A predictive control method for cement firing process based on state decomposition technology

Abstract

This invention belongs to the field of control engineering technology and discloses a predictive control method for cement calcination process based on state decomposition technology. First, a generalized state-space model of the calcination process in cement production is established and applied to a generalized polyhedral uncertain system. Then, based on actual production line requirements, system control input and output constraints are designed. Through state decomposition technology, an equivalent structural model and equivalent input and output constraints are obtained. A novel state-decomposed feedback predictive controller is designed, and the decomposed components of the feedback predictive controller are solved using the linear matrix inequality method to obtain the overall predictive controller. This invention effectively handles the generalized characteristics of generalized polyhedral uncertain systems, while reducing computational complexity, improving system response speed, ensuring system robustness and stability, and resulting in better control of the cement calcination process.

Description

Technical Field

[0001] This invention belongs to the field of control engineering technology, specifically relating to a predictive control method for cement firing process models based on state decomposition technology. Background Technology

[0002] Cement production processes are often characterized by high nonlinearity, multiple variables, strong coupling, and time-varying nature, making it difficult to establish accurate mathematical models. Even when mathematical models can be established for some processes, their structures are extremely complex, making effective control difficult to design and implement. Adaptive and self-tuning control technologies, which have developed alongside this situation, can address these problems to some extent, but they still fundamentally require online identification of the object model, resulting in complex algorithms, high computational load, and limited application scope. Since the 1970s, in addition to strengthening research on production process modeling, system identification, adaptive control, and robust control, researchers have begun to break free from the constraints of traditional control thinking, attempting to address the characteristics of industrial processes and seeking algorithms with low model requirements, convenient online computation, and good control effects. Furthermore, the development of smaller, higher-speed, larger-capacity, and lower-cost computers has provided the necessary equipment for these algorithms. Predictive control is a new type of computer control algorithm that has developed under these circumstances.

[0003] Predictive control, also known as rolling time-domain control, is an advanced model-based control technique. Emerging in the late 1970s, it's a new type of computer control algorithm that doesn't require high model accuracy and can estimate the system's control performance over a specified time period. It primarily incorporates three control concepts: model prediction, feedback correction, and rolling optimization. Based on a predictive model, it employs a quadratic online rolling optimization performance index and feedback correction strategy to overcome the influence of controlled object model errors and factors such as parameter and environmental changes, exhibiting strong robustness and widespread application in industrial control. Common predictive control algorithms at this stage include Model Algorithmic Control (MAC), Dynamic Matrix Control (DMC), and Generalized Predictive Control (GPC). However, most of these algorithms are based on linear or quasi-linear optimization cases, making them extremely difficult to study in situations involving multivariables, multiple constraints, and nonlinearity.

[0004] Since the mid-1990s, research in predictive control theory has shifted from "stability of algorithms" to "stability of algorithms." This shift is characterized by moving beyond quantitative analysis of existing predictive control algorithms and focusing on theoretically designing algorithms to ensure stability or other control performance guarantees. In recent years, numerous research papers with profound academic value and methodological innovation have emerged, bringing new highlights to the study of optimal control of constrained systems. However, most research results are rarely applied in industrial fields, and the comprehensive research approach has some fundamental shortcomings. For example, the heavy online computational burden is unacceptable for practical applications. Therefore, how to reduce computational complexity while ensuring system stability, optimality, and robustness remains a highly worthy topic of discussion. Summary of the Invention

[0005] The purpose of this invention is to provide a predictive control method for cement firing process model based on state decomposition technology, in order to solve the technical problems of high computational complexity, insufficient system response speed, and especially difficulty in ensuring the robustness and stability of the system in the existing technology.

[0006] The method for predictive control of cement firing process model based on state decomposition technology includes the following steps.

[0007] Step 1: Establish a generalized polyhedral uncertainty model of the cement firing process system and initialize the system state.

[0008] Step 2: Based on the state feedback strategy, establish a closed-loop system using a model predictive controller and impose constraints on the control input and output.

[0009] Step 3: Using state decomposition techniques, establish an equivalent structural model of the state decomposition, the controller, and equivalent constraints.

