective of control method, industrial microwave metallurgical furnaces generally use "proportional-integral-derivative" (PID) control method to adjust the input electric power of the magnetron, and after using the priority negotiation-based multi-agent model predictive control method of the microwave metallurgical process, the energy utilization can be optimized while ensuring the temperature demand of the metallurgical material, the working energy consumption is reduced, the economic benefit is improved, and the control performance is improved.

[0071] The beneficial effects of the application are:

[0072] 1. The application can realize accurate temperature following of the metallurgical material in the microwave metallurgical process, and the temperature control is more accurate.

[0073] 2. The application can effectively reduce energy consumption while ensuring accurate temperature control of the microwave metallurgical process.

[0074] 3. The method described in this invention can be used not only in microwave metallurgical furnaces with six magnetrons as described in this invention, but also in microwave metallurgical furnaces with other numbers of magnetrons, and is applicable to various industrial processes that utilize microwave heating technology for production, thus exhibiting high versatility.

[0075] 4. The method described in this invention can be used not only for magnetron power control of microwave metallurgical furnaces, but also for other multi-body control scenarios such as metal pickling, heavy oil fractionation, and accelerated cooling of steel rolling, making it highly versatile. Attached Figure Description

[0076] Figure 1 This is the overall process of the invention participating in practical applications;

[0077] Figure 2 This is a flowchart illustrating steps 1 and 2 of the present invention;

[0078] Figure 3 This is a flowchart illustrating steps 3 and 4 of the present invention;

[0079] Figure 4 This is a flowchart illustrating steps 5 and 6 of the present invention;

[0080] Figure 5 From microwave source intelligent agent From the perspective of [the present invention], the overall implementation process of the present invention;

[0081] Figure 6 These are three views of the microwave metallurgical furnace including a magnetron as described in this invention; wherein, the upper left is the front view, the lower left is the top view, and the upper right is the left view.

[0082] Figure 7 This is a perspective view of the microwave metallurgical furnace including the magnetron described in this invention. Detailed Implementation

[0083] Example 1: As Figures 1-7 As shown, a multi-agent model predictive control method for microwave metallurgical processes based on priority negotiation is presented. The specific steps of the method are as follows:

[0084] Step 1: Establish a predictive mathematical model of the microwave metallurgical process based on its actual dynamic characteristics. The microwave metallurgical process regulates the output microwave power of the magnetron by adjusting its input electrical power. The microwaves generated by the magnetron are fed into the resonant cavity of the metallurgical furnace, where they resonate, thereby heating the metallurgical material and extracting metals or metal compounds from it at a predetermined temperature. The metallurgical furnace used in the microwave metallurgical process is equipped with N... aa magnetron, the control input of each magnetron is its input electric power, the input electric power is continuously adjustable in the range of 0.075-1.5 kW, and the metallurgical furnace can withstand the metallurgical temperature in the range of room temperature-1200℃.

[0085] The process mathematical model with the prediction function is obtained through formulas (1) and (2), as shown in formula (3);

[0086] y P,i (k) = y Pol (k) + A i Δu P,i (k) (1)

[0087]

[0088]

[0089] wherein y P,i (k) is the system output prediction value related to the i-th magnetron, y Pol (k) is the open-loop prediction value of the system output, A i is the dynamic matrix of the system with respect to the control input excitation of the i-th magnetron, Δu P,i (k) is the prediction value of the control input increment of the i-th magnetron, M S is the shift matrix, is the matrix composed of unit step responses, Δu(k-1) is the actual control input increment of each agent at the time step k-1, h is the prediction error correction matrix, and e(k) is the prediction error at the time step k; N a is the number of magnetrons installed in the device used in the microwave metallurgical process.

[0090] Step 2, the microwave metallurgical process is multi-agentized, the control input, the controlled variable and each item of soft and hard constraints of the microwave metallurgical process are determined, the relationship between the control input, the controlled variable and the input and output of the agent system of the microwave metallurgical process is clarified, and the multi-agent system is formed;

