A cement production control method based on equivalent input disturbance-linear matrix inequality

Abstract

This invention belongs to the field of control engineering technology, specifically relating to a cement production control method based on equivalent input disturbance-linear matrix inequality (LMI). This method establishes a linear discrete time delay model predictive control system based on EID-LMI. In the establishment process, firstly, a control system structure consisting of the controlled object, an observer, and a low-pass filter is constructed using the disturbance compensation concept. Then, the EID estimate is obtained based on the equivalent input disturbance (EID) method, and a disturbance suppression law is designed. Next, using Lyapunov stability theory and combining performance indices, the index function is transformed into a minimized Lyapunov function. The design algorithm for the predictive controller is obtained through the LMI method. This invention has good anti-interference capability, high disturbance suppression performance, and the resulting control system is robust and stable.

Description

Technical Field

[0001] This invention belongs to the field of control engineering technology, specifically relating to a cement production control method based on equivalent input disturbance-linear matrix inequality. Background Technology

[0002] The cement production process is characterized by high nonlinearity, multivariability, strong coupling, and time-varying nature. During production control, numerous and uncontrollable factors affect control stability. Equipment aging, raw material changes, and process flow variations can lead to model distortion and decreased system control stability. Furthermore, processes such as cement kiln-related CKK (cement kiln waste management system), co-processing of solid and hazardous waste, and alternative fuels introduce significant uncertainties and disturbances, causing the system to fail to meet production control requirements. The numerous uncertainties and disturbances in the production process pose a major challenge to traditional control algorithms, making it difficult to establish accurate mathematical models. Therefore, there is a need to find an algorithm with low model requirements, convenient online calculation, and good control performance. In addition, the production process is inevitably affected by external disturbances (measurable or unmeasurable), which not only reduce the system's dynamic performance but also disrupt the stability of the closed-loop system. Taking the temperature control of the cement production decomposition furnace as an example, it is usually affected by disturbances such as secondary air temperature, tertiary air temperature, and feed rate, resulting in temperature control failing to meet expectations and unstable operation. Therefore, to ensure good control performance, a disturbance suppression design method is needed to improve the system's anti-interference capability.

[0003] Predictive control technology can estimate the control performance of a system over a specified time period. It mainly includes three control concepts: model prediction, feedback correction, and rolling optimization. Based on a predictive model, it employs a strategy of quadratic online rolling optimization of performance indicators and feedback correction to overcome the influence of controlled object model errors and factors such as parameter and environmental changes. It exhibits strong robustness and has been widely applied in industrial control. However, existing predictive control techniques often consider unknown bounded disturbances and cannot eliminate them; therefore, the disturbance suppression performance of predictive control needs further improvement. Summary of the Invention

[0004] The purpose of this invention is to provide a cement production control method based on equivalent input disturbance-linear matrix inequality, in order to solve the technical problems of insufficient anti-interference ability, poor optimization performance, and inability to simultaneously meet the multiple requirements of stable, efficient, energy-saving and environmentally friendly production line operation in existing cement production control methods.

[0005] The aforementioned cement production control method based on equivalent input disturbance-linear matrix inequality establishes a linear discrete time delay model predictive control system based on EID-LMI for external disturbances of arbitrary form and without any known information. The process involves first constructing a control system structure consisting of the controlled object, an observer, and a low-pass filter using the disturbance compensation concept; then, obtaining the EID estimate based on the equivalent input disturbance EID method and designing a disturbance suppression law; finally, utilizing Lyapunov stability theory and combining performance indices, transforming the index function into a minimized Lyapunov function, and obtaining the predictive controller design algorithm through the linear matrix inequality (LMI) method.

[0006] Preferably, the cement production control method specifically includes the following steps.

[0007] Step 1) Construct a model predictive control system based on the EID method. First, design a state observer and a low-pass filter to estimate the value of EID. Then, combine the model predictive controller and the estimated value of EID to design the corresponding control law.

[0008] Step 2) Establish the state-space model of the closed-loop system.

[0009] Step 3) Design model predictive control using the LMI method.

[0010] Step 4) Establish a predictive control algorithm based on EID-LMI.