[0010] Step 4: Based on the linear matrix inequality method and Lyapunov theory, the controller is set to ensure the continuous and stable operation of the control system.

[0011] Preferably, step 1 includes: establishing a generalized polyhedral uncertainty system for the cement firing process system, with the following expression:

[0012]

[0013] Where x(k)∈R n It is the system state, u(k)∈R m It is the control input, y(k)∈R qThis is the measurement output, k is the current sampling time, R represents the corresponding space, and the superscripts n, m, q correspond to the dimensions of the space. E is the generalized matrix, while A(k), B(k), C(k) are unknown matrices of appropriate dimensions, belonging to the polyhedron set.

[0014] Ω=Co{[A1 B1 C1], [A2 B2 C2],…,[A L B L C L ]},

[0015] Where Co is a convex hull used to describe the uncertainty of a polyhedral uncertain system, and the subscript L is the number of sub-control systems. Therefore, when [ABC]∈Ω, we have This includes the weighting coefficients λ1, λ2, ..., λ for each sub-control system. L These weight coefficients are non-negative and satisfy the following conditions:

[0016] Preferably, step 2 includes: the expression for the designed state feedback model predictive controller is:

[0017] u(k+i|k)=K(k+i|k)x(k+i|k),

[0018] Where x(k+i|k) is the predicted state value at time k+i, u(k+i|k) is the latest control signal with the performance index at time k+i, and K(k+i|k) is the corresponding feedback gain through optimization design; combined with the generalized polyhedral uncertainty system established in step 1, the closed-loop system is obtained:

[0019]

[0020] Where K(k) is the feedback gain at time k.

[0021] Preferably, based on the engineering requirements of the cement firing process, the control input and control output are subject to the following constraints:

[0022] y min (k)≤y(k)≤y max (k),

[0023] u min (k)≤u(k)≤u max (k),

[0024] Δy min (k)≤Δy(k)≤Δy max (k),

[0025] Δu min (k)≤Δu(k)≤Δu max (k), where ymin (k) and y max (k) represents the minimum and maximum values ​​of the control output y(k) at time k, respectively; u min (k) and u max (k) represents the minimum and maximum values ​​of the control input u(k) at time k, respectively; Δy min (k) and Δy max (k) represents the minimum and maximum values ​​of the control output change Δy(k) at time k; Δu min (k) and Δu max (k) represents the minimum and maximum values ​​of the control input change Δu(k) at time k.

[0026] Preferably, step 3 includes: there exist two invertible matrices H and G such that the following equation holds:

[0027]

[0028]

[0029] The closed-loop system established in step 2 is transformed into an equivalent structural model using the state decomposition method:

[0030]

[0031] in, [K1(k+i) K2(k+i)]=K(k+i)G.

[0032] Similarly, a state feedback controller in the form of state decomposition can be obtained:

[0033]

[0034] Where [K1(k+i) K2(k+i)]=K(k+i)G.

[0035] Preferably, step 4 includes:

[0036] Step 4.1: Establish and optimize performance indicators, specifically performance indicator J. N The formula for calculating (k) is as follows:

[0037]

[0038] Where W1≥0 and W2≥0 are given weighted real matrices, x(k+i|k) is the state prediction value at time k+i, u(k+i|k) is the latest control signal of the performance index at time k+i, and N is the control time domain.

[0039] Step 4.2: Establish a system stabilization model and set the controller based on the linear matrix inequality method.

[0040] Step 4.3: After determining the controller parameters and their corresponding calculation methods, establish the predictive control algorithm.

[0041] Preferably, in step 4.2, a Lyapunov function with a state decomposition form is introduced, namely:

[0042]

[0043] And the Lyapunov function satisfies the following constraints:

[0044]

[0045] in

[0046] Subsequently, based on the free weight matrix technique, the zero inequality technique, and Lyapunov stability analysis theory, the optimization problem of the controller is transformed into a linear matrix inequality to be solved, and the feedback gain K(k) is obtained, which makes the generalized polyhedral uncertainty system stable during the cement firing process.

[0047] Preferably, step 4.3 includes...