[0091] The multi-agentization of the microwave metallurgy process in step 2 refers to regarding each magnetron and its corresponding control component as an agent, called a microwave source agent, that is, the i-th magnetron and its corresponding control component is the i-th microwave source agent; the control input of the microwave metallurgy process is determined as the input electric power of each magnetron; the controlled variable is determined as the temperature of the metallurgical material, that is, the temperature of the temperature measuring point in actual operation; the upper and lower limits of the input electric power constraint of the magnetron are determined as 1.5 kW and 0.075 kW respectively, and the upper and lower limits of the temperature constraint of the metallurgical material in the metallurgical process are determined as 1200 DEG C and room temperature respectively; the control input of the corresponding multi-agent system is the input electric power of each microwave source agent, that is, the control input of the microwave metallurgy process, therefore, the upper and lower limits of the control input constraint of the multi-agent system are 1.5 kW and 0.075 kW respectively; the output of the system is the temperature of the metallurgical material, that is, the controlled variable, and the upper and lower limits of the constraint are 1200 DEG C and room temperature respectively, the number of temperature measuring points is consistent with the number of system outputs; the formed multi-agent system has N a microwave source agents.

[0092] Step 3, establishing an agent priority negotiation mechanism based on interactive game;

[0093] In step 3, the agent priority negotiation mechanism based on interactive game established is as follows:

[0094] The interaction between microwave source agents is modeled as an interactive game between multi-agents, denoted as The definition is as follows:

[0095] Time step: a game is performed at each time step k;

[0096] Agent: the set of all microwave source agents is denoted as The i-th microwave source agent

[0097] is denoted as

[0098] Strategy: each microwave source agent selects its own strategy in the strategy set Ω i ={0,1}; at time step k, the microwave source agent selects its strategy by interacting with its neighbors to minimize its cost function

[0099]

[0100] The cost function of the microwave source agent is:

[0101]

[0102] The value of the cost function formula (4) is the priority of the microwave source agent at time step k, and the smaller the value is, the higher the priority is; wherein, represents the neighbors of the microwave source agent ; in the cost function formula (4) is the cost function when the agent and the agent play the game against each other, which is specifically shown in formula (5),

[0103]

[0104] Wherein, s ij ∈Ω i is the strategy selected by the agent when playing the game against the agent , the “PN” in the upper subscript of some symbols is the English abbreviation of Priority Negotiation, and sgn() is a sign function, represents as follows:

[0105]

[0106] Wherein, y t (k) is the temperature target of each temperature measurement point, refers to the output prediction of the multi-agent system about the agent in the priority negotiation stage, is a vector for tensor operation on y t (k), is a Kronecker product for tensor calculation, is a “winner takes all” control scheme, Q PN1 is a weight matrix about the deviation between the system output and the target, which is specifically:

[0107]

[0108] Wherein, y Pol (k) is an open-loop prediction value of the system output, and the lower subscript N O indicates that there are N O system outputs in total, and N P is a prediction time domain, is a weight matrix of the n-th system output corresponding to the deviation between the sum and the target when negotiating the priority, and n=1, 2, …, N O , and are the weight values of the n-th system output corresponding to the deviation between the sum and the target at each time step in the prediction time domain N P .

[0109] Step 4, establishing a multi-agent system model predictive control mechanism under the sequential game framework;

[0110] The multi-agent system model predictive control mechanism under the sequential game framework established in step 4 is as follows:

[0111] At time step k, each microwave source agent obtains its optimal control input increment prediction value from high to low by solving the optimization problem (6) according to the priority obtained by the agent priority negotiation mechanism based on interactive game. P,i (k),

[0112]

[0113] where y t (k) is the temperature target of each temperature measurement point, is a vector for tensor operation on y t (k), N P is the prediction horizon, y P,i (k) is the system output prediction value related to the i-th magnetron, denotes the neighbors of the microwave source agent , and "SG" in the upper subscript of part of the symbol is the English abbreviation of Sequential Game, A j' and Δu P,j' (k) are the dynamic matrix and optimal control input increment sequence of the agent whose priority is higher than that of the microwave source agent at time step k, A j and are the dynamic matrix of the agent whose priority is lower than that of the microwave source agent at time step k and the optimal control input increment sequence obtained at time step k-1 after shifting, respectively, Δu P,i (k) is the prediction value of the control input increment of the i-th magnetron, u i (k-1) is the actual control input of the microwave source agent at time step k-1, M u,i is a matrix with unit lower triangular matrix as diagonal elements, is a vector for tensor operation on the control input and its increment; u min,i and u max,i are the lower and upper limits of the control input of the microwave source agent , Δu min,i and Δu max,i are the lower and upper limits of the control input increment of the microwave source agent , y min and y max are the lower and upper limits of the system output, QSG1 , and These refer to the deviation between the system output and the objective, and the agent's behavior during sequential game theory. The weight matrices for the control input increment and the total control input are as follows:

[0114]

[0115]

[0116]

[0117] Where, N I,i Represents a microwave source intelligent agent There are a total of N I,i One control input, N C For predicting the time domain and N C ≤N P , The weight matrix corresponding to the output of the nth system in a sequential game, where n = 1, 2, ..., N O N O This indicates that there are a total of N. O System output, Microwave source intelligent agent for sequential game The weight matrix corresponding to the increment of the m-th control input, from arrive Microwave source intelligent agent The increment of the m-th control input in the control time domain N C The weight value corresponding to each time step within the time frame. Microwave source intelligent agent for sequential game The weight matrix corresponding to the total amount of the m-th control input, from arrive Microwave source intelligent agent The total amount of the m-th control input in the control time domain N C The weight value corresponding to each time step within the time frame.

[0118] Step 5: At each time step k, each agent obtains its own computational priority through an agent priority negotiation mechanism based on interactive game theory.

[0119] In step 5, at each time step k, each agent obtains its own computational priority through an agent priority negotiation mechanism based on interactive game theory, specifically in steps 5-1, 5-2, and 5-3.

[0120] Step 5-1: Each agent obtains the "winner-takes-all" control scheme, i.e., the optimal control input increment sequence, by solving the optimization problem (7).

[0121]

[0122] wherein, represents the microwave source agent the total cost function in the priority negotiation phase, not used as actual metallurgical furnace control, only for calculating the agent priority, y t (k) is the temperature target of each temperature measurement point, refers to the output prediction of the multi-agent system about the agent in the priority negotiation phase, N P is the prediction time domain; is the Kronecker product, which is used for tensor calculation, u i (k-1) is the actual control input of the microwave source agent at time step k-1, M u,i is a matrix with diagonal elements being unit lower triangular matrix; u min,i and u max,i are the lower limit and upper limit of the control input of the i-th microwave source agent, respectively; Δu min,i and Δu max,i are the lower limit and upper limit of the increment of the control input of the i-th microwave source agent, respectively, y min and y max are the lower limit and upper limit of the system output, respectively; Q PN1 is the weight matrix about the deviation between the system output and the target, and are the weight matrices of the control input increment and the total control input of the agent , which are specifically:

[0123]

[0124]

[0125] wherein, is the weight matrix corresponding to the increment of the m-th control input of the microwave source agent when the priority negotiation is performed, from to are the weight values corresponding to the increment of the m-th control input of the microwave source agent at each time step within the control time domain N C , is the weight matrix corresponding to the total amount of the m-th control input of the microwave source agent when the priority negotiation is performed, from to respectively the total amount of the mth control input of the microwave source agent in each time step within the control time domain N C corresponding to the weight value of each time step within the control time domain N

[0126] Step 5-2, each microwave source agent obtains the priority of itself according to the obtained The revenue brought by the "winner takes all" scheme is obtained by solving formula (8):

[0127]

[0128] Step 5-3, each agent calculates the calculation priority of itself by calculating the value of formula (4) at each time step k. Step 5-3, each agent calculates the calculation priority of itself by calculating the value of formula (4) at each time step k.

[0129] Step 6, at each time step k, each agent calculates the optimal control input increment sequence of itself by solving the optimization problem (6) based on the calculation priority obtained in step 5, and takes the first element in the sequence as the actual optimal control input increment of itself.

[0130] Step 7, at each time step k, each agent obtains the result based on the foregoing steps 5 and 6, and performs real-time dynamic control on the microwave metallurgical process with the optimal control input increment, thereby realizing the optimization control of the microwave metallurgical process.

[0131] In this embodiment and embodiment 1, the same flow steps are adopted, wherein, as shown in the following table, the microwave metallurgical process multi-agent model predictive control method based on priority negotiation according to the present application mainly involves the following mechanisms: the agent priority negotiation mechanism based on interactive game and the multi-agent system model predictive control mechanism under the sequential game framework; the agent priority negotiation mechanism based on interactive game is used for the agent to determine its priority among adjacent agents at time step k; the multi-agent system model predictive control mechanism under the sequential game framework is used for the agent after obtaining its priority at time step k. Figure 1

[0132] Meanwhile, the specific implementation of the method according to the present application is described below with the metallurgical process in a microwave metallurgical furnace as shown in the following table as an example: Figure 6 Figure 7

[0133] ​​​First, the metallurgical process in the microwave smelting furnace is analyzed, and nine temperature measuring points are set inside the material to measure the temperature of the reaction material. The microwave smelting process has six magnetrons and nine temperature measuring points, and the control input of each magnetron is its input electric power. The input electric power of each magnetron ranges from 0.075 to 1.5 kW continuously adjustable, and the temperature range that the smelting furnace can withstand is room temperature to 1200℃.