[0011] Preferably, in step 1), a linear discrete system is established, with the following expression:

[0012]

[0013] in This is the system state at time k. It is the control input at time k. It is the external disturbance at time k. The measurement outputs at time k are A1, A2, B, B. d C is a parametric matrix of appropriate dimension. This represents the corresponding dimensional space, with its corresponding superscripts n, m, n w q represents the dimension of the corresponding dimensional space and is the same as the dimension of the corresponding matrix.

[0014] The expression for the state observer is as follows:

[0015]

[0016] in It is the observed value of the system state x(k), u f (k) is the input to the state observer. is the output value of the state observer, and L is the gain of the state observer.

[0017] The low-pass filter established is as follows:

[0018]

[0019] in, The interference signal is input to the low-pass filter, estimated using EID, x F (k) represents the filter state at time k, A F B F , C F These are all parameter matrices of low-pass filters. It is the output of the low-pass filter.

[0020] Preferably, in step 1), for the linear discrete system, the selected optimization performance index function is:

[0021]

[0022] Where Q1 and Q2 are given weighting matrices, and Q1 > 0, Q2 > 0, x(k+i|k) is the predicted system state at time k+i, u(k+i|k) is the control signal that minimizes the performance index at time k+i, N is the control time domain, and J N (k) is a performance metric.

[0023] The formula for calculating the EID estimate is: Among them, u f (k) is the sampled state feedback controller, calculated as u f (k) = Kx(k), where K is the feedback gain through optimized design, and B + =B T (B T B) -1 ,

[0024] Preferably, in step 2), the expression for the state-space model is: in,

[0025]

[0026]

[0027] x F (k) represents the filter state at time k, A F B F , C F These are all parameter matrices of low-pass filters.

[0028] Preferably, in step 3), the selected Lyapunov function is as follows:

[0029]

[0030] Where P and Z are the corresponding system matrices in the Lyapunov function; the optimization performance index function is abbreviated as follows:

[0031]

[0032] in, R = [K 0 -C F ];

[0033] At every sampling time k, the following inequality holds:

[0034]

[0035] For this inequality, superimposing from i=0 to i=N-1, we get: Simultaneously, terminal equality constraints are added: Then there is

[0036] Preferably, in step 3), the optimization problem of the controller is transformed into a linear matrix inequality to be solved based on the optimization performance index function, and the closed-loop system stability and predictive controller parameters are determined. The predictive controller parameters include the feedback gain K and the gain L of the state observer.

[0037] Preferably, step 4) specifically includes:

[0038] Step 1: Select time k and control time domain N, obtain the system information at the current time, and provide performance-related weighting matrices Q1 and Q2;

[0039] Step 2: Based on the model predictive control design completed in step 3), solve the optimization problem in the [k, N] time zone to obtain the feedback gain K and the state observer gain L, so that the optimization performance index is minimized online;

[0040] Step 3: Substitute the feedback gain K and the state observer gain L calculated at time k into the state-space equation of the closed-loop system established in step 2) to obtain the state prediction value at time k+1 at time k.

[0041] Step 4: Let k = k + 1, and repeat steps 1 to 4.

[0042] This invention has the following advantages: it possesses good anti-interference capability and high disturbance suppression performance, resulting in a robust and stable control system. This invention designs a secondary online rolling optimization performance index. By introducing this performance index, the actual needs of cement production can be better considered, and the optimal cement production control can be ensured by adjusting the corresponding weighting matrix. Therefore, this method not only provides a stability criterion for the system but also ensures that the designed controller can meet the optimal performance index, taking into account multiple requirements. This method can achieve real-time online optimization. Attached Figure Description

[0043] Figure 1 This is a flowchart of a cement production control method based on equivalent input disturbance-linear matrix inequality according to the present invention.

[0044] Figure 2 A schematic diagram of the linear discrete time-delay system structure of MPC based on EID-LMI established for the application of this invention.

[0045] 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 17 steps under zero initial conditions. Detailed Implementation

[0046] 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.

[0047] The Equivalent Input Disturbance (EID) method, also known as disturbance compensation, equates the impact of external disturbances on the system to the impact of the EID signal on the control input on the system output. By estimating this EID value and compensating accordingly, the goal of improving disturbance suppression can be achieved.