[0048] Step 4.3.1: Select time k and control time domain N, obtain the system information at the current time, and provide the performance-related matrix W. 11 W 22 ,

[0049] Step 4.3.2: Solve the optimization problem of linear matrix inequalities in the [k, N] time zone. The right side gives the feedback gain K(k) of the system at time k, which minimizes the optimization performance index online.

[0050] Step 4.3.3: Substitute the feedback gain K(k) of the system at time k into the equivalent structural model of the closed-loop system to obtain the state prediction value at time k.

[0051] Step 4.3.4: Let k = k + 1, and repeat steps 1 to 4.

[0052] This invention offers the following advantages: It targets generalized polyhedral uncertain systems, effectively addressing the generalized characteristics within these systems. Generalized systems have a broader application scope than linear systems, exhibiting more general forms and making them suitable for complex systems in large-scale cement processing, better reflecting the actual conditions of cement firing processes. The most significant advantage of the state decomposition method is its ability to minimize computational complexity and improve system response speed during the establishment of a system stability framework. Furthermore, the state decomposition method emphasizes system robustness, combining system constraints to ensure robustness and stabilization, thereby enabling continuous, stable, and efficient cement firing production. Attached Figure Description

[0053] Figure 1 This is a flowchart of a cement firing process model prediction and control method based on state decomposition technology according to the present invention.

[0054] Figure 2 This is a schematic diagram of the cement firing system using the present invention.

[0055] Figure 3 This is a schematic diagram of the output response of the decomposition furnace outlet temperature control system of the present invention running for 10 steps under zero initial conditions.

[0056] Figure 4 This is a schematic diagram illustrating the state response of the decomposition furnace outlet temperature control system of the present invention under zero initial conditions for 10 steps.

[0057] Figure 5 This is a schematic diagram of the input response of the decomposition furnace outlet temperature control system of the present invention running for 10 steps under zero initial conditions. Detailed Implementation

[0058] The following detailed description of the embodiments, with reference to the accompanying drawings, will further illustrate the specific implementation of the present invention, in order to help those skilled in the art to have a more complete, accurate, and thorough understanding of the inventive concept and technical solutions of the present invention.

[0059] The cement calcination system is the core component of cement clinker production, and its main equipment includes a five-stage preheater, a cement decomposition furnace, a rotary kiln, and a grate cooler. This process involves many controlled variables, such as the carbon monoxide content at the high-temperature fan outlet, kiln head temperature, kiln head negative pressure, kiln current, pressure at the first stage of the grate cooler, and the decomposition furnace outlet temperature. These can be controlled by parameters such as the high-temperature fan frequency, kiln head coal feed rate, kiln rotation speed, oscillating exhaust fan, grate cooler grate speed, and coal feed rate.

[0060] like Figure 1-5 As shown, the present invention provides a predictive control method for cement firing process model based on state decomposition technology, which includes the following steps.

[0061] Step 1: Establish a generalized polyhedral uncertainty model of the cement firing process system and initialize the system state.

[0062] A control model is established based on the sub-control system of the cement firing system, and the expression is as follows:

[0063]

[0064] For the i-th sub-control system, x i (k) represents the subsystem state at time k, a i (k) represents the control input at time k, b i (k) represents the control output at time k, A i B i C i D i Let be the parameter matrices corresponding to the sub-control system, and the system ∑1 is further rewritten as:

[0065]

[0066] in,

[0067]

[0068] A=diag(A1,A2,…,A6), B=diag(B1,B2,…,B6),

[0069] C=diag(C1,C2,…,C6), D=diag(D,D2,…,D6),

[0070] The above sub-control systems are linearly related, therefore the system ∑2 can be further transformed into:

[0071]

[0072] In this context, for a large system like the cement firing system, u(k) represents the total control input, and y(k) represents the total measurement output; L ij R ij Both are coefficient matrices of suitable dimension i, j = 1, 2.

[0073] Let x e (k)=[x T (k), a T (k), b T (k), y T (k)] T ,y e From the above expression, we can further obtain: y(k) = y(k)

[0074]

[0075] in,

[0076]

[0077] Therefore, this method establishes a generalized system model ∑ based on the cement firing process system. e .