[0134] Different magnetrons are turned on respectively, and multiple heating tests are conducted on the microwave smelting process. When the same magnetron is working, the temperature of the smelting material at each time step is sampled, and the matrix A in the mathematical model formulas (2) and (3) is established according to the obtained sampling data i and Then, according to the principle of N C ≤N P , the control time domain N C = 30 is set, and the prediction time domain N P = 50.

[0135] Second, the metallurgical process in the microwave smelting furnace is considered as a multi-agent system, which has six microwave source agents and nine system outputs, and the control input of each microwave source agent is its input electric power. The input electric power of each magnetron ranges from 0.075 to 1.5 kW continuously adjustable, and the temperature range that the smelting furnace can withstand is room temperature to 1200℃. The control input of the microwave smelting process is determined as the input electric power of the six microwave source agents; the controlled variables are the temperatures of the smelting material measured by the nine temperature measuring points; the upper and lower limits of the input electric power of the microwave source agents are 1.5 kW and 0.075 kW respectively, and the upper and lower limits of the smelting material temperature are 1200℃ and room temperature respectively; the input of the corresponding agent system is the input electric power of the six microwave source agents (i.e. the control input of the microwave smelting process), and the output is the temperature of the smelting material measured by the nine temperature measuring points (i.e. the controlled variable). The control objective of the system is to make each output temperature of the system in the microwave smelting process reach the target and tend to be consistent through the coordination between the microwave source agents, while reducing energy consumption.

[0136] Third, assuming that the current time step is k, for the microwave source agent , the "winner takes all" control scheme (i.e. the optimal control input increment sequence is obtained by solving the optimization problem formula (7), which is not used for actual control but only for priority calculation), and then the obtained is substituted into formula (8) to obtain the revenue of the "winner takes all" scheme. Finally, the of the microwave source agent and the revenue of the adjacent microwave source agent are compared. Substitute equation (5) into equation (4) to obtain the calculation priority of the microwave source agent and each of its neighbors The game result Then substitute all into equation (4) to obtain the calculation priority of the microwave source agent

[0137] Fourth, assuming that the current time step is k, the calculation priority obtained in the third step is the calculation order of the microwave source agent among its neighboring microwave source agents. When the priority is higher than that of the agent , the agent will send information to the microwave source agent When the microwave source agent receives the information for a number of times equal to , the microwave source agent begins to calculate; the microwave source agent uses the multi-agent system model predictive control mechanism under the sequential game framework to solve the optimization problem equation (6) to obtain the optimal control input increment sequence Δu P,i (k) of the microwave source agent at time step k, and the first element in the sequence is used as the actual optimal control input increment of the microwave source agent itself and is actually applied to control.

[0138] Fifth, at the next time step, i.e., time step k+1, each agent executes the third and fourth steps again; further, at each time step, each agent first executes the third step and then executes the fourth step.

[0139] The specific embodiments of the application are described in detail above in combination with the drawings, but the application is not limited to the above-described embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the purpose of the application.​