[0048] The Linear Matrix Inequality Method (LMI) transforms the problem of finding the optimal value of a performance index into a positive semidefinite problem consisting of an objective function and linear matrix inequalities.

[0049] like Figure 1-2As shown, this invention provides a cement production control method based on equivalent input disturbance-linear matrix inequality. For external disturbances of arbitrary form and without any known information, a linear discrete time delay model predictive control system based on EID-LMI is established. In the establishment process, firstly, the disturbance compensation idea (EID) is used to construct a control system structure consisting of the controlled object, an observer, and a low-pass filter. Then, based on the EID method, the EID estimate is obtained, and the disturbance suppression law is designed. Next, using Lyapunov stability theory and combined with performance indices, the index function is transformed into a minimized Lyapunov function, and the design algorithm for the predictive controller is obtained through the LMI method.

[0050] The method specifically includes the following steps.

[0051] Step 1) Construct a model predictive control system based on the EID method. First, design a state observer and a low-pass filter to estimate the EID value. Then, combine the model predictive controller with the estimated EID value to design the corresponding control law. Details are as follows.

[0052] Establish a linear discrete system, with the following expression:

[0053]

[0054] in This is the system state at time k. It is the control input at time k. It is the external disturbance at time k. The measurement outputs at time k are A1, A2, B, B. d C is a parametric matrix of appropriate dimension. This represents the corresponding dimensional space, with its corresponding superscripts n, m, n w q represents the dimension of the corresponding dimensional space and is the same as the dimension of the corresponding matrix.

[0055] This linear discrete system uses a state observer to reconstruct the system state and estimate the value of EID. The expression for the state observer is as follows:

[0056]

[0057] in It is the observed value of the system state x(k), u f (k) is the input to the state observer. is the output value of the state observer, and L is the gain of the state observer.

[0058] The low-pass filter established is as follows:

[0059]

[0060] in, It is the interference signal input to the low-pass filter, x F (k) represents the filter state at time k, A F B F , C F These are all parameter matrices of low-pass filters. It is the output of the low-pass filter.

[0061] For this linear discrete system, the chosen optimization performance index function is:

[0062]

[0063] Where Q1 and Q2 are given weighting matrices, and Q1 > 0, Q2 > 0, x(k+i|k) is the predicted system state at time k+i, u(k+i|k) is the control signal that minimizes the performance index at time k+i, N is the control time domain, and J N (k) is a performance metric.

[0064] The formula for calculating the EID estimate is: Among them, u f (k) is the sampled state feedback controller, calculated as u f (k) = Kx(k), where K is the feedback gain through optimized design, and B + =B T (B T B) -1 ,

[0065] Step 2) Establish the state-space model of the closed-loop system, as follows:

[0066]

[0067] Where, x F (k) represents the filter state at time k, A F B F , C F These are all parameter matrices of low-pass filters.

[0068] The state-space equations of the above closed-loop system can be further simplified as follows: in,

[0069]

[0070]

[0071] Step 3) Design model predictive control using the LMI method.

[0072] The Lyapunov function selected for this step is as follows:

[0073]

[0074] Where P and Z are the corresponding system matrices in the Lyapunov function.

[0075] Based on the simplified form of the state-space equations of the closed-loop system, the corresponding optimization performance index function can be simplified as follows:

[0076]

[0077] in, R = [K 0 -C F ].

[0078] At every sampling time k, the following inequality holds:

[0079]

[0080] For this inequality, superimposing from i=0 to i=N-1, we get: Simultaneously, terminal equality constraints are added: Then there is

[0081] From the above, we can see that For performance index J N Therefore, this method transforms the performance index minimization problem into a problem of finding an upper bound for (k). The minimization problem. When there exists a nonnegative variable γ(k) that satisfies... It is possible to minimize γ(k).

[0082] Therefore, at each sampling time k, given the weighting matrices Q1, Q2, and α > 0, there exists a positive definite matrix. Let Z, and appropriate dimension matrices W(k), W1(k), and γ(k) hold such that the following linear matrix inequality (LMI) holds:

[0083] minγ(k)

[0084] st

[0085]

[0086]

[0087] in,

[0088]

[0089]

[0090]

[0091] and It is a positive definite matrix.