[0078] Based on the uncertainties in parameters on the production line, the generalized system model ∑ e The generalized polyhedral uncertainty system, transformed into a cement firing process system, is expressed as follows:

[0079]

[0080] Where x(k)∈R n It is the system state, u(k)∈R m It is the control input, y(k)∈R q This is the measurement output, k is the current sampling time, R represents the corresponding space, and the superscripts n, m, q correspond to the dimensions of the space. E is the generalized matrix, while A(k), B(k), C(k) are unknown matrices of appropriate dimensions, belonging to the polyhedron set.

[0081] Ω=Co{[A1 B1 C1], [A2 B2 C2],…,[A L B L C L ]},

[0082] Where Co is a convex hull used to describe the uncertainty of a polyhedral uncertain system, and the subscript L is the number of sub-control systems. Therefore, when [ABC]∈Ω, we have This includes the weighting coefficients λ1, λ2, ..., λ for each sub-control system. L These weight coefficients are non-negative and satisfy the following conditions:

[0083] Step 2: Based on the state feedback strategy, establish a closed-loop system using a model predictive controller and impose constraints on the control input and output.

[0084] The expression for the state feedback model predictive controller is as follows:

[0085] u(k+i|k)=K(k+i|k)x(k+i|k),

[0086] Where x(k+i|k) is the predicted state value at time k+i, u(k+i|k) is the latest control signal for performance indicators at time k+i, and K(k+i|k) is the corresponding feedback gain through optimized design; according to the engineering requirements of cement firing process, the following constraints are imposed on the control input and control output:

[0087] y min (k)≤y(k)≤y max (k),

[0088] u min (k)≤u(k)≤u max (k),

[0089] Δy min (k)≤Δy(k)≤Δy max (k),

[0090] Δu min (k)≤Δu(k)≤Δu max (k),

[0091] Where y min (k) and y max (k) represents the minimum and maximum values ​​of the control output y(k) at time k, respectively; u min (k) and u max (k) represents the minimum and maximum values ​​of the control input u(k) at time k, respectively; Δy min (k) and Δy max (k) represents the minimum and maximum values ​​of the control output change Δy(k) at time k; Δu min (k) and Δu max (k) represents the minimum and maximum values ​​of the control input change Δu(k) at time k.

[0092] The closed-loop system is obtained by predicting the controller and constraints using the feedback model described above, combined with the generalized polyhedral uncertainty system established in step 1:

[0093]

[0094] Where K(k) is the feedback gain at time k.

[0095] Step 3: Using state decomposition techniques, establish an equivalent structural model of the state decomposition, the controller, and equivalent constraints.

[0096] Due to the properties of the generalized matrix E, there exist two invertible matrices H and G such that the following equation holds:

[0097]

[0098]

[0099] The closed-loop system established in step 2 is transformed into an equivalent structural model using the state decomposition method:

[0100]

[0101] in,

[0102] Similarly, a state feedback controller in the form of state decomposition can be obtained:

[0103]

[0104] Where [K1(k+i) K2(k+i)]=K(k+i)G.

[0105] Step 4: Based on the Linear Matrix Inequality (LMI) method and Lyapunov theory, configure the controller to ensure continuous and stable operation of the control system. This step specifically includes the following sub-steps.

[0106] Step 4.1: Establish optimized performance metrics.

[0107] Models are built using the minimum-maximum cost function to predict control performance metrics. Among them, the optimized performance index J N The formula for calculating (k) is as follows:

[0108]

[0109] Where W1≥0 and W2≥0 are given weighted real matrices, x(k+i|k) is the state prediction value at time k+i, u(k+i|k) is the latest control signal of the performance index at time k+i, and N is the control time domain.

[0110] Step 4.2: Establish a system stabilization model and configure the controller based on the linear matrix inequality method. Details are as follows.

[0111] Introduce Lyapunov functions with state decomposition form, namely:

[0112]

[0113] And the Lyapunov function satisfies the following constraints:

[0114]

[0115] in

[0116] Simultaneously, terminal equality constraints are added: Then there is Then, by superimposing the inequalities constrained by the Lyapunov function from i=0 to i=N-1, we obtain the following inequalities: From this inequality, we can see that, For performance index J N An upper bound on (k) is found, therefore the problem of minimizing the performance index can be transformed into finding an upper bound. The problem of minimizing [the negative variables]. If there exists a nonnegative variable γ(k) that satisfies [the following conditions], then [the problem is] minimizing [the negative variables]. We can solve for minimizing γ(k). Therefore, we can obtain...