Claims

1. A priority negotiation based multi-agent model predictive control method for microwave metallurgical process, characterized in that: The specific steps of the method are as follows: Step 1, a process mathematical model with prediction function is established according to the actual dynamic characteristics of the microwave metallurgy process; Step 2, the microwave metallurgy process is multi-agentized, the control input, controlled variable and various soft and hard constraints of the microwave metallurgy process are determined, the relationship between the control input, controlled variable and the input and output of the agent system of the microwave metallurgy process is clarified, and a multi-agent system is formed; Step 3, an agent priority negotiation mechanism based on interactive game is established; Step 4, a multi-agent system model predictive control mechanism under a sequential game framework is established; Step 5, at each time step k, each agent obtains its own calculation priority through the agent priority negotiation mechanism based on interactive game; Step 6, at each time step k, each agent calculates its own optimal control input increment based on the calculation priority in step 5 using the multi-agent system model predictive control mechanism under the sequential game framework; Step 7, at each time step k, each agent obtains the results based on the aforementioned steps 5 and 6, and uses the optimal control input increment to perform real-time dynamic control on the microwave metallurgy process, thereby realizing the optimal control of the microwave metallurgy process; In step 3, the agent priority negotiation mechanism based on interactive game is as follows: The interaction between the microwave source agents is modeled as a multi-agent interaction game, denoted as which is defined as follows: Time step: a game is performed at each time step k; Agent: The set of all microwave source agents is denoted as , and the i-th microwave source agent is denoted as ; Policy: Each microwave source agent selects its own policy from a set of policies At time step k, the microwave source agent selects its policy by interacting with its neighbors to minimize its cost function ; Microwave source agent The cost function for the agent is: (4) The value of cost function formula (4) is the priority of the microwave source agent at time step k, and the smaller the value is, the higher the priority is; wherein, represents the neighbors of the microwave source agent ; in the cost function formula (4) , the value of is the cost function when the agent and the agent carry out the interactive game, which is specifically shown in formula (5), (5) wherein is the agent In the interaction game with the agent The PN in the superscript of some symbols is the first letter abbreviation of Priority Negotiation, and sgn() is a sign function, is expressed as follows: wherein is the temperature target for each temperature measurement point, is the output prediction of the multi-agent system with respect to the agent at the priority negotiation stage, is the vector of tensor operations on , is the Kronecker product for tensor computation, is the "winner-takes-all" control scheme, is the dynamic matrix of the system with respect to the control input excitation of the i-th magnetron, is the weight matrix with respect to the deviation between the system output and the target, which is specifically ； ； wherein, is the open loop prediction value output by the system, the subscript denotes a total of system outputs, is the prediction horizon, is the weight matrix of the inter-target deviation corresponding to the n-th system output when priority negotiation is performed and the target is , , and are the weight values of the inter-target deviation corresponding to each time step within the prediction horizon , and of the n-th system output, respectively.

2. The priority negotiation based microwave metallurgical process multi-agent model predictive control method according to claim 1, characterized in that: The microwave metallurgical process in the step 1 is adjusted by adjusting the input electric power of the magnetron to change the output microwave power of the magnetron, the microwave generated by the magnetron is fed into the resonant cavity of the metallurgical furnace and forms resonance therein, thereby heating the metallurgical material and extracting metal or metal compound from the metallurgical material at a predetermined temperature; the metallurgical furnace used in the microwave metallurgical process is installed with a magnetron, the control input of each magnetron is its input electric power, the input electric power is continuously adjustable in the range of 0.075-1.5 kW, and the metallurgical temperature range that the metallurgical furnace can withstand is room temperature-1200℃.

3. The priority negotiation based microwave metallurgical process multi-agent model predictive control method according to claim 1, characterized in that: The process mathematical model with prediction function in step 1 is obtained through formulas (1) and (2), as shown in formula (3); (1) (2) (3) wherein, is the system output prediction value related to the i-th magnetron, is the open loop prediction value of the system output, is the dynamic matrix of the system with respect to the control input excitation of the i-th magnetron, is the prediction value of the control input increment of the i-th magnetron, is the shift matrix, is the matrix of unit step responses, is the time step is the actual control input increment of each agent, h is the prediction error correction matrix, is the prediction error at time step k; is the number of magnetrons installed in the apparatus used in the microwave metallurgical process.

4. The priority negotiation based microwave metallurgical process multi-agent model predictive control method according to claim 1, characterized in that: The multi-agentization of the microwave metallurgy process in step 2 refers to regarding each magnetron and its corresponding control component as an agent, called a microwave source agent, that is, the i th magnetron and its corresponding control component is the i th microwave source agent; the control input of the microwave metallurgy process is determined as the input electric power of each magnetron; the controlled variable is determined as the temperature of the metallurgical material, that is, the temperature of the temperature measuring point in actual operation; the upper and lower limits of the input electric power constraint of the magnetron are respectively 1.5 kW and 0.075 kW, and the upper and lower limits of the temperature constraint of the metallurgical material in the metallurgical process are respectively 1200℃ and room temperature; the control input of the corresponding multi-agent system is the input electric power of each microwave source agent, that is, the control input of the microwave metallurgy process, therefore, the upper and lower limits of the control input constraint of the multi-agent system are respectively 1.5 kW and 0.075 kW; the output of the system is the temperature of the metallurgical material, that is, the controlled variable, and the upper and lower limits of the constraint are respectively 1200℃ and room temperature, the number of temperature measuring points is consistent with the number of system outputs; the formed multi-agent system has microwave source agents.