[0092] Therefore, the closed-loop system is stable and the predictive controller parameters are as follows:

[0093]

[0094] Among them, C + =C T (C T C) -1 .

[0095] Step 4) Establish a predictive control algorithm based on EID-LMI.

[0096] This step specifically includes the following steps.

[0097] Step 1: Select time k and control time domain N, obtain the system information at the current time, and provide the performance-related weighting matrices Q1 and Q2.

[0098] Step 2: Based on the model predictive control design completed in step 3), solve the optimization problem in the [k, N] time zone to obtain the feedback gain K and the gain L of the state observer, so that the optimization performance index is minimized online.

[0099] Step 3: Substitute the feedback gain K and the state observer gain L calculated at time k into the state-space equation of the closed-loop system established in step 2) to obtain the state prediction value at time k+1 at time k.

[0100] Step 4: Let k = k + 1, and repeat steps 1 to 4.

[0101] This method is applied to the cement production field to control related production systems. The established system model is first simulated offline using data from the actual production line, and then applied to the actual cement production line for testing. Based on the test results, feedback correction is implemented to finally determine the corresponding parameters in the model.

[0102] Taking the decomposition furnace outlet temperature control system in cement production as an example, the decomposition furnace outlet temperature is a key process parameter for the cement kiln decomposition rate. The decomposition furnace is directly connected to the rotary kiln and the suspension preheater, resulting in significant equipment correlation. The combustion, heat transfer, and decomposition processes within the furnace are complex, thus the combustion process in the decomposition furnace presents control challenges such as nonlinearity, pure time delay, multiple variables, input-output constraints, and uncertain disturbances. Improving the stability of the decomposition furnace temperature control is of great significance for improving the quality and production efficiency of cement clinker products.

[0103] The outlet temperature of the decomposer is mainly controlled by adjusting the coal feed rate using a pulverized coal scale. In addition, it is affected by disturbances such as secondary air temperature, tertiary air temperature, and feed rate. 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 linear discrete system model established by this method, the physical meaning of the measured output y(k) is the outlet temperature, the physical meaning of the control input u(k) is the coal feed rate, and the external disturbance d(k) includes the secondary air temperature, tertiary air temperature, and feed rate. The corresponding control matrix is ​​shown in Table 1.

[0104] Table 1: Control Matrix Relationship of the Decomposition Furnace Outlet Temperature Control System

[0105]

[0106]

[0107] The method used here is to determine the parameter matrices of the linear discrete system as follows:

[0108] h = 1, C = [1 0],

[0109] Simultaneously, this method also constructs a corresponding state observer and a low-pass filter, wherein the filter parameters are: A F =-100, B F =100, C F =1. Selected Q2 = 1, α = 20. The external disturbance is determined as d = sin(3.14k+1).

[0110] The observer gain L and controller gain K can be obtained at each time step by solving the linear matrix inequality of the theorem.

[0111] like Figure 3 As shown, the system operates under zero initial conditions and the continuous action of an external disturbance d = sin(3.14k+1) for 17 steps, producing its output response. The output response curves demonstrate that the control system is robust and stable, and it is evident that the maximum tracking error is significantly reduced compared to the output without EID. At k = 11, the error decreases from 0.99 to 0.96, indicating that the EID-LMI-based predictive control algorithm possesses disturbance suppression capabilities.

[0112] This patent designs a secondary online rolling optimization performance index. By introducing performance indicators, we can better meet the actual needs of cement production and ensure optimal cement production control. For example, on a coal mill production line, the controlled variables are the outlet temperature and the inlet temperature, corresponding to... When we focus on the mill outlet temperature y2(k), we can achieve this by adjusting the corresponding weighting matrix Q1.

[0113] 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.