[0117] For the equivalent structure model of the closed-loop system, at each sampling time k, given the weighted real matrix W 11 W 22 , There exists a positive definite matrix Given matrices of appropriate dimensions Y1(k), Y2(k), and γ(k), the following linear matrix inequality (LMI) holds:

[0118] minγ(k)

[0119] st

[0120]

[0121]

[0122] in,

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130] Based on the above, the closed-loop system is stable, and the corresponding controller parameters are as follows:

[0131]

[0132] Step 4.3: After determining the controller parameters and their corresponding calculation methods, establish the predictive control algorithm. The specific steps are as follows.

[0133] Step 4.3.1: Select time k and control time domain N, obtain the system information at the current time, and provide the performance-related matrix W. 11 W 22 ,

[0134] Step 4.3.2: Solve the optimization problem of linear matrix inequalities in the [k, N] time zone. The right side gives the feedback gain K(k) of the system at time k, which minimizes the optimization performance index online.

[0135] Step 4.3.3: Substitute the feedback gain K(k) of the system at time k into the equivalent structural model of the closed-loop system to obtain the state prediction value at time k.

[0136] Step 4.3.4: Let k = k + 1, and repeat steps 1 to 4.

[0137] This method is applied to the cement firing process. The established system model is first simulated offline using data from the actual production line, and then applied to the actual firing process production line for testing. Based on the test results, feedback correction is implemented to finally determine the corresponding parameters in the model.

[0138] Taking the decomposer outlet temperature control system as an example, the decomposer outlet temperature is mainly controlled by the coal feed rate and air volume, and is also affected by disturbances such as the kiln feed rate and blower pressure. Considering a practical decomposer outlet temperature control system, under certain constraints and operating conditions, the mathematical model of the system can be approximated as a second-order object. Using the generalized polyhedral uncertainty system description established by this method, the physical meaning of the measured output y(k) is the outlet temperature, and the physical meaning of the control input u(k) is the coal feed rate. The parameters of this generalized polyhedral uncertainty system are determined as follows:

[0139]

[0140]

[0141] Where σ(k) is an uncertain parameter and a time-varying parameter, satisfying 0≤σ(k)≤1. Furthermore, based on the properties of the generalized polyhedral uncertain system, the system matrix satisfies the condition describing the uncertainty of the polyhedral uncertain system, namely: [A(k) B(k) C(k)]∈Ω=Co{[A1 B1 C1],[A2 B2 C2]}.

[0142] The relevant parameters of the controller were further determined as follows: L=1, thus determining the controller, enabling model-based control and prediction of the cement firing process.

[0143] Simulation was performed using MATLAB's LMI toolbox. Figure 3 , Figure 4 and Figure 5 The system under zero initial conditions The state response, output response, and input response were measured after 10 steps of simulation. The simulation results show that the control system is robust and stable.

[0144] The present invention has been described above by way of example with reference to the accompanying drawings. Obviously, the specific implementation of the present invention is not limited to the above-described manner. Any non-substantial improvements made using the inventive concept and technical solution of the present invention, or the direct application of the inventive concept and technical solution of the present invention to other occasions without modification, are all within the protection scope of the present invention.