5. The priority negotiation based microwave metallurgical process multi-agent model predictive control method according to claim 1, characterized in that: The multi-agent system model predictive control mechanism under the sequential game framework established in step 4 is as follows: At time step k, each microwave source agent gets its optimal control input increment prediction value from high to low by solving optimization formula (6) according to the priority obtained based on the agent priority negotiation mechanism for interactive game , ； (6) ； wherein is the temperature target of each temperature measurement point, is the vector of tensor operations, is the prediction horizon, is the system output prediction value related to the i-th magnetron, denotes the neighbors of the microwave source agent SG is the acronym of Sequential Game in the partial symbol subscript, and are the dynamic matrix and the optimal control input increment sequence of the agents with higher priority than the microwave source agent at time step k, respectively, and are the dynamic matrix of the agents with lower priority than the microwave source agent at time step k and its optimal control input increment sequence after shifting the time step , is the prediction value of the control input increment of the i-th magnetron, is the actual control input of the microwave source agent at time step , is a matrix with diagonal elements being unit lower triangular matrices, is a vector of tensor operations on the control input and its increment; and are the lower and upper limits of the control input of the microwave source agent , respectively, and are the lower and upper limits of the control input increment of the microwave source agent , respectively, and are the lower and upper limits of the system output, respectively, is the weight matrix of the deviation between the system output and the target when performing the sequential game, is the weight matrix of the control input increment of the agent when performing the sequential game, is the weight matrix of the total amount of the control input of the agent when performing the sequential game, which are specifically:​ ； ； ； ； ； ； wherein, represents the microwave source agent there are in total control inputs, is the prediction horizon and , is the weight matrix corresponding to the nth system output of the microwave source agent , there are in total system outputs, is the weight matrix corresponding to the increment of the mth control input of the microwave source agent from to are the weight values corresponding to each time step within the control horizon of the increment of the mth control input of the microwave source agent , is the weight matrix corresponding to the total amount of the mth control input of the microwave source agent from to are the weight values corresponding to each time step within the control horizon of the total amount of the mth control input of the microwave source agent .

6. The priority negotiation based microwave metallurgical process multi-agent model predictive control method according to claim 1, characterized in that: In step 5, at each time step k, each agent obtains its own calculation priority through the agent priority negotiation mechanism based on interactive game, which is specifically divided into steps 5-1, 5-2 and 5-3; Step 5-1. Each agent obtains a winner-take-all control scheme, i.e., the optimal control input increment sequence, by solving the optimization equation (7) : (7) wherein, represents the microwave source agent is the total cost function in the priority negotiation phase, is not used as actual metallurgical furnace control, but only for calculating the agent priority, is the temperature target of each temperature measurement point, refers to the output prediction of the multi-agent system about the agent in the priority negotiation phase, , ; is the prediction time domain; is the Kronecker product, which is used for tensor calculation, is the actual control input of the microwave source agent at time step , is a matrix with diagonal elements being unit lower triangular matrix; and are the lower limit and upper limit of the constraint of the control input of the i-th microwave source agent, respectively; and are the lower limit and upper limit of the constraint of the control input increment of the i-th microwave source agent, respectively, and are the lower limit and upper limit of the system output, respectively; is the weight matrix about the deviation between the system output and the target, and are the weight matrix of the control input increment and the total amount of the control input of the agent , which are specifically: ； ； ； ； in, Microwave source intelligent agent for priority negotiation The weight matrix corresponding to the increment of the m-th control input, from arrive Microwave source intelligent agent The increment of the m-th control input in the control time domain The weight value corresponding to each time step within the time frame. Microwave source intelligent agent for priority negotiation The weight matrix corresponding to the total amount of the m-th control input, from arrive Microwave source intelligent agent The total amount of the m-th control input in the control time domain The weight value corresponding to each time step within the time step; Step 5-2, each microwave source agent calculates the payoff from the resulting The payoff from the winner-take-all solution is obtained by solving equation (8): (8) Step 5 - 3, each agent The self's computation priority is obtained by computing the value of equation (4) at each time step k.

7. The priority negotiation based microwave metallurgical process multi-agent model predictive control method according to claim 5, characterized in that: In step 6, at each time step k, each agent calculates its own optimal control input increment sequence based on the calculation priority in step 5 using the multi-agent system model predictive control mechanism under the sequential game framework, that is, solving the optimization formula (6), and taking the first element in the sequence as its actual optimal control input increment.

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