[0114] 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 cement production control method based on equivalent input disturbance-linear matrix inequality, characterized in that: For external disturbances of arbitrary form and without any known information, a linear discrete time delay model predictive control system based on EID-LMI was established. In the establishment process, firstly, the control system structure consisting of the controlled object, observer, and low-pass filter was constructed using the disturbance compensation concept. Then, the EID estimate was obtained based on the equivalent input disturbance EID method, and a disturbance suppression law was designed. Next, using Lyapunov stability theory and combining performance indices, the index function was transformed into a minimized Lyapunov function, and the design algorithm for the predictive controller was obtained through the linear matrix inequality LMI method. The cement production control method specifically includes the following steps: Step 1) Construct a model predictive control system based on the EID method. First, design a state observer and a low-pass filter to estimate the value of EID. Then, combine the model predictive controller and the estimated value of EID to design the corresponding control law. Step 2) Establish the state-space model of the closed-loop system; Step 3) Design model predictive control using the LMI method; Step 4) Establish a predictive control algorithm based on EID-LMI.

2. The cement production control method based on equivalent input disturbance-linear matrix inequality according to claim 1, characterized in that: In step 1), Establish a linear discrete system, with the following expression: in This is the system state at time k. It is the control input at time k. It is the external disturbance at time k. The measurement outputs at time k are A1, A2, B, B. d C is a parametric matrix of appropriate dimension. This represents the corresponding dimensional space, with its corresponding superscripts n, m, n w q represents the dimension of the corresponding dimensional space and is the same as the dimension of the corresponding matrix; The expression for the state observer is as follows: in It is the observed value of the system state x(k), u f (k) is the input to the state observer. is the output value of the state observer, and L is the gain of the state observer; The low-pass filter established is as follows: in, The interference signal is input to the low-pass filter, estimated using EID, x F (k) represents the filter state at time k, A F B F C F These are all parameter matrices of low-pass filters. It is the output of the low-pass filter.

3. The cement production control method based on equivalent input disturbance-linear matrix inequality according to claim 2, characterized in that: In step 1), for this linear discrete system, the selected optimization performance index function is: Where Q1 and Q2 are given weighting matrices, and Q1 > 0, Q2 > 0, x(k+i|k) is the predicted system state at time k+i, u(k+i|k) is the control signal that minimizes the performance index at time k+i, N is the control time domain, and J N (k) is a performance metric; The formula for calculating the EID estimate is: Among them, u f (k) is the input quantity of the sampled state feedback controller, calculated as u f (k) = Kx(k), where K is the feedback gain through optimized design, and B + =B T (B T B) -1 , 4. The cement production control method based on equivalent input disturbance-linear matrix inequality according to claim 3, characterized in that: In step 2), the expression for the state-space model is: in, x F (k) represents the filter state at time k, A F B F C F These are all parameter matrices of low-pass filters.

5. A cement production control method based on equivalent input disturbance-linear matrix inequality according to claim 4, characterized in that: In step 3), the selected Lyapunov function is as follows: Where P and Z are the corresponding system matrices in the Lyapunov function; the optimization performance index function is abbreviated as follows: in, R = [K 0 -C F ]; At every sampling time k, the following inequality holds: For this inequality, superimposing from i=0 to i=N-1, we get: Simultaneously, terminal equality constraints are added: Then there is 6. The cement production control method based on equivalent input disturbance-linear matrix inequality according to claim 5, characterized in that: In step 3), based on the performance index function, the optimization problem of the controller is transformed into a linear matrix inequality to be solved, and the closed-loop system stability and predictive controller parameters are determined. The predictive controller parameters include the feedback gain K and the gain L of the state observer.

7. A cement production control method based on equivalent input disturbance-linear matrix inequality according to claim 6, characterized in that: Step 4) specifically includes: Step 1: Select time k and control time domain N, obtain the system information at the current time, and provide performance-related weighting matrices Q1 and Q2; Step 2: Based on the model predictive control design completed in step 3), solve the optimization problem in the [k,N] time zone to obtain the feedback gain K and the gain L of the state observer, so that the optimization performance index is minimized online; Step 3: Substitute the feedback gain K and the state observer gain L calculated at time k into the state-space equation of the closed-loop system established in step 2) to obtain the state prediction value at time k+1 at time k. Step 4: Let k = k + 1, and repeat steps 1 to 4.

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