Claims

1. A predictive control method for cement firing process model based on state decomposition technology, characterized in that: Includes the following steps: Step 1: Establish a generalized polyhedral uncertainty model of the cement firing process system and initialize the system state; Step 2: Based on the state feedback strategy, establish a closed-loop system using a model predictive controller and impose constraints on the control input and output; Step 3: Using state decomposition techniques, establish an equivalent structural model of the state decomposition, the controller, and equivalent constraints; Step 4: Based on the linear matrix inequality method and Lyapunov theory, the controller is set to ensure the continuous and stable operation of the control system; Step 1 includes: establishing a generalized polyhedral uncertainty system for the cement firing process system, with the following expression: Where x(k)∈R n It is the system state, u(k)∈R m It is the control input, y(k)∈R q This is the measurement output, k is the current sampling time, R represents the corresponding space, and the superscripts n, m, q correspond to the dimensions of the space. E is the generalized matrix, while A(k), B(k), C(k) are unknown matrices of appropriate dimensions, belonging to the polyhedron set. Ω=Co{[A1 B1 C1],[A2 B2 C2],…,[A L B L C L ]}, Where Co is a convex hull used to describe the uncertainty of a polyhedral uncertain system, and the subscript L is the number of sub-control systems. Therefore, when [ABC]∈Ω, we have This includes the weighting coefficients λ1, λ2, ..., λ corresponding to each sub-control system. L These weight coefficients are non-negative and satisfy the following conditions: Step 2 includes: the expression for the designed state feedback model predictive controller is: u(k+i|k)=K(k+i|k)x(k+i|k), Where x(k+i|k) is the predicted state value at time k+i, u(k+i|k) is the latest control signal with the performance index at time k+i, and K(k+i|k) is the corresponding feedback gain through optimization design; combined with the generalized polyhedral uncertainty system established in step 1, the closed-loop system is obtained: Where K(k) is the feedback gain at time k; Based on the engineering requirements of cement firing process, the following constraints are imposed on the control input and control output: y min (k)≤y(k)≤y max (k), you min (k)≤u(k)≤u max (k), Δy min (k)≤Δy(k)≤Δy max (k), Δu min (k)≤Δu(k)≤Δu max (k), where y min (k) and y max (k) represents the minimum and maximum values ​​of the control output y(k) at time k, respectively; u min (k) and u max (k) represent the minimum and maximum values ​​of the control input u(k) at time k, respectively; Δy min (k) and Δy max (k) represents the minimum and maximum values ​​of the control output change Δy(k) at time k; Δu min (k) and Δu max (k) represents the minimum and maximum values ​​of the control input change Δu(k) at time k; Step 3 includes: There exist two invertible matrices H and G such that the following equation holds: The closed-loop system established in step 2 is transformed into an equivalent structural model using the state decomposition method: in, [K1(k+i)K2(k+i)]=K(k+i)G; Similarly, a state feedback controller in the form of state decomposition can be obtained: Where [K1(k+i)K2(k+i)]=K(k+i)G.

2. The cement firing process model prediction and control method based on state decomposition technology according to claim 1, characterized in that: Step 4 includes: Step 4.1: Establish and optimize performance indicators, specifically performance indicator J. N The formula for calculating (k) is as follows: Where W1≥0, W2≥0 are given weighted real matrices, x(k+i|k) is the state prediction value at time k+i, u(k+i|k) is the latest control signal of the performance index at time k+i, and N is the control time domain; Step 4.2: Establish a system stabilization model and set the controller based on the linear matrix inequality method; Step 4.3: After determining the controller parameters and their corresponding calculation methods, establish the predictive control algorithm.

3. The cement firing process model prediction and control method based on state decomposition technology according to claim 2, characterized in that: In step 4.2, a Lyapunov function with a state decomposition form is introduced, namely: Furthermore, the Lyapunov function satisfies the following constraints: in Subsequently, based on the free weight matrix technique, the zero inequality technique, and Lyapunov stability analysis theory, the optimization problem of the controller is transformed into a linear matrix inequality to be solved, and the feedback gain K(k) is obtained, which makes the generalized polyhedral uncertainty system stable during the cement firing process.

4. The cement firing process model prediction and control method based on state decomposition technology according to claim 3, characterized in that: Step 4.3 includes: Step 4.3.1: Select time k and control time domain N, obtain the system information at the current time, and provide the performance-related matrix W. 11 ,W 22 , Step 4.3.2: Solve the optimization problem of linear matrix inequalities in the [k,N] time zone. The right side yields the feedback gain K(k) of the system at time k, which minimizes the optimization performance index online. Step 4.3.3: Substitute the feedback gain K(k) of the system at time k into the equivalent structural model of the closed-loop system to obtain the state prediction value at time k. Step 4.3.4: Let k = k + 1, and repeat steps 1 to 4.

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